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Mod-2-Cohomology of N_Co3(4A), a group of order 46080

About the group

Ring generators

Ring relations

Completion information

Restriction maps

General information on the group

• N_Co3(4A), the Normalizer in Co3 of a 4A-element, is a group of order 46080.
• The group order factors as 2¹⁰ · 3² · 5.
• The group is defined by Group([(1,15,200,138)(2,91,235,226)(3,120,183,173)(4,133,121,201)(5,190,37,67)(6,231,209,230)(7,272,242,155)(8,170,176,64)(9,84,55,154)(10,188,13,208)(11,243,47,276)(12,46,261,82)(14,185)(16,36,19,206)(17,135,140,38)(18,259,156,26)(20,199,116,102)(22,179,25,105)(23,229,66,57)(24,51,210,255)(27,194,166,98)(28,45,58,78)(29,132,158,48)(30,251,86,205)(31,192)(32,106,207,174)(33,223,44,195)(34,254,103,219)(35,152,172,101)(39,171)(41,141,234,107)(42,252,202,96)(43,216,177,163)(49,147,108,149)(50,88,169,126)(53,125,193,79)(54,175)(56,165,265,139)(59,273,186,248)(60,65,80,184)(61,109,214,191)(62,204,225,257)(63,213,85,263)(68,110,97,100)(69,113,196,123)(70,253,130,83)(71,81,244,232)(72,256,260,112)(73,215)(74,180,267,233)(75,118,203,131)(76,228,262,157)(77,99,136,119)(87,144,218,189)(89,250,94,274)(90,239,160,143)(92,238,269,151)(95,164,198,266)(104,145,240,182)(111,236,129,148)(115,270)(117,142,246,146)(122,181,249,264)(124,237,168,212)(127,211)(137,153)(150,247,222,271)(197,224,217,220)(221,241)(268,275),(1,200)(2,235)(3,183)(4,121)(5,37)(6,209)(7,242)(8,176)(9,55)(10,13)(11,47)(12,261)(15,138)(16,19)(17,140)(18,156)(20,116)(22,25)(23,66)(24,210)(26,259)(27,166)(28,58)(29,158)(30,86)(32,207)(33,44)(34,103)(35,172)(36,206)(38,135)(41,234)(42,202)(43,177)(45,78)(46,82)(48,132)(49,108)(50,169)(51,255)(53,193)(56,265)(57,229)(59,186)(60,80)(61,214)(62,225)(63,85)(64,170)(65,184)(67,190)(68,97)(69,196)(70,130)(71,244)(72,260)(74,267)(75,203)(76,262)(77,136)(79,125)(81,232)(83,253)(84,154)(87,218)(88,126)(89,94)(90,160)(91,226)(92,269)(95,198)(96,252)(98,194)(99,119)(100,110)(101,152)(102,199)(104,240)(105,179)(106,174)(107,141)(109,191)(111,129)(112,256)(113,123)(117,246)(118,131)(120,173)(122,249)(124,168)(133,201)(139,165)(142,146)(143,239)(144,189)(145,182)(147,149)(148,236)(150,222)(151,238)(155,272)(157,228)(163,216)(164,266)(180,233)(181,264)(188,208)(195,223)(197,217)(204,257)(205,251)(212,237)(213,263)(219,254)(220,224)(230,231)(243,276)(247,271)(248,273)(250,274),(2,116)(3,216)(5,247)(6,196)(7,242)(8,253)(9,85)(10,78)(11,117)(12,48)(13,45)(14,221)(16,108)(17,33)(18,191)(19,49)(20,235)(22,204)(23,74)(24,42)(25,257)(26,214)(27,193)(28,188)(29,46)(30,122)(31,115)(32,197)(34,218)(35,68)(36,149)(37,271)(38,195)(39,275)(40,128)(41,198)(43,173)(44,140)(47,246)(50,81)(51,252)(52,162)(53,166)(54,175)(55,63)(56,72)(57,233)(58,208)(59,111)(60,99)(61,259)(62,105)(64,70)(65,136)(66,267)(67,150)(69,209)(71,126)(73,211)(75,89)(76,168)(77,184)(79,194)(80,119)(82,158)(83,176)(84,263)(86,249)(87,103)(88,244)(90,182)(91,102)(92,269)(94,203)(95,234)(96,255)(97,172)(98,125)(100,101)(104,239)(106,224)(107,164)(109,156)(110,152)(112,139)(113,230)(118,250)(120,177)(123,231)(124,262)(127,215)(129,186)(130,170)(131,274)(132,261)(134,161)(135,223)(137,153)(141,266)(142,243)(143,240)(144,219)(145,160)(146,276)(147,206)(148,248)(151,238)(154,213)(155,272)(157,237)(159,227)(163,183)(165,256)(167,178)(169,232)(171,268)(174,220)(179,225)(180,229)(181,251)(185,241)(187,245)(189,254)(190,222)(192,270)(199,226)(202,210)(205,264)(207,217)(212,228)(236,273)(260,265),(2,157,42)(3,163,242)(4,48,12)(5,195,99)(6,152,203)(7,183,216)(9,87,13)(10,55,218)(11,182,126)(14,127,192)(16,141,109)(17,222,65)(18,164,49)(19,107,191)(20,210,212)(22,264,220)(23,193,148)(24,237,116)(25,181,224)(26,95,149)(27,74,248)(28,254,213)(29,46,133)(30,225,32)(31,185,211)(33,136,190)(34,63,78)(35,118,230)(36,234,214)(37,223,119)(38,247,60)(39,153,268)(40,128,258)(41,61,206)(43,155,120)(44,77,67)(45,103,85)(47,145,88)(50,243,104)(51,168,102)(52,162,114)(53,236,66)(56,260,269)(57,125,129)(58,219,263)(59,194,180)(62,207,86)(68,113,250)(69,89,100)(71,90,117)(72,92,265)(73,241,115)(75,209,101)(76,252,91)(79,111,229)(80,135,271)(81,239,142)(82,201,158)(84,144,208)(93,134,161)(94,110,196)(96,226,262)(97,123,274)(98,233,186)(105,249,217)(106,251,257)(108,156,266)(112,151,165)(121,132,261)(122,197,179)(124,199,255)(131,231,172)(137,275,171)(139,256,238)(140,150,184)(143,146,232)(147,259,198)(154,189,188)(159,167,245)(160,246,244)(166,267,273)(169,276,240)(173,177,272)(174,205,204)(178,227,187)(202,235,228)(215,221,270),(2,41,78,61,249,237,64,86)(3,272,173,7,183,155,120,242)(4,158,68,75,238,56,152,113)(5,142,60,240)(6,46,231,261,209,82,230,12)(8,205,91,141,28,109,264,168)(9,98,225,228,130,179,210,186)(10,147,206,198,218,42,79,217)(11,44,77,244,90,17,222,88)(13,149,36,95,87,202,125,197)(14,192,215,115,185,31,73,270)(16,266,189,252,53,220,188,108)(18,106,263,23,74,148,219,199)(19,164,144,96,193,224,208,49)(20,26,32,85,57,233,129,103)(21,40,161,167,162,245,128,93)(22,51,273,154,166,204,76,253)(24,59,55,194,62,157,70,105)(25,255,248,84,27,257,262,83)(29,97,203,151,265,101,123,121)(30,235,234,45,214,122,212,170)(33,136,71,160,140,150,126,47)(34,116,259,207,63,229,180,111)(35,69,201,132,100,131,92,139)(37,146,80,104)(38,247,50,276,223,119,81,143)(39,137,54,275)(43,163,177,216)(48,110,118,269,165,172,196,133)(52,227,159,178,114,134,187,258)(58,191,181,124,176,251,226,107)(65,182,190,246)(66,267,236,254,102,156,174,213)(67,117,184,145)(72,94,256,274,260,89,112,250)(99,232,239,135,271,169,243,195)(127,211)(153,175,268,171),(2,105)(3,216)(4,201)(5,222)(6,75)(7,242)(8,176)(9,13)(10,55)(11,240)(12,158)(14,127)(15,138)(16,191)(17,195)(18,108)(19,109)(20,225)(22,226)(23,53)(24,86)(25,91)(26,149)(27,267)(28,263)(29,261)(30,210)(32,212)(33,38)(36,214)(37,150)(39,268)(40,161)(42,249)(43,120)(44,135)(45,85)(46,132)(47,104)(48,82)(49,156)(50,88)(51,251)(52,162)(56,256)(57,125)(58,213)(60,136)(61,206)(62,116)(63,78)(65,99)(66,193)(67,271)(69,94)(71,232)(72,165)(73,241)(74,166)(76,224)(77,80)(79,229)(81,244)(83,253)(84,188)(89,196)(90,146)(92,151)(93,258)(96,264)(98,233)(100,110)(101,152)(102,257)(106,168)(107,141)(112,265)(113,250)(117,143)(118,230)(119,184)(121,133)(122,202)(123,274)(124,174)(126,169)(128,134)(131,231)(139,260)(140,223)(142,160)(144,189)(145,243)(147,259)(148,236)(154,208)(157,217)(159,245)(163,183)(164,266)(171,275)(173,177)(179,235)(180,194)(181,252)(182,276)(185,211)(187,227)(190,247)(197,228)(199,204)(203,209)(205,255)(207,237)(215,221)(219,254)(220,262)(238,269)(239,246)(248,273),(1,2,49,155,156,105)(3,74,252,173,180,42)(4,61,225,151,199,19)(5,112,189,56,150,141)(6,12,10,239,136,207)(7,259,22,138,91,149)(8,217,63,248,45,228)(9,29,203,212,80,117)(11,196,129,89,240,70)(13,143,77,32,209,261)(14,73,153,241,127,54)(15,226,147,242,26,25)(16,121,214,62,238,102)(17,223,172,140,195,35)(18,179,200,235,108,272)(20,206,201,109,204,92)(23,193,169,57,79,88)(24,232,205,255,71,86)(27,163,122,98,43,264)(28,262,64,220,263,59)(30,210,81,251,51,244)(31,268,171,192,275,39)(33,101,135)(34,198)(36,133,191,257,269,116)(37,256,144,265,222,107)(38,44,152)(40,161,162,159,245,52)(41,190,260,87,139,247)(46,208,160,99,174,230)(47,69,111,94,104,130)(48,131,168,184,146,84)(50,229,125,126,66,53)(55,158,75,237,60,246)(58,76,170,224,213,186)(65,142,154,132,118,124)(67,72,218,165,271,234)(78,157,176,197,85,273)(82,188,90,119,106,231)(83,243,113,148,274,182)(93,258,114)(95,103)(96,120,233,202,183,267)(100,110)(115,270)(123,236,250,145,253,276)(128,187,167,227,134,178)(137,221,211,175,185,215)(164,254)(166,216,249,194,177,181)(219,266)]).
• It is non-abelian.
• It has 2-Rank 4.
• The centre of a Sylow 2-subgroup has rank 1.
• Its Sylow 2-subgroup has 20 conjugacy classes of maximal elementary abelian subgroups, which are of rank 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 and 4, respectively.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 4 and depth 4.
• The depth exceeds the Duflot bound, which is 1.
• The Poincaré series is

  1  −  2·t  +  4·t2  −  3·t3  +  4·t4  −  2·t5  +  t6

  ( − 1  +  t)4 · (1  +  t  +  t2) · (1  +  t2)2

• The a-invariants are -∞,-∞,-∞,-∞,-4. They were obtained using the filter regular HSOP of the Hilbert-Poincaré test.
• The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Ring generators

The cohomology ring has 15 minimal generators of maximal degree 8:

1. b_1_0, an element of degree 1
2. b_2_0, an element of degree 2
3. b_3_5, an element of degree 3
4. b_3_2, an element of degree 3
5. b_3_1, an element of degree 3
6. b_3_0, an element of degree 3
7. b_4_9, an element of degree 4
8. b_4_6, an element of degree 4
9. b_4_5, an element of degree 4
10. b_5_11, an element of degree 5
11. b_6_13, an element of degree 6
12. b_7_1, an element of degree 7
13. b_7_0, an element of degree 7
14. b_8_10, an element of degree 8
15. c_8_5, a Duflot element of degree 8

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Ring relations

There are 59 minimal relations of maximal degree 16:

1. b_2_0·b_3_5 + b_2_0·b_3_2 + b_2_0·b_3_0
2. b_3_0² + b_1_0³·b_3_0 + b_2_0·b_1_0·b_3_0
3. b_3_0·b_3_1 + b_1_0³·b_3_0 + b_2_0·b_1_0·b_3_0 + b_2_0·b_4_9
4. b_3_0·b_3_2 + b_1_0³·b_3_0 + b_2_0·b_1_0·b_3_0
5. b_3_0·b_3_5
6. b_3_1·b_3_5 + b_3_1·b_3_2 + b_1_0³·b_3_0 + b_2_0·b_1_0·b_3_0 + b_2_0·b_4_9
7. b_3_2² + b_3_1·b_3_2 + b_3_1² + b_1_0·b_5_11 + b_1_0³·b_3_5 + b_1_0³·b_3_2
      + b_4_5·b_1_0² + b_2_0·b_1_0·b_3_2 + b_2_0·b_1_0·b_3_1 + b_2_0·b_1_0·b_3_0
      + b_2_0·b_1_0⁴ + b_2_0·b_4_9 + b_2_0·b_4_6 + b_2_0·b_4_5 + b_2_0²·b_1_0² + b_2_0³
8. b_3_2·b_3_5 + b_3_1·b_3_2 + b_3_1² + b_1_0³·b_3_5 + b_2_0·b_1_0·b_3_2
      + b_2_0·b_1_0·b_3_1 + b_2_0·b_1_0·b_3_0 + b_2_0·b_1_0⁴ + b_2_0·b_4_9 + b_2_0·b_4_6
      + b_2_0·b_4_5 + b_2_0²·b_1_0² + b_2_0³
9. b_3_5² + b_3_1·b_3_2 + b_3_1² + b_1_0³·b_3_5 + b_2_0·b_1_0·b_3_2 + b_2_0·b_1_0·b_3_1
      + b_2_0·b_1_0·b_3_0 + b_2_0·b_1_0⁴ + b_2_0·b_4_9 + b_2_0·b_4_6 + b_2_0·b_4_5
      + b_2_0²·b_1_0² + b_2_0³
10. b_2_0·b_5_11 + b_2_0·b_1_0²·b_3_2 + b_2_0·b_1_0²·b_3_0 + b_2_0·b_4_5·b_1_0
       + b_2_0²·b_3_0
11. b_4_6·b_3_0 + b_4_5·b_3_0 + b_2_0·b_1_0²·b_3_0
12. b_4_6·b_3_5 + b_4_6·b_3_2 + b_4_5·b_3_5 + b_4_5·b_3_2 + b_2_0·b_1_0²·b_3_0
13. b_4_9·b_3_0 + b_4_9·b_1_0³ + b_2_0·b_4_9·b_1_0
14. b_4_9·b_3_1 + b_4_9·b_1_0³ + b_2_0·b_1_0²·b_3_0 + b_2_0²·b_3_0
15. b_4_9·b_3_2 + b_4_9·b_1_0³ + b_2_0·b_4_9·b_1_0
16. b_4_9·b_3_5
17. b_1_0·b_3_1·b_3_2 + b_1_0⁴·b_3_0 + b_4_6·b_3_2 + b_4_5·b_3_5 + b_4_5·b_3_2
       + b_2_0·b_1_0²·b_3_2 + b_2_0·b_1_0²·b_3_0 + b_2_0·b_4_9·b_1_0
18. b_4_6·b_4_9 + b_4_5·b_4_9 + b_2_0·b_4_9·b_1_0²
19. b_1_0⁵·b_3_0 + b_4_9·b_1_0⁴ + b_4_9² + b_2_0·b_4_9·b_1_0² + b_2_0²·b_1_0·b_3_0
20. b_1_0²·b_3_1² + b_4_9·b_1_0⁴ + b_4_9² + b_4_6² + b_4_5·b_1_0·b_3_5 + b_4_5²
       + b_2_0·b_1_0³·b_3_1 + b_2_0·b_4_9·b_1_0² + b_2_0·b_4_6·b_1_0²
       + b_2_0·b_4_5·b_1_0²
21. b_3_0·b_5_11 + b_4_5·b_1_0·b_3_0 + b_2_0·b_1_0³·b_3_0 + b_2_0²·b_1_0·b_3_0
22. b_3_1·b_5_11 + b_4_6·b_1_0·b_3_2 + b_4_5·b_1_0·b_3_5 + b_4_5·b_1_0·b_3_2
       + b_4_5·b_1_0·b_3_1 + b_2_0·b_1_0³·b_3_2 + b_2_0·b_1_0³·b_3_0 + b_2_0²·b_1_0·b_3_0
       + b_2_0²·b_4_9
23. b_3_2·b_5_11 + b_6_13·b_1_0² + b_4_9·b_1_0⁴ + b_4_9² + b_4_6·b_1_0·b_3_2
       + b_4_6·b_1_0·b_3_1 + b_4_5·b_1_0·b_3_5 + b_4_5·b_1_0·b_3_2 + b_4_5·b_1_0·b_3_1
       + b_4_5·b_4_6 + b_4_5² + b_2_0·b_1_0³·b_3_2 + b_2_0·b_1_0³·b_3_1
       + b_2_0·b_1_0³·b_3_0 + b_2_0·b_6_13 + b_2_0·b_4_5·b_1_0² + b_2_0²·b_1_0·b_3_0
       + b_2_0²·b_1_0⁴ + b_2_0³·b_1_0²
24. b_3_5·b_5_11 + b_1_0⁵·b_3_5 + b_4_6·b_1_0·b_3_2 + b_4_6² + b_4_5·b_1_0·b_3_5
       + b_4_5·b_1_0·b_3_2 + b_4_5² + b_2_0·b_1_0⁶ + b_2_0²·b_1_0·b_3_0 + b_2_0²·b_1_0⁴
       + b_2_0³·b_1_0²
25. b_4_6·b_5_11 + b_4_6·b_1_0²·b_3_2 + b_4_5·b_5_11 + b_4_5·b_1_0²·b_3_2
       + b_4_5·b_4_6·b_1_0 + b_4_5²·b_1_0 + b_2_0·b_1_0⁴·b_3_0 + b_2_0²·b_1_0²·b_3_0
26. b_4_9·b_5_11 + b_4_5·b_4_9·b_1_0 + b_2_0·b_4_9·b_1_0³ + b_2_0²·b_4_9·b_1_0
27. b_6_13·b_3_0 + b_4_9·b_1_0⁵ + b_4_9²·b_1_0 + b_4_5·b_1_0²·b_3_0
       + b_2_0²·b_1_0²·b_3_0
28. b_6_13·b_3_1 + b_4_9·b_1_0⁵ + b_4_9²·b_1_0 + b_4_6·b_1_0²·b_3_2
       + b_4_5·b_1_0²·b_3_5 + b_4_5·b_1_0²·b_3_2 + b_4_5·b_1_0²·b_3_0 + b_2_0·b_7_1
       + b_2_0·b_7_0 + b_2_0·b_1_0·b_3_1² + b_2_0·b_1_0⁴·b_3_1 + b_2_0·b_1_0⁴·b_3_0
       + b_2_0·b_4_9·b_1_0³ + b_2_0·b_4_6·b_3_1 + b_2_0·b_4_6·b_1_0³ + b_2_0²·b_1_0⁵
       + b_2_0³·b_3_2 + b_2_0³·b_1_0³
29. b_1_0⁶·b_3_5 + b_6_13·b_3_5 + b_4_6·b_1_0²·b_3_2 + b_4_6²·b_1_0 + b_4_5·b_1_0²·b_3_2
       + b_4_5²·b_1_0 + b_2_0·b_1_0⁴·b_3_2 + b_2_0·b_1_0⁴·b_3_0 + b_2_0·b_1_0⁷
       + b_2_0²·b_1_0²·b_3_0 + b_2_0²·b_1_0⁵ + b_2_0³·b_1_0³
30. b_4_6·b_1_0³·b_3_2 + b_4_6·b_6_13 + b_4_5·b_1_0³·b_3_2 + b_4_5·b_6_13
       + b_2_0·b_1_0⁵·b_3_1 + b_2_0·b_4_9·b_1_0⁴ + b_2_0·b_4_9² + b_2_0·b_4_6·b_1_0·b_3_1
       + b_2_0·b_4_6² + b_2_0·b_4_5·b_1_0·b_3_1 + b_2_0·b_4_5·b_1_0⁴ + b_2_0·b_4_5·b_4_6
       + b_2_0²·b_1_0³·b_3_2 + b_2_0²·b_1_0³·b_3_0 + b_2_0²·b_1_0⁶ + b_2_0²·b_6_13
       + b_2_0²·b_4_9·b_1_0² + b_2_0²·b_4_6·b_1_0² + b_2_0²·b_4_5·b_1_0²
       + b_2_0³·b_1_0·b_3_0 + b_2_0³·b_1_0⁴
31. b_4_9·b_1_0⁶ + b_4_9·b_6_13 + b_4_5·b_4_9·b_1_0² + b_2_0·b_4_9²
       + b_2_0²·b_1_0³·b_3_0 + b_2_0²·b_4_9·b_1_0² + b_2_0³·b_1_0·b_3_0
32. b_3_0·b_7_0 + b_1_0³·b_7_0 + b_4_6·b_6_13 + b_4_6²·b_1_0² + b_4_5·b_6_13
       + b_4_5²·b_1_0² + b_2_0·b_1_0·b_7_0 + b_2_0·b_4_9·b_1_0⁴ + b_2_0·b_4_9²
       + b_2_0·b_4_6·b_1_0·b_3_2 + b_2_0·b_4_6·b_1_0⁴ + b_2_0·b_4_6²
       + b_2_0·b_4_5·b_1_0·b_3_2 + b_2_0·b_4_5·b_1_0·b_3_0 + b_2_0·b_4_5·b_1_0⁴
       + b_2_0·b_4_5² + b_2_0²·b_1_0³·b_3_2 + b_2_0²·b_6_13 + b_2_0⁴·b_1_0²
33. b_3_0·b_7_1 + b_1_0³·b_7_0 + b_4_6·b_6_13 + b_4_6²·b_1_0² + b_4_5·b_6_13
       + b_4_5·b_4_9·b_1_0² + b_4_5²·b_1_0² + b_2_0·b_1_0·b_7_0 + b_2_0·b_4_9²
       + b_2_0·b_4_6·b_1_0·b_3_2 + b_2_0·b_4_6·b_1_0⁴ + b_2_0·b_4_6²
       + b_2_0·b_4_5·b_1_0·b_3_2 + b_2_0·b_4_5·b_1_0⁴ + b_2_0·b_4_5·b_4_9 + b_2_0·b_4_5²
       + b_2_0²·b_1_0³·b_3_2 + b_2_0²·b_1_0³·b_3_0 + b_2_0²·b_6_13 + b_2_0⁴·b_1_0²
34. b_3_1·b_7_0 + b_1_0³·b_7_0 + b_4_6·b_3_1·b_3_2 + b_4_6·b_3_1² + b_4_6·b_6_13
       + b_4_6²·b_1_0² + b_4_5·b_6_13 + b_4_5²·b_1_0² + b_2_0·b_1_0⁵·b_3_1 + b_2_0·b_8_10
       + b_2_0·b_4_9² + b_2_0·b_4_6·b_1_0·b_3_2 + b_2_0·b_4_6² + b_2_0·b_4_5·b_1_0⁴
       + b_2_0·b_4_5·b_4_6 + b_2_0²·b_1_0³·b_3_2 + b_2_0²·b_1_0³·b_3_0 + b_2_0²·b_6_13
       + b_2_0²·b_4_9·b_1_0² + b_2_0²·b_4_6·b_1_0² + b_2_0³·b_1_0·b_3_1
       + b_2_0³·b_1_0·b_3_0
35. b_3_1·b_7_1 + b_1_0³·b_7_0 + b_4_6·b_3_1·b_3_2 + b_4_6·b_3_1² + b_4_5·b_1_0³·b_3_5
       + b_4_5·b_1_0³·b_3_1 + b_4_5·b_1_0³·b_3_0 + b_4_5·b_4_9·b_1_0²
       + b_4_5·b_4_6·b_1_0² + b_4_5²·b_1_0² + b_2_0·b_1_0·b_7_1 + b_2_0·b_1_0·b_7_0
       + b_2_0·b_8_10 + b_2_0·b_4_9·b_1_0⁴ + b_2_0·b_4_9² + b_2_0·b_4_6·b_1_0·b_3_2
       + b_2_0·b_4_6·b_1_0·b_3_1 + b_2_0·b_4_6·b_1_0⁴ + b_2_0·b_4_6²
       + b_2_0·b_4_5·b_1_0·b_3_2 + b_2_0·b_4_5·b_1_0·b_3_1 + b_2_0·b_4_5·b_1_0⁴
       + b_2_0·b_4_5² + b_2_0²·b_3_1·b_3_2 + b_2_0²·b_1_0³·b_3_0 + b_2_0²·b_1_0⁶
       + b_2_0²·b_4_9·b_1_0² + b_2_0³·b_1_0·b_3_2 + b_2_0³·b_1_0⁴ + b_2_0³·b_4_6
       + b_2_0⁴·b_1_0²
36. b_3_2·b_7_0 + b_1_0³·b_7_0 + b_4_6·b_3_1² + b_4_6²·b_1_0² + b_4_5·b_1_0³·b_3_5
       + b_4_5·b_1_0³·b_3_0 + b_4_5²·b_1_0² + b_2_0·b_1_0·b_7_0 + b_2_0·b_1_0⁵·b_3_1
       + b_2_0·b_4_6·b_1_0·b_3_2 + b_2_0·b_4_6² + b_2_0·b_4_5·b_1_0·b_3_1
       + b_2_0·b_4_5·b_1_0·b_3_0 + b_2_0·b_4_5² + b_2_0²·b_1_0⁶ + b_2_0²·b_4_9·b_1_0²
       + b_2_0²·b_4_5·b_1_0² + b_2_0³·b_1_0·b_3_2 + b_2_0³·b_1_0⁴ + b_2_0³·b_4_6
       + b_2_0⁴·b_1_0²
37. b_3_5·b_7_0 + b_4_6·b_3_1² + b_4_6·b_6_13 + b_4_5·b_1_0³·b_3_5 + b_4_5·b_1_0³·b_3_0
       + b_4_5·b_6_13 + b_2_0·b_1_0⁵·b_3_1 + b_2_0·b_4_9·b_1_0⁴ + b_2_0·b_4_9²
       + b_2_0·b_4_6·b_1_0⁴ + b_2_0·b_4_5·b_1_0·b_3_2 + b_2_0·b_4_5·b_1_0·b_3_1
       + b_2_0·b_4_5·b_1_0⁴ + b_2_0²·b_1_0³·b_3_2 + b_2_0²·b_1_0⁶ + b_2_0²·b_6_13
       + b_2_0²·b_4_9·b_1_0² + b_2_0²·b_4_5·b_1_0² + b_2_0³·b_1_0·b_3_2
       + b_2_0³·b_1_0⁴ + b_2_0³·b_4_6
38. b_3_5·b_7_1 + b_6_13·b_1_0·b_3_5 + b_4_6·b_3_1² + b_4_5·b_1_0³·b_3_0
       + b_2_0·b_4_9·b_1_0⁴ + b_2_0·b_4_9² + b_2_0·b_4_6·b_1_0·b_3_2
       + b_2_0·b_4_6·b_1_0·b_3_1 + b_2_0·b_4_6·b_1_0⁴ + b_2_0·b_4_6²
       + b_2_0·b_4_5·b_1_0·b_3_2 + b_2_0·b_4_5·b_1_0·b_3_0 + b_2_0·b_4_5·b_4_6
       + b_2_0²·b_3_1·b_3_2 + b_2_0²·b_3_1² + b_2_0²·b_1_0³·b_3_2
       + b_2_0²·b_1_0³·b_3_0 + b_2_0²·b_4_9·b_1_0² + b_2_0²·b_4_6·b_1_0²
       + b_2_0³·b_1_0·b_3_1 + b_2_0³·b_1_0·b_3_0 + b_2_0³·b_1_0⁴ + b_2_0³·b_4_9
       + b_2_0³·b_4_5 + b_2_0⁴·b_1_0² + b_2_0⁵
39. b_5_11² + b_6_13·b_1_0·b_3_5 + b_6_13·b_1_0·b_3_2 + b_6_13·b_1_0⁴
       + b_4_6·b_1_0³·b_3_1 + b_4_6·b_6_13 + b_4_5·b_1_0·b_5_11 + b_4_5·b_1_0³·b_3_5
       + b_4_5·b_1_0³·b_3_1 + b_4_5·b_6_13 + b_4_5·b_4_6·b_1_0² + b_4_5²·b_1_0²
       + b_2_0·b_4_9·b_1_0⁴ + b_2_0·b_4_9² + b_2_0²·b_1_0³·b_3_1 + b_2_0²·b_1_0³·b_3_0
       + b_2_0²·b_1_0⁶ + b_2_0²·b_4_6·b_1_0²
40. b_4_6·b_7_0 + b_4_6²·b_3_2 + b_4_6²·b_3_1 + b_4_5·b_7_0 + b_4_5·b_4_6·b_3_2
       + b_4_5·b_4_6·b_3_1 + b_2_0·b_1_0²·b_7_1 + b_2_0·b_6_13·b_1_0³
       + b_2_0·b_4_9·b_1_0⁵ + b_2_0·b_4_9²·b_1_0 + b_2_0·b_4_6·b_1_0²·b_3_2
       + b_2_0·b_4_6·b_1_0⁵ + b_2_0·b_4_5·b_1_0²·b_3_2 + b_2_0·b_4_5·b_4_9·b_1_0
       + b_2_0²·b_7_1 + b_2_0²·b_7_0 + b_2_0²·b_1_0·b_3_1² + b_2_0²·b_1_0⁴·b_3_0
       + b_2_0²·b_6_13·b_1_0 + b_2_0²·b_4_9·b_1_0³ + b_2_0²·b_4_6·b_3_1
       + b_2_0²·b_4_5·b_3_0 + b_2_0³·b_1_0²·b_3_2 + b_2_0³·b_1_0²·b_3_1
       + b_2_0³·b_1_0²·b_3_0 + b_2_0³·b_4_9·b_1_0 + b_2_0³·b_4_5·b_1_0 + b_2_0⁴·b_3_2
       + b_2_0⁴·b_1_0³
41. b_4_6·b_7_1 + b_4_6·b_1_0⁴·b_3_1 + b_4_6·b_6_13·b_1_0 + b_4_6²·b_3_2 + b_4_6²·b_3_1
       + b_4_5·b_7_1 + b_4_5·b_1_0⁴·b_3_0 + b_4_5·b_6_13·b_1_0 + b_4_5·b_4_6·b_3_2
       + b_4_5·b_4_6·b_1_0³ + b_4_5²·b_3_5 + b_4_5²·b_3_1 + b_4_5²·b_1_0³
       + b_2_0·b_1_0²·b_7_0 + b_2_0·b_4_6·b_1_0²·b_3_2 + b_2_0·b_4_6·b_1_0²·b_3_1
       + b_2_0·b_4_6·b_1_0⁵ + b_2_0·b_4_5·b_1_0²·b_3_1 + b_2_0·b_4_5·b_1_0²·b_3_0
       + b_2_0²·b_7_1 + b_2_0²·b_7_0 + b_2_0²·b_1_0·b_3_1² + b_2_0²·b_1_0⁴·b_3_1
       + b_2_0²·b_1_0⁴·b_3_0 + b_2_0²·b_6_13·b_1_0 + b_2_0²·b_4_9·b_1_0³
       + b_2_0²·b_4_6·b_3_2 + b_2_0²·b_4_6·b_3_1 + b_2_0²·b_4_6·b_1_0³
       + b_2_0²·b_4_5·b_3_2 + b_2_0²·b_4_5·b_3_0 + b_2_0³·b_1_0²·b_3_0 + b_2_0³·b_1_0⁵
       + b_2_0³·b_4_6·b_1_0 + b_2_0⁴·b_3_2
42. b_4_9·b_7_1 + b_4_9·b_7_0 + b_4_5·b_1_0⁴·b_3_0 + b_4_5·b_4_9·b_1_0³
       + b_2_0·b_4_9²·b_1_0 + b_2_0²·b_1_0⁴·b_3_0 + b_2_0²·b_4_5·b_3_0
       + b_2_0³·b_1_0²·b_3_0
43. b_8_10·b_3_0 + b_8_10·b_1_0³ + b_4_6·b_6_13·b_1_0 + b_4_5·b_6_13·b_1_0
       + b_4_5·b_4_6·b_3_1 + b_4_5²·b_3_5 + b_4_5²·b_3_1 + b_2_0·b_1_0⁹ + b_2_0·b_8_10·b_1_0
       + b_2_0·b_4_6·b_1_0²·b_3_2 + b_2_0·b_4_6·b_1_0²·b_3_1 + b_2_0·b_4_6·b_1_0⁵
       + b_2_0·b_4_6²·b_1_0 + b_2_0·b_4_5·b_1_0⁵ + b_2_0·b_4_5²·b_1_0
       + b_2_0²·b_1_0⁴·b_3_2 + b_2_0²·b_1_0⁴·b_3_1 + b_2_0²·b_1_0⁴·b_3_0
       + b_2_0²·b_1_0⁷ + b_2_0²·b_6_13·b_1_0 + b_2_0²·b_4_9·b_1_0³
       + b_2_0²·b_4_5·b_3_0 + b_2_0²·b_4_5·b_1_0³ + b_2_0³·b_4_5·b_1_0
44. b_8_10·b_3_1 + b_8_10·b_1_0³ + b_4_6·b_6_13·b_1_0 + b_4_6²·b_3_2 + b_4_5·b_6_13·b_1_0
       + b_4_5·b_4_6·b_3_1 + b_4_5²·b_3_2 + b_4_5²·b_3_1 + b_2_0·b_1_0²·b_7_0
       + b_2_0·b_1_0⁶·b_3_1 + b_2_0·b_1_0⁹ + b_2_0·b_8_10·b_1_0 + b_2_0·b_4_6·b_1_0²·b_3_2
       + b_2_0·b_4_6·b_1_0⁵ + b_2_0·b_4_6²·b_1_0 + b_2_0·b_4_5·b_1_0²·b_3_2
       + b_2_0·b_4_5·b_1_0²·b_3_0 + b_2_0·b_4_5·b_1_0⁵ + b_2_0·b_4_5·b_4_6·b_1_0
       + b_2_0²·b_7_0 + b_2_0²·b_1_0⁴·b_3_2 + b_2_0²·b_1_0⁷ + b_2_0²·b_6_13·b_1_0
       + b_2_0²·b_4_9·b_1_0³ + b_2_0²·b_4_6·b_3_2 + b_2_0²·b_4_6·b_3_1
       + b_2_0²·b_4_5·b_3_0 + b_2_0³·b_1_0⁵ + b_2_0³·b_4_6·b_1_0 + b_2_0⁴·b_1_0³
       + b_2_0⁵·b_1_0
45. b_8_10·b_3_2 + b_8_10·b_1_0³ + b_4_6²·b_3_2 + b_4_6²·b_3_1 + b_4_5·b_4_6·b_3_2
       + b_4_5²·b_3_1 + b_2_0·b_1_0²·b_7_1 + b_2_0·b_1_0²·b_7_0 + b_2_0·b_1_0⁶·b_3_1
       + b_2_0·b_1_0⁹ + b_2_0·b_8_10·b_1_0 + b_2_0·b_4_6·b_1_0²·b_3_2
       + b_2_0·b_4_6·b_1_0⁵ + b_2_0·b_4_6²·b_1_0 + b_2_0·b_4_5·b_1_0²·b_3_1
       + b_2_0·b_4_5·b_1_0²·b_3_0 + b_2_0·b_4_5·b_1_0⁵ + b_2_0·b_4_5·b_4_9·b_1_0
       + b_2_0·b_4_5·b_4_6·b_1_0 + b_2_0²·b_7_1 + b_2_0²·b_7_0 + b_2_0²·b_1_0·b_3_1²
       + b_2_0²·b_1_0⁴·b_3_2 + b_2_0²·b_1_0⁷ + b_2_0²·b_4_6·b_3_1
       + b_2_0²·b_4_6·b_1_0³ + b_2_0²·b_4_5·b_3_0 + b_2_0²·b_4_5·b_1_0³
       + b_2_0³·b_1_0²·b_3_2 + b_2_0³·b_1_0⁵ + b_2_0³·b_4_6·b_1_0 + b_2_0⁴·b_3_2
       + b_2_0⁴·b_1_0³
46. b_8_10·b_3_5 + b_4_6·b_6_13·b_1_0 + b_4_6²·b_3_2 + b_4_6²·b_3_1 + b_4_5·b_6_13·b_1_0
       + b_4_5·b_4_6·b_3_2 + b_4_5·b_4_6·b_3_1 + b_4_5²·b_3_5 + b_2_0·b_1_0²·b_7_1
       + b_2_0·b_1_0²·b_7_0 + b_2_0·b_1_0⁶·b_3_1 + b_2_0·b_4_6·b_1_0²·b_3_1
       + b_2_0·b_4_5·b_1_0²·b_3_1 + b_2_0·b_4_5·b_1_0²·b_3_0 + b_2_0·b_4_5·b_4_9·b_1_0
       + b_2_0·b_4_5·b_4_6·b_1_0 + b_2_0·b_4_5²·b_1_0 + b_2_0²·b_7_1 + b_2_0²·b_7_0
       + b_2_0²·b_1_0·b_3_1² + b_2_0²·b_1_0⁴·b_3_1 + b_2_0²·b_1_0⁴·b_3_0
       + b_2_0²·b_6_13·b_1_0 + b_2_0²·b_4_9·b_1_0³ + b_2_0²·b_4_6·b_3_1
       + b_2_0²·b_4_6·b_1_0³ + b_2_0³·b_1_0²·b_3_2 + b_2_0³·b_1_0⁵
       + b_2_0³·b_4_6·b_1_0 + b_2_0³·b_4_5·b_1_0 + b_2_0⁴·b_3_2 + b_2_0⁴·b_1_0³
47. b_1_0⁴·b_7_0 + b_8_10·b_1_0³ + b_4_9·b_7_0 + b_4_9²·b_1_0³ + b_4_6²·b_1_0³
       + b_4_5·b_1_0⁴·b_3_0 + b_4_5·b_4_9·b_1_0³ + b_4_5·b_4_6·b_3_1 + b_4_5²·b_3_5
       + b_4_5²·b_3_1 + b_4_5²·b_1_0³ + b_2_0·b_1_0²·b_7_0 + b_2_0·b_1_0⁹
       + b_2_0·b_8_10·b_1_0 + b_2_0·b_4_9·b_1_0⁵ + b_2_0·b_4_6·b_1_0²·b_3_1
       + b_2_0·b_4_5·b_1_0²·b_3_2 + b_2_0²·b_1_0⁴·b_3_1 + b_2_0²·b_1_0⁴·b_3_0
       + b_2_0²·b_1_0⁷ + b_2_0²·b_4_9·b_1_0³ + b_2_0²·b_4_5·b_1_0³
       + b_2_0³·b_1_0²·b_3_0 + b_2_0³·b_4_9·b_1_0 + b_2_0³·b_4_5·b_1_0 + b_2_0⁴·b_1_0³
48. b_4_6·b_8_10 + b_4_6²·b_1_0·b_3_2 + b_4_5·b_8_10 + b_4_5·b_4_6·b_1_0·b_3_1
       + b_4_5·b_4_6² + b_4_5²·b_1_0·b_3_2 + b_4_5²·b_1_0·b_3_1 + b_4_5³
       + b_2_0·b_1_0³·b_7_1 + b_2_0·b_1_0³·b_7_0 + b_2_0·b_1_0⁷·b_3_1
       + b_2_0·b_8_10·b_1_0² + b_2_0·b_6_13·b_1_0⁴ + b_2_0·b_4_6·b_1_0⁶
       + b_2_0·b_4_6·b_6_13 + b_2_0·b_4_5·b_1_0³·b_3_1 + b_2_0·b_4_5·b_1_0³·b_3_0
       + b_2_0·b_4_5·b_1_0⁶ + b_2_0·b_4_5·b_6_13 + b_2_0·b_4_5·b_4_9·b_1_0²
       + b_2_0²·b_1_0·b_7_1 + b_2_0²·b_1_0·b_7_0 + b_2_0²·b_1_0⁵·b_3_1
       + b_2_0²·b_6_13·b_1_0² + b_2_0²·b_4_9·b_1_0⁴ + b_2_0²·b_4_5·b_1_0·b_3_0
       + b_2_0²·b_4_5·b_4_9 + b_2_0³·b_1_0³·b_3_0 + b_2_0³·b_1_0⁶ + b_2_0³·b_6_13
       + b_2_0³·b_4_9·b_1_0² + b_2_0³·b_4_6·b_1_0² + b_2_0⁴·b_1_0·b_3_2
       + b_2_0⁴·b_1_0·b_3_0 + b_2_0⁴·b_1_0⁴
49. b_8_10·b_1_0⁴ + b_4_9·b_1_0·b_7_0 + b_4_9·b_8_10 + b_4_9²·b_1_0⁴ + b_4_9³
       + b_4_6·b_6_13·b_1_0² + b_4_5·b_6_13·b_1_0² + b_4_5·b_4_9·b_1_0⁴
       + b_4_5·b_4_6·b_1_0·b_3_1 + b_4_5²·b_1_0·b_3_5 + b_4_5²·b_1_0·b_3_1
       + b_2_0·b_1_0³·b_7_0 + b_2_0·b_1_0¹⁰ + b_2_0·b_8_10·b_1_0²
       + b_2_0·b_4_9²·b_1_0² + b_2_0·b_4_6·b_1_0³·b_3_1 + b_2_0·b_4_6·b_1_0⁶
       + b_2_0·b_4_5·b_1_0³·b_3_2 + b_2_0·b_4_5·b_1_0⁶ + b_2_0·b_4_5·b_4_9·b_1_0²
       + b_2_0²·b_1_0·b_7_0 + b_2_0²·b_1_0⁸ + b_2_0²·b_4_9² + b_2_0²·b_4_6·b_1_0·b_3_2
       + b_2_0²·b_4_6·b_1_0⁴ + b_2_0²·b_4_6² + b_2_0²·b_4_5·b_1_0·b_3_2
       + b_2_0²·b_4_5·b_1_0⁴ + b_2_0²·b_4_5·b_4_9 + b_2_0²·b_4_5²
       + b_2_0³·b_1_0³·b_3_2 + b_2_0³·b_1_0³·b_3_1 + b_2_0³·b_1_0³·b_3_0
       + b_2_0³·b_6_13 + b_2_0³·b_4_6·b_1_0² + b_2_0³·b_4_5·b_1_0²
       + b_2_0⁴·b_1_0·b_3_0 + b_2_0⁴·b_1_0⁴ + b_2_0⁵·b_1_0²
50. b_5_11·b_7_0 + b_4_6·b_6_13·b_1_0² + b_4_6³ + b_4_5·b_1_0·b_7_0
       + b_4_5·b_6_13·b_1_0² + b_4_5·b_4_6² + b_4_5²·b_4_6 + b_4_5³ + b_2_0·b_1_0³·b_7_0
       + b_2_0·b_1_0⁷·b_3_1 + b_2_0·b_4_6·b_1_0³·b_3_1 + b_2_0·b_4_6·b_1_0⁶
       + b_2_0·b_4_6·b_6_13 + b_2_0·b_4_5·b_1_0³·b_3_1 + b_2_0·b_4_5·b_6_13
       + b_2_0·b_4_5·b_4_6·b_1_0² + b_2_0·b_4_5²·b_1_0² + b_2_0²·b_1_0·b_7_0
       + b_2_0²·b_1_0⁸ + b_2_0²·b_4_9·b_1_0⁴ + b_2_0²·b_4_9²
       + b_2_0²·b_4_6·b_1_0·b_3_2 + b_2_0²·b_4_6·b_1_0·b_3_1 + b_2_0²·b_4_6·b_1_0⁴
       + b_2_0²·b_4_5·b_1_0·b_3_2 + b_2_0²·b_4_5·b_1_0·b_3_1 + b_2_0²·b_4_5·b_1_0⁴
       + b_2_0²·b_4_5·b_4_6 + b_2_0²·b_4_5² + b_2_0³·b_1_0³·b_3_2
       + b_2_0³·b_1_0³·b_3_1 + b_2_0³·b_4_9·b_1_0² + b_2_0³·b_4_6·b_1_0²
       + b_2_0⁵·b_1_0²
51. b_6_13·b_7_0 + b_4_9·b_8_10·b_1_0 + b_4_9³·b_1_0 + b_4_6·b_6_13·b_1_0³
       + b_4_6³·b_1_0 + b_4_5·b_1_0²·b_7_0 + b_4_5·b_6_13·b_1_0³ + b_4_5·b_4_9·b_1_0⁵
       + b_4_5·b_4_9²·b_1_0 + b_4_5·b_4_6·b_1_0²·b_3_1 + b_4_5·b_4_6²·b_1_0
       + b_4_5²·b_1_0²·b_3_1 + b_4_5²·b_4_6·b_1_0 + b_4_5³·b_1_0 + b_2_0·b_1_0⁴·b_7_1
       + b_2_0·b_8_10·b_1_0³ + b_2_0·b_6_13·b_1_0⁵ + b_2_0·b_4_9²·b_1_0³
       + b_2_0·b_4_6·b_1_0⁴·b_3_1 + b_2_0·b_4_6·b_1_0⁷ + b_2_0·b_4_6·b_6_13·b_1_0
       + b_2_0·b_4_6²·b_1_0³ + b_2_0·b_4_5·b_1_0⁴·b_3_0 + b_2_0·b_4_5·b_6_13·b_1_0
       + b_2_0·b_4_5·b_4_6·b_3_1 + b_2_0·b_4_5²·b_3_2 + b_2_0·b_4_5²·b_3_1
       + b_2_0²·b_1_0²·b_7_0 + b_2_0²·b_1_0⁶·b_3_1 + b_2_0²·b_1_0⁹
       + b_2_0²·b_4_9²·b_1_0 + b_2_0²·b_4_6·b_1_0²·b_3_2 + b_2_0²·b_4_6·b_1_0²·b_3_1
       + b_2_0²·b_4_6·b_1_0⁵ + b_2_0²·b_4_5²·b_1_0 + b_2_0³·b_7_1 + b_2_0³·b_7_0
       + b_2_0³·b_1_0·b_3_1² + b_2_0³·b_1_0⁴·b_3_1 + b_2_0³·b_1_0⁷
       + b_2_0³·b_6_13·b_1_0 + b_2_0³·b_4_9·b_1_0³ + b_2_0³·b_4_6·b_3_1
       + b_2_0³·b_4_5·b_1_0³ + b_2_0⁴·b_1_0²·b_3_1 + b_2_0⁴·b_1_0⁵
       + b_2_0⁴·b_4_9·b_1_0 + b_2_0⁴·b_4_6·b_1_0 + b_2_0⁴·b_4_5·b_1_0 + b_2_0⁵·b_3_2
       + b_2_0⁵·b_1_0³
52. b_8_10·b_5_11 + b_4_6·b_6_13·b_1_0³ + b_4_6²·b_1_0²·b_3_2 + b_4_6³·b_1_0
       + b_4_5·b_8_10·b_1_0 + b_4_5·b_6_13·b_1_0³ + b_4_5·b_4_6²·b_1_0
       + b_4_5²·b_1_0²·b_3_5 + b_4_5²·b_1_0²·b_3_2 + b_4_5²·b_4_6·b_1_0 + b_4_5³·b_1_0
       + b_2_0·b_1_0⁸·b_3_1 + b_2_0·b_8_10·b_1_0³ + b_2_0·b_6_13·b_1_0⁵
       + b_2_0·b_4_9·b_6_13·b_1_0 + b_2_0·b_4_9²·b_1_0³ + b_2_0·b_4_6·b_1_0⁷
       + b_2_0·b_4_6·b_6_13·b_1_0 + b_2_0·b_4_5·b_1_0⁴·b_3_0 + b_2_0·b_4_5·b_6_13·b_1_0
       + b_2_0·b_4_5·b_4_9·b_1_0³ + b_2_0·b_4_5·b_4_6·b_3_1 + b_2_0·b_4_5²·b_3_2
       + b_2_0·b_4_5²·b_3_1 + b_2_0·b_4_5²·b_3_0 + b_2_0²·b_1_0⁶·b_3_1 + b_2_0²·b_1_0⁹
       + b_2_0²·b_8_10·b_1_0 + b_2_0²·b_4_9·b_1_0⁵ + b_2_0²·b_4_6·b_1_0²·b_3_2
       + b_2_0²·b_4_6·b_1_0²·b_3_1 + b_2_0²·b_4_6·b_1_0⁵ + b_2_0²·b_4_6²·b_1_0
       + b_2_0²·b_4_5²·b_1_0 + b_2_0³·b_1_0⁴·b_3_2 + b_2_0³·b_1_0⁴·b_3_1
       + b_2_0³·b_6_13·b_1_0 + b_2_0³·b_4_9·b_1_0³ + b_2_0³·b_4_6·b_1_0³
       + b_2_0³·b_4_5·b_3_0 + b_2_0⁴·b_4_5·b_1_0
53. b_6_13·b_8_10 + b_4_9·b_1_0³·b_7_0 + b_4_9·b_8_10·b_1_0² + b_4_9²·b_6_13
       + b_4_9³·b_1_0² + b_4_6·b_6_13·b_1_0⁴ + b_4_6²·b_6_13 + b_4_6³·b_1_0²
       + b_4_5·b_8_10·b_1_0² + b_4_5·b_6_13·b_1_0⁴ + b_4_5·b_4_9·b_6_13
       + b_4_5·b_4_9²·b_1_0² + b_4_5·b_4_6·b_6_13 + b_4_5·b_4_6²·b_1_0²
       + b_4_5²·b_4_9·b_1_0² + b_4_5²·b_4_6·b_1_0² + b_4_5³·b_1_0²
       + b_2_0·b_1_0⁹·b_3_1 + b_2_0·b_6_13·b_1_0⁶ + b_2_0·b_4_9·b_1_0·b_7_0
       + b_2_0·b_4_9·b_8_10 + b_2_0·b_4_6·b_1_0⁸ + b_2_0·b_4_6·b_6_13·b_1_0²
       + b_2_0·b_4_6²·b_1_0⁴ + b_2_0·b_4_5·b_1_0·b_7_1 + b_2_0·b_4_5·b_1_0·b_7_0
       + b_2_0·b_4_5·b_1_0⁵·b_3_1 + b_2_0·b_4_5·b_1_0⁸ + b_2_0·b_4_5·b_4_9²
       + b_2_0·b_4_5·b_4_6·b_1_0·b_3_1 + b_2_0·b_4_5·b_4_6·b_1_0⁴
       + b_2_0·b_4_5²·b_1_0·b_3_2 + b_2_0·b_4_5²·b_1_0·b_3_1 + b_2_0·b_4_5²·b_1_0⁴
       + b_2_0·b_4_5²·b_4_9 + b_2_0²·b_1_0³·b_7_1 + b_2_0²·b_1_0¹⁰
       + b_2_0²·b_8_10·b_1_0² + b_2_0²·b_6_13·b_1_0⁴ + b_2_0²·b_4_9²·b_1_0²
       + b_2_0²·b_4_6·b_1_0⁶ + b_2_0²·b_4_6²·b_1_0² + b_2_0²·b_4_5·b_1_0³·b_3_2
       + b_2_0²·b_4_5·b_1_0³·b_3_0 + b_2_0²·b_4_5·b_1_0⁶ + b_2_0²·b_4_5·b_6_13
       + b_2_0²·b_4_5·b_4_9·b_1_0² + b_2_0²·b_4_5·b_4_6·b_1_0²
       + b_2_0²·b_4_5²·b_1_0² + b_2_0³·b_1_0·b_7_0 + b_2_0³·b_1_0⁸
       + b_2_0³·b_4_6·b_1_0·b_3_2 + b_2_0³·b_4_6·b_1_0·b_3_1 + b_2_0³·b_4_5·b_1_0·b_3_1
       + b_2_0³·b_4_5·b_1_0·b_3_0 + b_2_0³·b_4_5·b_4_9 + b_2_0³·b_4_5·b_4_6
       + b_2_0³·b_4_5² + b_2_0⁴·b_1_0³·b_3_2 + b_2_0⁴·b_1_0³·b_3_0
       + b_2_0⁴·b_4_9·b_1_0² + b_2_0⁴·b_4_6·b_1_0² + b_2_0⁵·b_1_0⁴ + b_2_0⁶·b_1_0²
54. b_7_0² + b_4_9·b_1_0³·b_7_0 + b_4_9·b_8_10·b_1_0² + b_4_6²·b_3_1·b_3_2
       + b_4_6²·b_6_13 + b_4_5·b_1_0³·b_7_0 + b_4_5·b_4_9²·b_1_0² + b_4_5·b_4_6·b_6_13
       + b_4_5·b_4_6²·b_1_0² + b_4_5²·b_1_0³·b_3_5 + b_4_5³·b_1_0²
       + b_2_0·b_4_9²·b_1_0⁴ + b_2_0·b_4_9³ + b_2_0·b_4_6·b_1_0⁵·b_3_1
       + b_2_0·b_4_6²·b_1_0·b_3_2 + b_2_0·b_4_6²·b_1_0⁴ + b_2_0·b_4_5·b_1_0·b_7_0
       + b_2_0·b_4_5·b_1_0⁵·b_3_1 + b_2_0·b_4_5·b_4_6² + b_2_0·b_4_5²·b_1_0·b_3_0
       + b_2_0·b_4_5²·b_1_0⁴ + b_2_0·b_4_5²·b_4_9 + b_2_0·b_4_5³ + b_2_0²·b_1_0⁷·b_3_1
       + b_2_0²·b_4_6²·b_1_0² + b_2_0²·b_4_5·b_1_0³·b_3_0 + b_2_0²·b_4_5·b_1_0⁶
       + b_2_0²·b_4_5·b_6_13 + b_2_0²·b_4_5·b_4_9·b_1_0² + b_2_0³·b_1_0⁵·b_3_1
       + b_2_0³·b_1_0⁸ + b_2_0³·b_4_9² + b_2_0³·b_4_6·b_1_0·b_3_1
       + b_2_0³·b_4_6·b_1_0⁴ + b_2_0³·b_4_5·b_1_0·b_3_1 + b_2_0³·b_4_5·b_1_0·b_3_0
       + b_2_0³·b_4_5·b_1_0⁴ + b_2_0³·b_4_5·b_4_6 + b_2_0⁴·b_1_0³·b_3_2
       + b_2_0⁴·b_1_0⁶ + b_2_0⁴·b_6_13 + b_2_0⁴·b_4_6·b_1_0² + b_2_0⁴·b_4_5·b_1_0²
       + b_2_0⁵·b_1_0⁴ + b_2_0⁶·b_1_0² + c_8_5·b_1_0³·b_3_0 + b_2_0·c_8_5·b_1_0·b_3_0
55. b_7_0·b_7_1 + b_4_9·b_1_0³·b_7_0 + b_4_9·b_8_10·b_1_0² + b_4_6·b_6_13·b_1_0⁴
       + b_4_6²·b_3_1·b_3_2 + b_4_5·b_8_10·b_1_0² + b_4_5·b_6_13·b_1_0⁴
       + b_4_5·b_4_6²·b_1_0² + b_4_5²·b_1_0³·b_3_0 + b_4_5²·b_4_9·b_1_0²
       + b_4_5³·b_1_0² + b_2_0·b_1_0⁵·b_7_1 + b_2_0·b_1_0⁹·b_3_1 + b_2_0·b_6_13·b_1_0⁶
       + b_2_0·b_4_9·b_1_0·b_7_0 + b_2_0·b_4_9·b_8_10 + b_2_0·b_4_9²·b_1_0⁴
       + b_2_0·b_4_9³ + b_2_0·b_4_6·b_1_0⁵·b_3_1 + b_2_0·b_4_6³ + b_2_0·b_4_5·b_1_0·b_7_0
       + b_2_0·b_4_5·b_1_0⁵·b_3_1 + b_2_0·b_4_5·b_1_0⁸ + b_2_0·b_4_5·b_8_10
       + b_2_0·b_4_5·b_4_6·b_1_0·b_3_1 + b_2_0·b_4_5·b_4_6·b_1_0⁴ + b_2_0·b_4_5·b_4_6²
       + b_2_0·b_4_5²·b_1_0·b_3_2 + b_2_0·b_4_5²·b_1_0·b_3_1 + b_2_0·b_4_5²·b_1_0·b_3_0
       + b_2_0·b_4_5²·b_1_0⁴ + b_2_0·b_4_5²·b_4_9 + b_2_0·b_4_5²·b_4_6 + b_2_0·b_4_5³
       + b_2_0²·b_1_0³·b_7_1 + b_2_0²·b_1_0³·b_7_0 + b_2_0²·b_1_0⁷·b_3_1
       + b_2_0²·b_1_0¹⁰ + b_2_0²·b_8_10·b_1_0² + b_2_0²·b_6_13·b_1_0⁴
       + b_2_0²·b_4_9·b_6_13 + b_2_0²·b_4_9²·b_1_0² + b_2_0²·b_4_6·b_3_1²
       + b_2_0²·b_4_6·b_1_0⁶ + b_2_0²·b_4_6²·b_1_0² + b_2_0²·b_4_5·b_1_0³·b_3_0
       + b_2_0²·b_4_5·b_1_0⁶ + b_2_0²·b_4_5·b_4_9·b_1_0² + b_2_0²·b_4_5²·b_1_0²
       + b_2_0³·b_1_0·b_7_0 + b_2_0³·b_4_9² + b_2_0³·b_4_6·b_1_0·b_3_2
       + b_2_0³·b_4_6·b_1_0·b_3_1 + b_2_0³·b_4_6² + b_2_0³·b_4_5·b_1_0·b_3_2
       + b_2_0³·b_4_5·b_1_0·b_3_0 + b_2_0³·b_4_5·b_4_6 + b_2_0⁴·b_1_0³·b_3_0
       + b_2_0⁴·b_6_13 + b_2_0⁴·b_4_9·b_1_0² + b_2_0⁵·b_1_0·b_3_2 + b_2_0⁵·b_1_0·b_3_0
       + b_2_0⁵·b_1_0⁴ + b_2_0⁵·b_4_6 + c_8_5·b_1_0³·b_3_0 + b_2_0·c_8_5·b_1_0·b_3_0
56. b_7_1² + b_6_13·b_1_0·b_7_1 + b_6_13·b_1_0³·b_5_11 + b_6_13·b_1_0⁵·b_3_5
       + b_4_9·b_1_0³·b_7_0 + b_4_9³·b_1_0² + b_4_6²·b_3_1·b_3_2 + b_4_6²·b_1_0⁶
       + b_4_6²·b_6_13 + b_4_6³·b_1_0² + b_4_5·b_1_0⁵·b_5_11 + b_4_5·b_1_0⁷·b_3_2
       + b_4_5²·b_1_0³·b_3_5 + b_4_5²·b_1_0³·b_3_2 + b_4_5²·b_1_0³·b_3_0
       + b_4_5²·b_6_13 + b_4_5³·b_1_0² + b_2_0·b_1_0⁵·b_7_1 + b_2_0·b_6_13·b_1_0⁶
       + b_2_0·b_4_9·b_1_0·b_7_0 + b_2_0·b_4_9·b_8_10 + b_2_0·b_4_9³ + b_2_0·b_4_6·b_1_0⁸
       + b_2_0·b_4_6·b_6_13·b_1_0² + b_2_0·b_4_6²·b_1_0·b_3_2 + b_2_0·b_4_5·b_1_0·b_7_1
       + b_2_0·b_4_5·b_1_0⁵·b_3_1 + b_2_0·b_4_5·b_4_6·b_1_0⁴ + b_2_0·b_4_5²·b_1_0·b_3_2
       + b_2_0·b_4_5²·b_4_9 + b_2_0·b_4_5²·b_4_6 + b_2_0·b_4_5³ + b_2_0²·b_1_0⁷·b_3_1
       + b_2_0²·b_8_10·b_1_0² + b_2_0²·b_6_13·b_1_0⁴ + b_2_0²·b_4_9²·b_1_0²
       + b_2_0²·b_4_6·b_1_0³·b_3_1 + b_2_0²·b_4_6·b_1_0⁶ + b_2_0²·b_4_5·b_1_0³·b_3_1
       + b_2_0²·b_4_5·b_6_13 + b_2_0²·b_4_5·b_4_9·b_1_0² + b_2_0²·b_4_5·b_4_6·b_1_0²
       + b_2_0³·b_1_0·b_7_0 + b_2_0³·b_6_13·b_1_0² + b_2_0³·b_4_6·b_1_0·b_3_2
       + b_2_0³·b_4_6·b_1_0·b_3_1 + b_2_0³·b_4_6² + b_2_0³·b_4_5·b_1_0·b_3_2
       + b_2_0³·b_4_5·b_1_0·b_3_1 + b_2_0³·b_4_5·b_1_0·b_3_0 + b_2_0³·b_4_5·b_1_0⁴
       + b_2_0³·b_4_5·b_4_9 + b_2_0³·b_4_5·b_4_6 + b_2_0⁴·b_3_1·b_3_2 + b_2_0⁴·b_3_1²
       + b_2_0⁴·b_1_0³·b_3_2 + b_2_0⁴·b_1_0³·b_3_0 + b_2_0⁴·b_4_6·b_1_0²
       + b_2_0⁴·b_4_5·b_1_0² + b_2_0⁵·b_1_0·b_3_2 + b_2_0⁵·b_1_0·b_3_1 + b_2_0⁵·b_4_9
       + b_2_0⁵·b_4_6 + b_2_0⁵·b_4_5 + b_2_0⁶·b_1_0² + b_2_0⁷ + c_8_5·b_1_0·b_5_11
       + c_8_5·b_1_0³·b_3_2 + b_4_5·c_8_5·b_1_0²
57. b_8_10·b_7_0 + b_4_9·b_8_10·b_1_0³ + b_4_9²·b_6_13·b_1_0 + b_4_9³·b_1_0³
       + b_4_6²·b_6_13·b_1_0 + b_4_6³·b_3_1 + b_4_5·b_4_9²·b_1_0³ + b_4_5²·b_1_0⁴·b_3_0
       + b_4_5²·b_6_13·b_1_0 + b_4_5²·b_4_9·b_1_0³ + b_4_5²·b_4_6·b_3_2
       + b_4_5²·b_4_6·b_3_1 + b_4_5³·b_3_2 + b_2_0·b_4_9·b_8_10·b_1_0 + b_2_0·b_4_9³·b_1_0
       + b_2_0·b_4_6·b_6_13·b_1_0³ + b_2_0·b_4_6²·b_1_0⁵ + b_2_0·b_4_6³·b_1_0
       + b_2_0·b_4_5·b_1_0²·b_7_0 + b_2_0·b_4_5·b_1_0⁶·b_3_1 + b_2_0·b_4_5·b_8_10·b_1_0
       + b_2_0·b_4_5·b_4_6·b_1_0²·b_3_1 + b_2_0·b_4_5·b_4_6·b_1_0⁵
       + b_2_0·b_4_5²·b_1_0²·b_3_2 + b_2_0·b_4_5²·b_1_0²·b_3_1
       + b_2_0·b_4_5²·b_4_9·b_1_0 + b_2_0·b_4_5³·b_1_0 + b_2_0²·b_1_0⁴·b_7_1
       + b_2_0²·b_1_0⁸·b_3_1 + b_2_0²·b_8_10·b_1_0³ + b_2_0²·b_6_13·b_1_0⁵
       + b_2_0²·b_4_9·b_7_0 + b_2_0²·b_4_6·b_1_0⁷ + b_2_0²·b_4_5·b_7_0
       + b_2_0²·b_4_5·b_1_0⁷ + b_2_0²·b_4_5·b_6_13·b_1_0 + b_2_0²·b_4_5·b_4_6·b_3_2
       + b_2_0²·b_4_5·b_4_6·b_1_0³ + b_2_0²·b_4_5²·b_3_2 + b_2_0²·b_4_5²·b_3_1
       + b_2_0²·b_4_5²·b_3_0 + b_2_0²·b_4_5²·b_1_0³ + b_2_0³·b_1_0²·b_7_0
       + b_2_0³·b_1_0⁶·b_3_1 + b_2_0³·b_4_5·b_1_0²·b_3_0 + b_2_0³·b_4_5·b_4_6·b_1_0
       + b_2_0³·b_4_5²·b_1_0 + b_2_0⁴·b_7_1 + b_2_0⁴·b_7_0 + b_2_0⁴·b_1_0·b_3_1²
       + b_2_0⁴·b_1_0⁴·b_3_2 + b_2_0⁴·b_1_0⁴·b_3_1 + b_2_0⁴·b_1_0⁴·b_3_0
       + b_2_0⁴·b_6_13·b_1_0 + b_2_0⁴·b_4_6·b_3_1 + b_2_0⁴·b_4_5·b_3_0
       + b_2_0⁴·b_4_5·b_1_0³ + b_2_0⁵·b_1_0²·b_3_1 + b_2_0⁵·b_1_0²·b_3_0
       + b_2_0⁵·b_4_9·b_1_0 + b_2_0⁵·b_4_6·b_1_0 + b_2_0⁶·b_3_2 + b_2_0⁶·b_1_0³
       + c_8_5·b_1_0⁴·b_3_0 + b_4_9·c_8_5·b_1_0³ + b_2_0·c_8_5·b_1_0²·b_3_0
       + b_2_0·b_4_9·c_8_5·b_1_0
58. b_8_10·b_7_1 + b_4_9·b_8_10·b_1_0³ + b_4_9²·b_6_13·b_1_0 + b_4_9³·b_1_0³
       + b_4_6·b_6_13·b_1_0⁵ + b_4_6²·b_6_13·b_1_0 + b_4_6³·b_3_1 + b_4_6³·b_1_0³
       + b_4_5·b_8_10·b_1_0³ + b_4_5·b_6_13·b_1_0⁵ + b_4_5·b_4_9·b_7_0
       + b_4_5·b_4_9·b_6_13·b_1_0 + b_4_5·b_4_9²·b_1_0³ + b_4_5·b_4_6²·b_3_1
       + b_4_5·b_4_6²·b_1_0³ + b_4_5²·b_1_0⁴·b_3_0 + b_4_5²·b_6_13·b_1_0
       + b_4_5²·b_4_9·b_1_0³ + b_4_5²·b_4_6·b_1_0³ + b_4_5³·b_3_5 + b_4_5³·b_1_0³
       + b_2_0·b_1_0⁶·b_7_1 + b_2_0·b_1_0¹⁰·b_3_1 + b_2_0·b_4_9·b_8_10·b_1_0
       + b_2_0·b_4_6·b_1_0⁹ + b_2_0·b_4_6·b_6_13·b_1_0³ + b_2_0·b_4_6²·b_1_0²·b_3_2
       + b_2_0·b_4_6³·b_1_0 + b_2_0·b_4_5·b_1_0⁹ + b_2_0·b_4_5·b_8_10·b_1_0
       + b_2_0·b_4_5·b_4_9·b_1_0⁵ + b_2_0·b_4_5·b_4_6·b_1_0²·b_3_1
       + b_2_0·b_4_5·b_4_6²·b_1_0 + b_2_0·b_4_5²·b_1_0²·b_3_1
       + b_2_0·b_4_5²·b_1_0²·b_3_0 + b_2_0·b_4_5²·b_1_0⁵ + b_2_0²·b_1_0⁴·b_7_1
       + b_2_0²·b_1_0¹¹ + b_2_0²·b_8_10·b_1_0³ + b_2_0²·b_6_13·b_1_0⁵
       + b_2_0²·b_4_6·b_1_0⁴·b_3_1 + b_2_0²·b_4_6·b_1_0⁷ + b_2_0²·b_4_6·b_6_13·b_1_0
       + b_2_0²·b_4_6²·b_3_2 + b_2_0²·b_4_6²·b_3_1 + b_2_0²·b_4_6²·b_1_0³
       + b_2_0²·b_4_5·b_1_0⁴·b_3_1 + b_2_0²·b_4_5·b_1_0⁷ + b_2_0²·b_4_5·b_4_6·b_3_2
       + b_2_0²·b_4_5²·b_3_1 + b_2_0²·b_4_5²·b_1_0³ + b_2_0³·b_1_0²·b_7_1
       + b_2_0³·b_1_0²·b_7_0 + b_2_0³·b_1_0⁶·b_3_1 + b_2_0³·b_1_0⁹
       + b_2_0³·b_8_10·b_1_0 + b_2_0³·b_6_13·b_1_0³ + b_2_0³·b_4_9·b_1_0⁵
       + b_2_0³·b_4_6·b_1_0²·b_3_1 + b_2_0³·b_4_6·b_1_0⁵ + b_2_0³·b_4_6²·b_1_0
       + b_2_0³·b_4_5·b_1_0²·b_3_2 + b_2_0³·b_4_5·b_1_0²·b_3_1
       + b_2_0³·b_4_5·b_1_0²·b_3_0 + b_2_0³·b_4_5·b_4_9·b_1_0 + b_2_0⁴·b_7_1
       + b_2_0⁴·b_7_0 + b_2_0⁴·b_1_0·b_3_1² + b_2_0⁴·b_1_0⁴·b_3_1 + b_2_0⁴·b_4_6·b_3_1
       + b_2_0⁴·b_4_6·b_1_0³ + b_2_0⁴·b_4_5·b_3_0 + b_2_0⁴·b_4_5·b_1_0³
       + b_2_0⁵·b_1_0²·b_3_2 + b_2_0⁵·b_1_0²·b_3_0 + b_2_0⁵·b_1_0⁵
       + b_2_0⁵·b_4_9·b_1_0 + b_2_0⁵·b_4_6·b_1_0 + b_2_0⁶·b_3_2 + b_2_0⁶·b_1_0³
       + c_8_5·b_1_0⁴·b_3_0 + b_4_9·c_8_5·b_1_0³ + b_2_0·c_8_5·b_1_0²·b_3_0
       + b_2_0·b_4_9·c_8_5·b_1_0
59. b_8_10² + b_4_9²·b_1_0·b_7_0 + b_4_9²·b_8_10 + b_4_9⁴ + b_4_6²·b_6_13·b_1_0²
       + b_4_6³·b_1_0·b_3_2 + b_4_6⁴ + b_4_5·b_4_9·b_1_0·b_7_0 + b_4_5·b_4_9³
       + b_4_5²·b_6_13·b_1_0² + b_4_5²·b_4_6·b_1_0·b_3_1 + b_4_5³·b_1_0·b_3_5
       + b_4_5³·b_1_0·b_3_2 + b_4_5³·b_1_0·b_3_1 + b_4_5⁴ + b_2_0·b_4_9·b_1_0³·b_7_0
       + b_2_0·b_4_6·b_1_0⁷·b_3_1 + b_2_0·b_4_6²·b_1_0⁶ + b_2_0·b_4_5·b_1_0³·b_7_1
       + b_2_0·b_4_5·b_4_9·b_6_13 + b_2_0·b_4_5·b_4_6·b_1_0⁶ + b_2_0·b_4_5·b_4_6·b_6_13
       + b_2_0·b_4_5²·b_1_0³·b_3_2 + b_2_0·b_4_5²·b_1_0⁶ + b_2_0·b_4_5²·b_6_13
       + b_2_0·b_4_5²·b_4_9·b_1_0² + b_2_0²·b_1_0⁹·b_3_1 + b_2_0²·b_1_0¹²
       + b_2_0²·b_4_9·b_1_0·b_7_0 + b_2_0²·b_4_9²·b_1_0⁴ + b_2_0²·b_4_6²·b_1_0⁴
       + b_2_0²·b_4_5·b_1_0·b_7_1 + b_2_0²·b_4_5·b_4_6·b_1_0·b_3_1
       + b_2_0²·b_4_5·b_4_6·b_1_0⁴ + b_2_0²·b_4_5·b_4_6² + b_2_0²·b_4_5²·b_1_0·b_3_2
       + b_2_0²·b_4_5²·b_1_0·b_3_1 + b_2_0²·b_4_5²·b_1_0·b_3_0
       + b_2_0²·b_4_5²·b_1_0⁴ + b_2_0²·b_4_5²·b_4_6 + b_2_0³·b_1_0⁷·b_3_1
       + b_2_0³·b_1_0¹⁰ + b_2_0³·b_4_9·b_6_13 + b_2_0³·b_4_6·b_1_0³·b_3_1
       + b_2_0³·b_4_6·b_1_0⁶ + b_2_0³·b_4_5·b_1_0³·b_3_1 + b_2_0³·b_4_5·b_1_0³·b_3_0
       + b_2_0³·b_4_5·b_6_13 + b_2_0³·b_4_5·b_4_9·b_1_0² + b_2_0³·b_4_5·b_4_6·b_1_0²
       + b_2_0³·b_4_5²·b_1_0² + b_2_0⁴·b_1_0⁵·b_3_1 + b_2_0⁴·b_1_0⁸
       + b_2_0⁴·b_4_9·b_1_0⁴ + b_2_0⁴·b_4_9² + b_2_0⁴·b_4_6·b_1_0·b_3_1
       + b_2_0⁴·b_4_6² + b_2_0⁴·b_4_5·b_1_0·b_3_2 + b_2_0⁴·b_4_5·b_1_0·b_3_1
       + b_2_0⁴·b_4_5·b_1_0⁴ + b_2_0⁴·b_4_5·b_4_6 + b_2_0⁵·b_1_0³·b_3_2
       + b_2_0⁵·b_1_0³·b_3_1 + b_2_0⁵·b_1_0⁶ + b_2_0⁵·b_6_13 + b_2_0⁵·b_4_5·b_1_0²
       + b_4_9·c_8_5·b_1_0⁴ + b_2_0·c_8_5·b_1_0³·b_3_0 + b_2_0·b_4_9·c_8_5·b_1_0²
       + b_2_0²·c_8_5·b_1_0·b_3_0

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Data used for the Hilbert-Poincaré test

• We proved completion in degree 24 using the Hilbert-Poincaré criterion.
• However, the last relation was already found in degree 16 and the last generator in degree 8.
• The following is a filter regular homogeneous system of parameters:
  1. b_1_0³·b_5_11 + b_1_0⁵·b_3_5 + b_1_0⁵·b_3_1 + b_1_0⁸ + b_8_10 + b_4_6·b_1_0⁴
        + b_4_5·b_1_0·b_3_2 + b_4_5·b_1_0·b_3_1 + b_4_5·b_1_0·b_3_0 + b_4_5·b_1_0⁴
        + b_4_5·b_4_9 + b_4_5·b_4_6 + b_2_0·b_3_1·b_3_2 + b_2_0·b_3_1² + b_2_0·b_1_0³·b_3_1
        + b_2_0·b_1_0⁶ + b_2_0·b_4_9·b_1_0² + b_2_0·b_4_5·b_1_0² + b_2_0²·b_1_0·b_3_1
        + b_2_0²·b_1_0·b_3_0 + b_2_0²·b_4_5 + b_2_0³·b_1_0² + c_8_5, an element of degree 8
  2. b_3_1³·b_3_2 + b_1_0⁹·b_3_2 + b_1_0⁹·b_3_1 + b_6_13² + b_4_9³ + b_4_6·b_1_0⁸
        + b_4_6²·b_1_0⁴ + b_4_5·b_1_0³·b_5_11 + b_4_5·b_1_0⁵·b_3_1 + b_4_5·b_8_10
        + b_4_5·b_4_6·b_1_0·b_3_1 + b_4_5·b_4_6·b_1_0⁴ + b_4_5·b_4_6² + b_4_5²·b_1_0·b_3_2
        + b_4_5²·b_1_0·b_3_0 + b_4_5²·b_1_0⁴ + b_4_5²·b_4_9 + b_4_5²·b_4_6
        + b_2_0·b_1_0³·b_7_0 + b_2_0·b_1_0⁷·b_3_1 + b_2_0·b_1_0¹⁰ + b_2_0·b_6_13·b_1_0⁴
        + b_2_0·b_4_9²·b_1_0² + b_2_0·b_4_6·b_3_1·b_3_2 + b_2_0·b_4_6·b_3_1²
        + b_2_0·b_4_5·b_3_1² + b_2_0·b_4_5·b_1_0³·b_3_2 + b_2_0·b_4_5·b_1_0³·b_3_1
        + b_2_0·b_4_5·b_1_0³·b_3_0 + b_2_0·b_4_5·b_4_6·b_1_0² + b_2_0²·b_1_0·b_7_0
        + b_2_0²·b_8_10 + b_2_0²·b_6_13·b_1_0² + b_2_0²·b_4_9·b_1_0⁴ + b_2_0²·b_4_9²
        + b_2_0²·b_4_6·b_1_0·b_3_1 + b_2_0²·b_4_6·b_1_0⁴ + b_2_0²·b_4_6²
        + b_2_0²·b_4_5·b_1_0·b_3_1 + b_2_0²·b_4_5² + b_2_0³·b_3_1·b_3_2
        + b_2_0³·b_1_0³·b_3_1 + b_2_0³·b_1_0⁶ + b_2_0³·b_4_9·b_1_0²
        + b_2_0³·b_4_5·b_1_0² + b_2_0⁴·b_1_0·b_3_2 + b_2_0⁴·b_4_9 + b_2_0⁴·b_4_5
        + c_8_5·b_1_0·b_3_2 + c_8_5·b_1_0·b_3_1 + c_8_5·b_1_0·b_3_0 + c_8_5·b_1_0⁴
        + b_4_6·c_8_5 + b_2_0²·c_8_5, an element of degree 12
  3. b_1_0⁹·b_5_11 + b_1_0¹¹·b_3_2 + b_6_13·b_1_0⁵·b_3_5 + b_6_13·b_1_0⁵·b_3_2
        + b_6_13²·b_1_0² + b_4_9·b_1_0³·b_7_0 + b_4_9·b_8_10·b_1_0² + b_4_9²·b_6_13
        + b_4_6·b_6_13·b_1_0⁴ + b_4_6²·b_3_1² + b_4_6²·b_6_13 + b_4_6³·b_1_0²
        + b_4_5·b_1_0⁵·b_5_11 + b_4_5·b_1_0⁷·b_3_2 + b_4_5·b_1_0¹⁰
        + b_4_5·b_6_13·b_1_0·b_3_2 + b_4_5·b_4_9²·b_1_0² + b_4_5·b_4_6²·b_1_0²
        + b_4_5²·b_3_1·b_3_2 + b_4_5²·b_3_1² + b_4_5²·b_1_0³·b_3_2
        + b_4_5²·b_1_0³·b_3_1 + b_4_5²·b_6_13 + b_2_0·b_3_1³·b_3_2 + b_2_0·b_1_0⁵·b_7_1
        + b_2_0·b_1_0⁹·b_3_1 + b_2_0·b_4_9·b_1_0·b_7_0 + b_2_0·b_4_9·b_8_10 + b_2_0·b_4_9³
        + b_2_0·b_4_6·b_1_0⁵·b_3_1 + b_2_0·b_4_6²·b_1_0·b_3_2 + b_2_0·b_4_6²·b_1_0⁴
        + b_2_0·b_4_6³ + b_2_0·b_4_5·b_1_0⁵·b_3_1 + b_2_0·b_4_5·b_8_10
        + b_2_0·b_4_5·b_4_6·b_1_0·b_3_1 + b_2_0·b_4_5·b_4_6·b_1_0⁴ + b_2_0·b_4_5·b_4_6²
        + b_2_0·b_4_5²·b_1_0·b_3_1 + b_2_0·b_4_5²·b_1_0·b_3_0 + b_2_0·b_4_5²·b_4_9
        + b_2_0²·b_1_0³·b_7_0 + b_2_0²·b_1_0⁷·b_3_1 + b_2_0²·b_1_0¹⁰
        + b_2_0²·b_6_13·b_1_0⁴ + b_2_0²·b_4_6·b_3_1² + b_2_0²·b_4_6·b_1_0³·b_3_1
        + b_2_0²·b_4_6²·b_1_0² + b_2_0²·b_4_5·b_3_1² + b_2_0²·b_4_5·b_1_0³·b_3_1
        + b_2_0²·b_4_5·b_1_0⁶ + b_2_0²·b_4_5²·b_1_0² + b_2_0³·b_1_0·b_7_1
        + b_2_0³·b_1_0·b_7_0 + b_2_0³·b_6_13·b_1_0² + b_2_0³·b_4_9²
        + b_2_0³·b_4_6·b_1_0·b_3_2 + b_2_0³·b_4_6·b_1_0·b_3_1 + b_2_0³·b_4_6·b_1_0⁴
        + b_2_0³·b_4_6² + b_2_0³·b_4_5·b_1_0·b_3_1 + b_2_0³·b_4_5·b_4_9 + b_2_0⁴·b_3_1²
        + b_2_0⁴·b_1_0³·b_3_2 + b_2_0⁴·b_1_0⁶ + b_2_0⁴·b_4_5·b_1_0²
        + b_2_0⁵·b_1_0·b_3_2 + b_2_0⁵·b_1_0·b_3_1 + b_2_0⁵·b_1_0·b_3_0 + b_2_0⁵·b_4_9
        + b_2_0⁷ + c_8_5·b_3_1·b_3_2 + c_8_5·b_3_1² + c_8_5·b_1_0³·b_3_2
        + c_8_5·b_1_0³·b_3_1 + b_6_13·c_8_5 + b_4_6·c_8_5·b_1_0² + b_2_0·c_8_5·b_1_0·b_3_0
        + b_2_0·b_4_9·c_8_5 + b_2_0·b_4_5·c_8_5 + b_2_0²·c_8_5·b_1_0² + b_2_0³·c_8_5, an element of degree 14
  4. b_1_0, an element of degree 1
• A Duflot regular sequence is given by c_8_5.
• The Raw Filter Degree Type of the filter regular HSOP is [-1, -1, -1, -1, 31].
• We found that there exists some filter regular HSOP over a finite extension field, formed by the first 2 terms of the above HSOP, together with 2 elements of degree 4.
• Modifying the above filter regular HSOP, we obtained the following parameters:
1. b_1_0³·b_5_11 + b_1_0⁵·b_3_5 + b_1_0⁵·b_3_1 + b_1_0⁸ + b_8_10 + b_4_6·b_1_0⁴
      + b_4_5·b_1_0·b_3_2 + b_4_5·b_1_0·b_3_1 + b_4_5·b_1_0·b_3_0 + b_4_5·b_1_0⁴
      + b_4_5·b_4_9 + b_4_5·b_4_6 + b_2_0·b_3_1·b_3_2 + b_2_0·b_3_1² + b_2_0·b_1_0³·b_3_1
      + b_2_0·b_1_0⁶ + b_2_0·b_4_9·b_1_0² + b_2_0·b_4_5·b_1_0² + b_2_0²·b_1_0·b_3_1
      + b_2_0²·b_1_0·b_3_0 + b_2_0²·b_4_5 + b_2_0³·b_1_0² + c_8_5, an element of degree 8
2. b_3_1³·b_3_2 + b_1_0⁹·b_3_2 + b_1_0⁹·b_3_1 + b_6_13² + b_4_9³ + b_4_6·b_1_0⁸
      + b_4_6²·b_1_0⁴ + b_4_5·b_1_0³·b_5_11 + b_4_5·b_1_0⁵·b_3_1 + b_4_5·b_8_10
      + b_4_5·b_4_6·b_1_0·b_3_1 + b_4_5·b_4_6·b_1_0⁴ + b_4_5·b_4_6² + b_4_5²·b_1_0·b_3_2
      + b_4_5²·b_1_0·b_3_0 + b_4_5²·b_1_0⁴ + b_4_5²·b_4_9 + b_4_5²·b_4_6
      + b_2_0·b_1_0³·b_7_0 + b_2_0·b_1_0⁷·b_3_1 + b_2_0·b_1_0¹⁰ + b_2_0·b_6_13·b_1_0⁴
      + b_2_0·b_4_9²·b_1_0² + b_2_0·b_4_6·b_3_1·b_3_2 + b_2_0·b_4_6·b_3_1²
      + b_2_0·b_4_5·b_3_1² + b_2_0·b_4_5·b_1_0³·b_3_2 + b_2_0·b_4_5·b_1_0³·b_3_1
      + b_2_0·b_4_5·b_1_0³·b_3_0 + b_2_0·b_4_5·b_4_6·b_1_0² + b_2_0²·b_1_0·b_7_0
      + b_2_0²·b_8_10 + b_2_0²·b_6_13·b_1_0² + b_2_0²·b_4_9·b_1_0⁴ + b_2_0²·b_4_9²
      + b_2_0²·b_4_6·b_1_0·b_3_1 + b_2_0²·b_4_6·b_1_0⁴ + b_2_0²·b_4_6²
      + b_2_0²·b_4_5·b_1_0·b_3_1 + b_2_0²·b_4_5² + b_2_0³·b_3_1·b_3_2
      + b_2_0³·b_1_0³·b_3_1 + b_2_0³·b_1_0⁶ + b_2_0³·b_4_9·b_1_0²
      + b_2_0³·b_4_5·b_1_0² + b_2_0⁴·b_1_0·b_3_2 + b_2_0⁴·b_4_9 + b_2_0⁴·b_4_5
      + c_8_5·b_1_0·b_3_2 + c_8_5·b_1_0·b_3_1 + c_8_5·b_1_0·b_3_0 + c_8_5·b_1_0⁴
      + b_4_6·c_8_5 + b_2_0²·c_8_5, an element of degree 12
3. b_4_5 + b_2_0², an element of degree 4
4. b_1_0, an element of degree 1

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Restriction maps

Expressing the generators as elements of H^*(N_Co3(Z_2(SylowSubgroup(Co3,2))); GF(2))

1. b_1_0 → b_1_1 + b_1_0
2. b_2_0 → b_1_2² + b_1_0·b_1_1 + b_2_2
3. b_3_5 → b_1_0²·b_1_2 + b_1_0²·b_1_1 + b_2_2·b_1_2
4. b_3_2 → b_3_0 + b_1_0²·b_1_1 + b_2_6·b_1_2 + b_2_6·b_1_1 + b_2_6·b_1_0
5. b_3_1 → b_3_1 + b_1_2³ + b_1_0²·b_1_1 + b_2_2·b_1_2
6. b_3_0 → b_3_11
7. b_4_9 → b_4_20
8. b_4_6 → b_1_0·b_1_2³ + b_4_10 + b_2_6·b_1_1² + b_2_6·b_1_0·b_1_1 + b_2_6·b_1_0² + b_2_6²
      + b_2_2·b_1_1² + b_2_2·b_1_0·b_1_2 + b_2_2·b_1_0²
9. b_4_5 → b_1_0·b_3_0 + b_4_10 + b_2_6·b_1_1² + b_2_6·b_1_0·b_1_2 + b_2_6·b_1_0·b_1_1
      + b_2_6·b_1_0² + b_2_6² + b_2_2·b_1_1² + b_2_2·b_1_0·b_1_2 + b_2_2·b_1_0²
      + b_2_2·b_2_6 + b_2_2²
10. b_5_11 → b_4_10·b_1_0 + b_2_6·b_3_0 + b_2_6·b_1_0²·b_1_2 + b_2_6·b_1_0²·b_1_1 + b_2_6²·b_1_2
       + b_2_2·b_1_0²·b_1_2 + b_2_2·b_1_0²·b_1_1 + b_2_2·b_1_0³ + b_2_2·b_2_6·b_1_2
       + b_2_2·b_2_6·b_1_1 + b_2_2·b_2_6·b_1_0 + b_2_2²·b_1_0
11. b_6_13 → b_2_6·b_1_1·b_3_0 + b_2_6·b_1_0·b_3_1 + b_2_6·b_1_0³·b_1_1 + b_2_6·b_4_10
       + b_2_6²·b_1_0·b_1_1 + b_2_2·b_1_0·b_3_1 + b_2_2·b_4_10 + b_2_2·b_2_6·b_1_0·b_1_1
       + b_2_2²·b_1_0·b_1_1 + b_2_2²·b_2_6 + b_2_2³
12. b_7_1 → b_7_0 + b_1_0⁶·b_1_1 + b_6_0·b_1_1 + b_2_6·b_1_0·b_1_2⁴ + b_2_6·b_1_0²·b_3_1
       + b_2_6·b_1_0⁴·b_1_1 + b_2_6·b_4_10·b_1_2 + b_2_6·b_4_10·b_1_1 + b_2_6²·b_3_1
       + b_2_6²·b_1_1³ + b_2_6²·b_1_0³ + b_2_2·b_1_2²·b_3_1 + b_2_2·b_1_0·b_1_2⁴
       + b_2_2·b_1_0²·b_3_1 + b_2_2·b_1_0²·b_1_2³ + b_2_2·b_1_0⁵ + b_2_2·b_4_10·b_1_0
       + b_2_2·b_2_6·b_3_1 + b_2_2·b_2_6·b_1_2³ + b_2_2·b_2_6·b_1_0³ + b_2_2·b_2_6²·b_1_1
       + b_2_2²·b_1_0·b_1_2² + b_2_2²·b_1_0²·b_1_2 + b_2_2²·b_2_6·b_1_2
       + b_2_2²·b_2_6·b_1_1 + b_2_2³·b_1_2 + b_2_2³·b_1_1
13. b_7_0 → b_7_28 + b_2_6·b_1_0·b_1_2⁴ + b_2_6·b_1_0⁴·b_1_1 + b_2_6²·b_1_2³
       + b_2_6²·b_1_0²·b_1_1 + b_2_2·b_1_0²·b_1_2³ + b_2_2·b_1_0³·b_1_2²
       + b_2_2·b_1_0⁴·b_1_2 + b_2_2·b_1_0⁵ + b_2_2·b_4_10·b_1_2 + b_2_2·b_2_6·b_1_2³
       + b_2_2·b_2_6·b_1_1³ + b_2_2·b_2_6·b_1_0²·b_1_1 + b_2_2·b_2_6²·b_1_1
       + b_2_2²·b_1_2³ + b_2_2²·b_1_1³ + b_2_2²·b_1_0·b_1_2² + b_2_2²·b_1_0²·b_1_2
       + b_2_2²·b_2_6·b_1_1 + b_2_2³·b_1_2 + b_2_2³·b_1_1 + b_2_2³·b_1_0
14. b_8_10 → b_8_52 + b_2_6·b_4_10·b_1_2² + b_2_6·b_4_10·b_1_0·b_1_2 + b_2_6²·b_1_2·b_3_1
       + b_2_6²·b_1_0·b_3_1 + b_2_6²·b_1_0·b_1_2³ + b_2_6²·b_1_0³·b_1_1
       + b_2_2·b_1_2³·b_3_1 + b_2_2·b_1_0⁶ + b_2_2·b_4_10·b_1_2²
       + b_2_2·b_2_6·b_1_2·b_3_1 + b_2_2·b_2_6·b_1_2⁴ + b_2_2·b_2_6·b_1_1⁴
       + b_2_2·b_2_6·b_1_0·b_3_1 + b_2_2·b_2_6·b_1_0·b_1_2³ + b_2_2·b_2_6·b_1_0²·b_1_2²
       + b_2_2·b_2_6·b_1_0³·b_1_2 + b_2_2·b_2_6·b_1_0⁴ + b_2_2·b_2_6·b_4_10
       + b_2_2·b_2_6²·b_1_2² + b_2_2·b_2_6²·b_1_1² + b_2_2·b_2_6²·b_1_0·b_1_2
       + b_2_2·b_2_6²·b_1_0² + b_2_2²·b_1_2⁴ + b_2_2²·b_1_1⁴
       + b_2_2²·b_1_0²·b_1_2² + b_2_2²·b_1_0³·b_1_2 + b_2_2²·b_1_0⁴ + b_2_2²·b_4_10
       + b_2_2²·b_2_6·b_1_0·b_1_2 + b_2_2²·b_2_6·b_1_0·b_1_1 + b_2_2³·b_1_2²
       + b_2_2³·b_1_0²
15. c_8_5 → b_1_0·b_7_0 + b_6_0·b_1_1² + b_6_0·b_1_0² + b_2_6·b_1_2³·b_3_1 + b_2_6·b_1_2⁶
       + b_2_6·b_1_0⁵·b_1_1 + b_2_6·b_6_0 + b_2_6·b_4_10·b_1_1² + b_2_6·b_4_10·b_1_0·b_1_2
       + b_2_6·b_4_10·b_1_0² + b_2_6²·b_1_2⁴ + b_2_6²·b_1_0·b_1_2³ + b_2_6³·b_1_2²
       + b_2_6³·b_1_1² + b_2_6³·b_1_0² + b_2_2·b_1_2³·b_3_1 + b_2_2·b_1_2⁶
       + b_2_2·b_1_0·b_1_2⁵ + b_2_2·b_1_0³·b_1_2³ + b_2_2·b_6_0
       + b_2_2·b_4_10·b_1_0·b_1_2 + b_2_2·b_4_10·b_1_0² + b_2_2·b_2_6·b_1_2⁴
       + b_2_2·b_2_6·b_1_0·b_3_1 + b_2_2·b_2_6·b_1_0³·b_1_1 + b_2_2·b_2_6·b_1_0⁴
       + b_2_2·b_2_6·b_4_10 + b_2_2·b_2_6²·b_1_1² + b_2_2·b_2_6²·b_1_0·b_1_2
       + b_2_2·b_2_6²·b_1_0² + b_2_2·b_2_6³ + b_2_2²·b_1_2⁴ + b_2_2²·b_1_0²·b_1_2²
       + b_2_2²·b_1_0³·b_1_2 + b_2_2²·b_1_0³·b_1_1 + b_2_2²·b_1_0⁴ + b_2_2²·b_4_10
       + b_2_2²·b_2_6² + b_2_2³·b_1_2² + b_2_2³·b_1_0² + b_2_2³·b_2_6 + c_8_11

Restriction map to the greatest el. ab. subgp. in the centre of a Sylow subgroup, which is of rank 1

1. b_1_0 → 0, an element of degree 1
2. b_2_0 → 0, an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → 0, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → 0, an element of degree 4
9. b_4_5 → 0, an element of degree 4
10. b_5_11 → 0, an element of degree 5
11. b_6_13 → 0, an element of degree 6
12. b_7_1 → 0, an element of degree 7
13. b_7_0 → 0, an element of degree 7
14. b_8_10 → 0, an element of degree 8
15. c_8_5 → c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 3 in a Sylow subgroup

1. b_1_0 → 0, an element of degree 1
2. b_2_0 → 0, an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → 0, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_2⁴ + c_1_1²·c_1_2² + c_1_1⁴, an element of degree 4
9. b_4_5 → c_1_2⁴ + c_1_1²·c_1_2² + c_1_1⁴, an element of degree 4
10. b_5_11 → 0, an element of degree 5
11. b_6_13 → c_1_1²·c_1_2⁴ + c_1_1⁴·c_1_2², an element of degree 6
12. b_7_1 → 0, an element of degree 7
13. b_7_0 → 0, an element of degree 7
14. b_8_10 → 0, an element of degree 8
15. c_8_5 → c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_2⁴
       + c_1_0⁴·c_1_1²·c_1_2² + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_1, an element of degree 1
2. b_2_0 → c_1_2² + c_1_1·c_1_2 + c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → c_1_1·c_1_2² + c_1_1²·c_1_2, an element of degree 3
5. b_3_1 → c_1_2³, an element of degree 3
6. b_3_0 → c_1_1·c_1_2² + c_1_1²·c_1_2, an element of degree 3
7. b_4_9 → c_1_1·c_1_2³ + c_1_1²·c_1_2², an element of degree 4
8. b_4_6 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1·c_1_2³ + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1⁴, an element of degree 4
9. b_4_5 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1·c_1_2³ + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2²
      + c_1_1³·c_1_2, an element of degree 4
10. b_5_11 → c_1_1·c_1_3⁴ + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2⁴ + c_1_1²·c_1_2·c_1_3²
       + c_1_1²·c_1_2²·c_1_3 + c_1_1²·c_1_2³ + c_1_1³·c_1_3² + c_1_1³·c_1_2·c_1_3
       + c_1_1³·c_1_2², an element of degree 5
11. b_6_13 → c_1_1²·c_1_3⁴ + c_1_1²·c_1_2²·c_1_3² + c_1_1³·c_1_2·c_1_3²
       + c_1_1³·c_1_2²·c_1_3 + c_1_1⁴·c_1_3² + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1²·c_1_2·c_1_3⁴
       + c_1_1²·c_1_2⁴·c_1_3 + c_1_1²·c_1_2⁵ + c_1_1³·c_1_3⁴
       + c_1_1³·c_1_2²·c_1_3² + c_1_1⁴·c_1_2³ + c_1_1⁵·c_1_3² + c_1_1⁵·c_1_2·c_1_3
       + c_1_1⁷ + c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2² + c_1_0²·c_1_1·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
13. b_7_0 → c_1_2³·c_1_3⁴ + c_1_2⁵·c_1_3² + c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁵·c_1_3
       + c_1_1·c_1_2⁶ + c_1_1³·c_1_2²·c_1_3² + c_1_1³·c_1_2³·c_1_3 + c_1_1³·c_1_2⁴
       + c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2² + c_1_0²·c_1_1·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
14. b_8_10 → c_1_1·c_1_2⁷ + c_1_1²·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2⁴·c_1_3²
       + c_1_1²·c_1_2⁶ + c_1_1³·c_1_2³·c_1_3² + c_1_1³·c_1_2⁴·c_1_3
       + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁷·c_1_2 + c_1_1⁸ + c_1_0·c_1_1²·c_1_2⁵
       + c_1_0·c_1_1³·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2³ + c_1_0·c_1_1⁵·c_1_2²
       + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2²
       + c_1_0²·c_1_1⁵·c_1_2 + c_1_0⁴·c_1_1·c_1_2³ + c_1_0⁴·c_1_1³·c_1_2, an element of degree 8
15. c_8_5 → c_1_2⁴·c_1_3⁴ + c_1_2⁶·c_1_3² + c_1_1·c_1_2⁵·c_1_3² + c_1_1·c_1_2⁶·c_1_3
       + c_1_1·c_1_2⁷ + c_1_1²·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2⁵·c_1_3
       + c_1_1³·c_1_2³·c_1_3² + c_1_1³·c_1_2⁴·c_1_3 + c_1_1³·c_1_2⁵
       + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁴·c_1_2⁴ + c_1_1⁵·c_1_2·c_1_3²
       + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁵·c_1_2³ + c_1_1⁶·c_1_3² + c_1_1⁶·c_1_2·c_1_3
       + c_1_1⁶·c_1_2² + c_1_0·c_1_1·c_1_2²·c_1_3⁴ + c_1_0·c_1_1·c_1_2⁴·c_1_3²
       + c_1_0·c_1_1²·c_1_2·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1²·c_1_2⁵
       + c_1_0·c_1_1³·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2·c_1_3² + c_1_0·c_1_1⁴·c_1_2²·c_1_3
       + c_1_0·c_1_1⁴·c_1_2³ + c_1_0·c_1_1⁵·c_1_2² + c_1_0²·c_1_2²·c_1_3⁴
       + c_1_0²·c_1_2⁴·c_1_3² + c_1_0²·c_1_1·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2⁴·c_1_3 + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1²·c_1_3⁴
       + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0²·c_1_1⁴·c_1_3²
       + c_1_0²·c_1_1⁴·c_1_2·c_1_3 + c_1_0²·c_1_1⁵·c_1_2 + c_1_0⁴·c_1_3⁴
       + c_1_0⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2·c_1_3²
       + c_1_0⁴·c_1_1·c_1_2²·c_1_3 + c_1_0⁴·c_1_1·c_1_2³ + c_1_0⁴·c_1_1²·c_1_3²
       + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2² + c_1_0⁴·c_1_1³·c_1_2
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_2 + c_1_1, an element of degree 1
2. b_2_0 → c_1_2² + c_1_1·c_1_2 + c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → c_1_1·c_1_2² + c_1_1²·c_1_2, an element of degree 3
5. b_3_1 → c_1_2³, an element of degree 3
6. b_3_0 → c_1_1·c_1_2² + c_1_1²·c_1_2, an element of degree 3
7. b_4_9 → c_1_1·c_1_2³ + c_1_1²·c_1_2², an element of degree 4
8. b_4_6 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1·c_1_2³ + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1⁴, an element of degree 4
9. b_4_5 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1³·c_1_2, an element of degree 4
10. b_5_11 → c_1_2·c_1_3⁴ + c_1_2³·c_1_3² + c_1_2⁵ + c_1_1·c_1_3⁴ + c_1_1·c_1_2³·c_1_3
       + c_1_1³·c_1_3² + c_1_1³·c_1_2·c_1_3 + c_1_1³·c_1_2², an element of degree 5
11. b_6_13 → c_1_2²·c_1_3⁴ + c_1_2⁴·c_1_3² + c_1_2⁶ + c_1_1·c_1_2³·c_1_3²
       + c_1_1·c_1_2⁴·c_1_3 + c_1_1²·c_1_3⁴ + c_1_1²·c_1_2³·c_1_3 + c_1_1²·c_1_2⁴
       + c_1_1³·c_1_2·c_1_3² + c_1_1³·c_1_2²·c_1_3 + c_1_1⁴·c_1_3²
       + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁴·c_1_2² + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_2³·c_1_3⁴ + c_1_2⁵·c_1_3² + c_1_2⁷ + c_1_1·c_1_2²·c_1_3⁴
       + c_1_1·c_1_2⁵·c_1_3 + c_1_1·c_1_2⁶ + c_1_1²·c_1_2·c_1_3⁴
       + c_1_1²·c_1_2³·c_1_3² + c_1_1³·c_1_3⁴ + c_1_1³·c_1_2²·c_1_3²
       + c_1_1³·c_1_2⁴ + c_1_1⁵·c_1_3² + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁵·c_1_2²
       + c_1_1⁶·c_1_2 + c_1_1⁷ + c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2²
       + c_1_0²·c_1_1·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1·c_1_2²
       + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
13. b_7_0 → c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁵
       + c_1_1³·c_1_2²·c_1_3² + c_1_1³·c_1_2³·c_1_3 + c_1_1³·c_1_2⁴
       + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁴·c_1_2²·c_1_3 + c_1_0·c_1_1²·c_1_2⁴
       + c_1_0·c_1_1⁴·c_1_2² + c_1_0²·c_1_1·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2
       + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
14. b_8_10 → c_1_1·c_1_2⁷ + c_1_1²·c_1_2⁶ + c_1_1³·c_1_2·c_1_3⁴ + c_1_1³·c_1_2³·c_1_3²
       + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁵·c_1_2³ + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_1⁷·c_1_2 + c_1_1⁸
       + c_1_0·c_1_1³·c_1_2⁴ + c_1_0·c_1_1⁵·c_1_2² + c_1_0²·c_1_1²·c_1_2⁴
       + c_1_0²·c_1_1⁵·c_1_2 + c_1_0⁴·c_1_1²·c_1_2² + c_1_0⁴·c_1_1³·c_1_2, an element of degree 8
15. c_8_5 → c_1_2⁴·c_1_3⁴ + c_1_2⁶·c_1_3² + c_1_2⁸ + c_1_1·c_1_2⁵·c_1_3²
       + c_1_1·c_1_2⁶·c_1_3 + c_1_1·c_1_2⁷ + c_1_1²·c_1_2⁴·c_1_3²
       + c_1_1²·c_1_2⁵·c_1_3 + c_1_1³·c_1_2·c_1_3⁴ + c_1_1³·c_1_2³·c_1_3²
       + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2³ + c_1_1⁶·c_1_3² + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2²
       + c_1_0·c_1_1·c_1_2²·c_1_3⁴ + c_1_0·c_1_1·c_1_2⁴·c_1_3²
       + c_1_0·c_1_1²·c_1_2·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1³·c_1_2⁴
       + c_1_0·c_1_1⁴·c_1_2·c_1_3² + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0·c_1_1⁵·c_1_2²
       + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3² + c_1_0²·c_1_1·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2⁴·c_1_3 + c_1_0²·c_1_1²·c_1_3⁴
       + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0²·c_1_1⁴·c_1_3²
       + c_1_0²·c_1_1⁴·c_1_2·c_1_3 + c_1_0²·c_1_1⁴·c_1_2² + c_1_0²·c_1_1⁵·c_1_2
       + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_2⁴
       + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1³·c_1_2
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_1, an element of degree 1
2. b_2_0 → c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → 0, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2² + c_1_1⁴, an element of degree 4
9. b_4_5 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2², an element of degree 4
10. b_5_11 → c_1_1·c_1_3⁴ + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2⁴ + c_1_1²·c_1_2·c_1_3²
       + c_1_1²·c_1_2²·c_1_3 + c_1_1³·c_1_3² + c_1_1³·c_1_2·c_1_3 + c_1_1³·c_1_2², an element of degree 5
11. b_6_13 → c_1_2²·c_1_3⁴ + c_1_2⁴·c_1_3² + c_1_1·c_1_2·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3
       + c_1_1²·c_1_3⁴ + c_1_1²·c_1_2²·c_1_3² + c_1_1²·c_1_2⁴ + c_1_1⁴·c_1_3²
       + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁴·c_1_2² + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_1³·c_1_3⁴ + c_1_1³·c_1_2²·c_1_3² + c_1_1³·c_1_2⁴
       + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁴·c_1_2²·c_1_3 + c_1_1⁵·c_1_3²
       + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁵·c_1_2² + c_1_1⁷, an element of degree 7
13. b_7_0 → 0, an element of degree 7
14. b_8_10 → c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_1⁸, an element of degree 8
15. c_8_5 → c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1·c_1_2⁴·c_1_3² + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1·c_1_2·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
       + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_2 + c_1_1, an element of degree 1
2. b_2_0 → c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → c_1_1·c_1_2², an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1·c_1_2³ + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1⁴, an element of degree 4
9. b_4_5 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3, an element of degree 4
10. b_5_11 → c_1_2·c_1_3⁴ + c_1_2³·c_1_3² + c_1_1·c_1_3⁴ + c_1_1·c_1_2³·c_1_3
       + c_1_1³·c_1_3² + c_1_1³·c_1_2·c_1_3, an element of degree 5
11. b_6_13 → c_1_1·c_1_2·c_1_3⁴ + c_1_1·c_1_2³·c_1_3² + c_1_1²·c_1_3⁴
       + c_1_1²·c_1_2³·c_1_3 + c_1_1²·c_1_2⁴ + c_1_1⁴·c_1_3² + c_1_1⁴·c_1_2·c_1_3
       + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1·c_1_2⁶
       + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁴·c_1_3 + c_1_1²·c_1_2⁵
       + c_1_1³·c_1_3⁴ + c_1_1³·c_1_2³·c_1_3 + c_1_1⁴·c_1_2·c_1_3²
       + c_1_1⁴·c_1_2²·c_1_3 + c_1_1⁵·c_1_3² + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁶·c_1_2
       + c_1_1⁷, an element of degree 7
13. b_7_0 → c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁵
       + c_1_1³·c_1_2²·c_1_3² + c_1_1³·c_1_2³·c_1_3 + c_1_1³·c_1_2⁴
       + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁴·c_1_2²·c_1_3 + c_1_1⁴·c_1_2³ + c_1_1⁵·c_1_2², an element of degree 7
14. b_8_10 → c_1_1²·c_1_2⁶ + c_1_1³·c_1_2·c_1_3⁴ + c_1_1³·c_1_2³·c_1_3²
       + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁴·c_1_2⁴ + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_1⁸, an element of degree 8
15. c_8_5 → c_1_2⁴·c_1_3⁴ + c_1_2⁶·c_1_3² + c_1_1·c_1_2⁵·c_1_3² + c_1_1·c_1_2⁶·c_1_3
       + c_1_1²·c_1_2⁴·c_1_3² + c_1_1²·c_1_2⁵·c_1_3 + c_1_1²·c_1_2⁶
       + c_1_1³·c_1_2·c_1_3⁴ + c_1_1³·c_1_2³·c_1_3² + c_1_1³·c_1_2⁵
       + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁶·c_1_3² + c_1_1⁶·c_1_2·c_1_3
       + c_1_0·c_1_1·c_1_2²·c_1_3⁴ + c_1_0·c_1_1·c_1_2⁴·c_1_3²
       + c_1_0·c_1_1²·c_1_2·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁴·c_1_3
       + c_1_0·c_1_1⁴·c_1_2·c_1_3² + c_1_0·c_1_1⁴·c_1_2²·c_1_3
       + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3² + c_1_0²·c_1_1·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2⁴·c_1_3 + c_1_0²·c_1_1²·c_1_3⁴
       + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0²·c_1_1²·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3 + c_1_0²·c_1_1⁴·c_1_2²
       + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_2⁴
       + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_3, an element of degree 1
2. b_2_0 → c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → c_1_1·c_1_3² + c_1_1³, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_3³ + c_1_1·c_1_2·c_1_3²
      + c_1_1·c_1_2²·c_1_3 + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2²
      + c_1_1³·c_1_3, an element of degree 4
9. b_4_5 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2², an element of degree 4
10. b_5_11 → c_1_2²·c_1_3³ + c_1_2⁴·c_1_3 + c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2²·c_1_3²
       + c_1_1²·c_1_2·c_1_3² + c_1_1²·c_1_2²·c_1_3, an element of degree 5
11. b_6_13 → c_1_1·c_1_2²·c_1_3³ + c_1_1·c_1_2⁴·c_1_3 + c_1_1²·c_1_3⁴
       + c_1_1²·c_1_2·c_1_3³ + c_1_1²·c_1_2²·c_1_3² + c_1_1³·c_1_2·c_1_3²
       + c_1_1³·c_1_2²·c_1_3, an element of degree 6
12. b_7_1 → c_1_1·c_1_3⁶ + c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1²·c_1_3⁵
       + c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2²·c_1_3³ + c_1_1³·c_1_2·c_1_3³
       + c_1_1³·c_1_2²·c_1_3² + c_1_1⁵·c_1_3², an element of degree 7
13. b_7_0 → c_1_1²·c_1_3⁵ + c_1_1²·c_1_2²·c_1_3³ + c_1_1²·c_1_2⁴·c_1_3
       + c_1_1³·c_1_2·c_1_3³ + c_1_1³·c_1_2⁴ + c_1_1⁴·c_1_3³ + c_1_1⁵·c_1_2·c_1_3
       + c_1_1⁵·c_1_2², an element of degree 7
14. b_8_10 → c_1_1²·c_1_3⁶ + c_1_1³·c_1_2²·c_1_3³ + c_1_1³·c_1_2⁴·c_1_3
       + c_1_1⁴·c_1_2·c_1_3³ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁵·c_1_2·c_1_3²
       + c_1_1⁵·c_1_2²·c_1_3, an element of degree 8
15. c_8_5 → c_1_2²·c_1_3⁶ + c_1_2⁴·c_1_3⁴ + c_1_1·c_1_2·c_1_3⁶ + c_1_1·c_1_2²·c_1_3⁵
       + c_1_1²·c_1_3⁶ + c_1_1²·c_1_2·c_1_3⁵ + c_1_1²·c_1_2²·c_1_3⁴
       + c_1_1³·c_1_3⁵ + c_1_1³·c_1_2²·c_1_3³ + c_1_1³·c_1_2⁴·c_1_3
       + c_1_1⁴·c_1_2·c_1_3³ + c_1_1⁴·c_1_2⁴ + c_1_1⁶·c_1_3² + c_1_1⁶·c_1_2·c_1_3
       + c_1_1⁶·c_1_2² + c_1_1⁷·c_1_3 + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1·c_1_2⁴·c_1_3² + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1·c_1_2·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
       + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_3, an element of degree 1
2. b_2_0 → c_1_3² + c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → c_1_3³ + c_1_1³, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2² + c_1_1³·c_1_3, an element of degree 4
9. b_4_5 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2², an element of degree 4
10. b_5_11 → c_1_3⁵ + c_1_2²·c_1_3³ + c_1_2⁴·c_1_3 + c_1_1·c_1_2·c_1_3³
       + c_1_1·c_1_2²·c_1_3² + c_1_1²·c_1_3³ + c_1_1²·c_1_2·c_1_3²
       + c_1_1²·c_1_2²·c_1_3, an element of degree 5
11. b_6_13 → c_1_3⁶ + c_1_2²·c_1_3⁴ + c_1_2⁴·c_1_3² + c_1_1·c_1_2·c_1_3⁴
       + c_1_1·c_1_2⁴·c_1_3 + c_1_1²·c_1_3⁴ + c_1_1³·c_1_2·c_1_3²
       + c_1_1³·c_1_2²·c_1_3, an element of degree 6
12. b_7_1 → c_1_3⁷ + c_1_2²·c_1_3⁵ + c_1_2⁴·c_1_3³ + c_1_1·c_1_2·c_1_3⁵
       + c_1_1·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2⁴·c_1_3
       + c_1_1³·c_1_2·c_1_3³ + c_1_1³·c_1_2²·c_1_3² + c_1_1⁴·c_1_2·c_1_3²
       + c_1_1⁴·c_1_2²·c_1_3 + c_1_1⁵·c_1_3², an element of degree 7
13. b_7_0 → c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1²·c_1_3⁵
       + c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2²·c_1_3³ + c_1_1³·c_1_2·c_1_3³
       + c_1_1³·c_1_2⁴ + c_1_1⁴·c_1_3³ + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁴·c_1_2²·c_1_3
       + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁵·c_1_2², an element of degree 7
14. b_8_10 → c_1_1²·c_1_3⁶ + c_1_1⁴·c_1_3⁴, an element of degree 8
15. c_8_5 → c_1_3⁸ + c_1_2²·c_1_3⁶ + c_1_2⁴·c_1_3⁴ + c_1_1·c_1_2·c_1_3⁶
       + c_1_1·c_1_2²·c_1_3⁵ + c_1_1²·c_1_3⁶ + c_1_1²·c_1_2·c_1_3⁵
       + c_1_1²·c_1_2⁴·c_1_3² + c_1_1³·c_1_2·c_1_3⁴ + c_1_1³·c_1_2²·c_1_3³
       + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2·c_1_3³ + c_1_1⁴·c_1_2⁴ + c_1_1⁵·c_1_3³
       + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_1⁷·c_1_3 + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1·c_1_2⁴·c_1_3² + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1·c_1_2·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
       + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_3 + c_1_2, an element of degree 1
2. b_2_0 → c_1_3² + c_1_1·c_1_2 + c_1_1², an element of degree 2
3. b_3_5 → c_1_1·c_1_2² + c_1_1²·c_1_2, an element of degree 3
4. b_3_2 → c_1_1·c_1_2² + c_1_1²·c_1_2, an element of degree 3
5. b_3_1 → c_1_3³ + c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_1²·c_1_2 + c_1_1³, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_2²·c_1_3² + c_1_2³·c_1_3 + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2³
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1³·c_1_3 + c_1_1³·c_1_2, an element of degree 4
9. b_4_5 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3, an element of degree 4
10. b_5_11 → c_1_3⁵ + c_1_2·c_1_3⁴ + c_1_2²·c_1_3³ + c_1_2³·c_1_3² + c_1_1·c_1_2·c_1_3³
       + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2³·c_1_3 + c_1_1·c_1_2⁴ + c_1_1²·c_1_3³
       + c_1_1²·c_1_2·c_1_3² + c_1_1²·c_1_2²·c_1_3 + c_1_1²·c_1_2³, an element of degree 5
11. b_6_13 → c_1_3⁶ + c_1_2⁴·c_1_3² + c_1_1·c_1_2·c_1_3⁴ + c_1_1·c_1_2²·c_1_3³
       + c_1_1·c_1_2³·c_1_3² + c_1_1·c_1_2⁴·c_1_3 + c_1_1²·c_1_3⁴
       + c_1_1²·c_1_2·c_1_3³ + c_1_1²·c_1_2²·c_1_3² + c_1_1²·c_1_2³·c_1_3, an element of degree 6
12. b_7_1 → c_1_3⁷ + c_1_2·c_1_3⁶ + c_1_2²·c_1_3⁵ + c_1_2³·c_1_3⁴ + c_1_2⁴·c_1_3³
       + c_1_2⁶·c_1_3 + c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1·c_1_2⁶
       + c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2⁴·c_1_3 + c_1_1²·c_1_2⁵ + c_1_1³·c_1_2⁴
       + c_1_1⁴·c_1_2²·c_1_3 + c_1_1⁵·c_1_3² + c_1_1⁶·c_1_2, an element of degree 7
13. b_7_0 → c_1_2²·c_1_3⁵ + c_1_2³·c_1_3⁴ + c_1_2⁴·c_1_3³ + c_1_2⁵·c_1_3²
       + c_1_1·c_1_2·c_1_3⁵ + c_1_1·c_1_2⁵·c_1_3 + c_1_1²·c_1_3⁵
       + c_1_1²·c_1_2²·c_1_3³ + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁴·c_1_3
       + c_1_1⁴·c_1_3³ + c_1_1⁴·c_1_2·c_1_3², an element of degree 7
14. b_8_10 → c_1_2²·c_1_3⁶ + c_1_2⁶·c_1_3² + c_1_1·c_1_2·c_1_3⁶ + c_1_1·c_1_2²·c_1_3⁵
       + c_1_1·c_1_2⁶·c_1_3 + c_1_1·c_1_2⁷ + c_1_1²·c_1_3⁶ + c_1_1²·c_1_2·c_1_3⁵
       + c_1_1²·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2⁵·c_1_3 + c_1_1³·c_1_2³·c_1_3²
       + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2⁴ + c_1_1⁵·c_1_2·c_1_3²
       + c_1_1⁵·c_1_2³, an element of degree 8
15. c_8_5 → c_1_3⁸ + c_1_2²·c_1_3⁶ + c_1_2⁵·c_1_3³ + c_1_2⁶·c_1_3² + c_1_1·c_1_2·c_1_3⁶
       + c_1_1·c_1_2³·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3³ + c_1_1·c_1_2⁷ + c_1_1²·c_1_3⁶
       + c_1_1²·c_1_2⁴·c_1_3² + c_1_1²·c_1_2⁵·c_1_3 + c_1_1³·c_1_2⁵
       + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2³·c_1_3
       + c_1_1⁴·c_1_2⁴ + c_1_1⁵·c_1_3³ + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3
       + c_1_1⁶·c_1_3² + c_1_1⁷·c_1_3 + c_1_1⁷·c_1_2 + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1·c_1_2⁴·c_1_3² + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1·c_1_2·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
       + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_2, an element of degree 1
2. b_2_0 → c_1_3² + c_1_2·c_1_3 + c_1_1·c_1_3 + c_1_1·c_1_2 + c_1_1², an element of degree 2
3. b_3_5 → c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_1·c_1_3² + c_1_1·c_1_2² + c_1_1²·c_1_3
      + c_1_1²·c_1_2, an element of degree 3
4. b_3_2 → c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_1·c_1_3² + c_1_1·c_1_2² + c_1_1²·c_1_3
      + c_1_1²·c_1_2, an element of degree 3
5. b_3_1 → c_1_3³ + c_1_2²·c_1_3 + c_1_1·c_1_2·c_1_3 + c_1_1²·c_1_3 + c_1_1²·c_1_2 + c_1_1³, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_2·c_1_3³ + c_1_2²·c_1_3² + c_1_1·c_1_2³ + c_1_1²·c_1_2·c_1_3 + c_1_1³·c_1_2, an element of degree 4
9. b_4_5 → 0, an element of degree 4
10. b_5_11 → c_1_2³·c_1_3² + c_1_2⁴·c_1_3 + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2⁴
       + c_1_1²·c_1_2²·c_1_3 + c_1_1²·c_1_2³, an element of degree 5
11. b_6_13 → c_1_1·c_1_2³·c_1_3² + c_1_1·c_1_2⁴·c_1_3 + c_1_1²·c_1_2³·c_1_3, an element of degree 6
12. b_7_1 → c_1_2·c_1_3⁶ + c_1_2³·c_1_3⁴ + c_1_2⁴·c_1_3³ + c_1_2⁵·c_1_3² + c_1_1·c_1_3⁶
       + c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1·c_1_2⁵·c_1_3
       + c_1_1·c_1_2⁶ + c_1_1²·c_1_3⁵ + c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2³·c_1_3²
       + c_1_1²·c_1_2⁴·c_1_3 + c_1_1²·c_1_2⁵ + c_1_1³·c_1_3⁴ + c_1_1³·c_1_2⁴
       + c_1_1⁴·c_1_3³ + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁵·c_1_3² + c_1_1⁶·c_1_3
       + c_1_1⁶·c_1_2, an element of degree 7
13. b_7_0 → c_1_1·c_1_2⁴·c_1_3² + c_1_1·c_1_2⁵·c_1_3 + c_1_1²·c_1_2·c_1_3⁴
       + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁴·c_1_3 + c_1_1⁴·c_1_2·c_1_3², an element of degree 7
14. b_8_10 → c_1_2³·c_1_3⁵ + c_1_2⁵·c_1_3³ + c_1_2⁶·c_1_3² + c_1_2⁷·c_1_3
       + c_1_1·c_1_2²·c_1_3⁵ + c_1_1·c_1_2³·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3³
       + c_1_1·c_1_2⁷ + c_1_1²·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2³·c_1_3³
       + c_1_1²·c_1_2⁴·c_1_3² + c_1_1³·c_1_2²·c_1_3³ + c_1_1³·c_1_2³·c_1_3²
       + c_1_1³·c_1_2⁴·c_1_3 + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁵·c_1_2³, an element of degree 8
15. c_8_5 → c_1_2·c_1_3⁷ + c_1_2²·c_1_3⁶ + c_1_2³·c_1_3⁵ + c_1_2⁷·c_1_3
       + c_1_1·c_1_2·c_1_3⁶ + c_1_1·c_1_2³·c_1_3⁴ + c_1_1·c_1_2⁶·c_1_3 + c_1_1·c_1_2⁷
       + c_1_1²·c_1_3⁶ + c_1_1²·c_1_2³·c_1_3³ + c_1_1²·c_1_2⁴·c_1_3²
       + c_1_1³·c_1_3⁵ + c_1_1³·c_1_2·c_1_3⁴ + c_1_1³·c_1_2²·c_1_3³
       + c_1_1³·c_1_2³·c_1_3² + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_2²·c_1_3²
       + c_1_1⁴·c_1_2⁴ + c_1_1⁵·c_1_3³ + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁶·c_1_3²
       + c_1_1⁷·c_1_2 + c_1_0·c_1_1·c_1_2²·c_1_3⁴ + c_1_0·c_1_1·c_1_2⁴·c_1_3²
       + c_1_0·c_1_1²·c_1_2·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁴·c_1_3
       + c_1_0·c_1_1⁴·c_1_2·c_1_3² + c_1_0·c_1_1⁴·c_1_2²·c_1_3
       + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3² + c_1_0²·c_1_1·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2⁴·c_1_3 + c_1_0²·c_1_1²·c_1_3⁴
       + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0²·c_1_1²·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3 + c_1_0²·c_1_1⁴·c_1_2²
       + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_2⁴
       + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_1, an element of degree 1
2. b_2_0 → c_1_3² + c_1_2² + c_1_1·c_1_3 + c_1_1·c_1_2 + c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → c_1_1·c_1_3² + c_1_1·c_1_2² + c_1_1²·c_1_3 + c_1_1²·c_1_2, an element of degree 3
5. b_3_1 → c_1_3³ + c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_2³, an element of degree 3
6. b_3_0 → c_1_1·c_1_3² + c_1_1·c_1_2² + c_1_1²·c_1_3 + c_1_1²·c_1_2, an element of degree 3
7. b_4_9 → c_1_1·c_1_3³ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3 + c_1_1·c_1_2³
      + c_1_1²·c_1_3² + c_1_1²·c_1_2², an element of degree 4
8. b_4_6 → c_1_2²·c_1_3² + c_1_1·c_1_3³ + c_1_1·c_1_2³ + c_1_1²·c_1_2·c_1_3 + c_1_1⁴, an element of degree 4
9. b_4_5 → c_1_2²·c_1_3² + c_1_1·c_1_3³ + c_1_1·c_1_2³ + c_1_1²·c_1_3²
      + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2² + c_1_1³·c_1_3 + c_1_1³·c_1_2, an element of degree 4
10. b_5_11 → c_1_1·c_1_3⁴ + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2⁴ + c_1_1²·c_1_3³
       + c_1_1²·c_1_2³ + c_1_1³·c_1_3² + c_1_1³·c_1_2·c_1_3 + c_1_1³·c_1_2², an element of degree 5
11. b_6_13 → c_1_1²·c_1_2²·c_1_3² + c_1_1³·c_1_2·c_1_3² + c_1_1³·c_1_2²·c_1_3
       + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1²·c_1_3⁵ + c_1_1²·c_1_2⁵
       + c_1_1³·c_1_2²·c_1_3² + c_1_1⁴·c_1_3³ + c_1_1⁴·c_1_2·c_1_3²
       + c_1_1⁴·c_1_2²·c_1_3 + c_1_1⁴·c_1_2³ + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁷
       + c_1_0·c_1_1²·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2² + c_1_0²·c_1_1·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_3 + c_1_0²·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1·c_1_3²
       + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_3 + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
13. b_7_0 → c_1_2²·c_1_3⁵ + c_1_2³·c_1_3⁴ + c_1_2⁴·c_1_3³ + c_1_2⁵·c_1_3²
       + c_1_1·c_1_3⁶ + c_1_1·c_1_2·c_1_3⁵ + c_1_1·c_1_2⁵·c_1_3 + c_1_1·c_1_2⁶
       + c_1_1³·c_1_3⁴ + c_1_1³·c_1_2·c_1_3³ + c_1_1³·c_1_2³·c_1_3 + c_1_1³·c_1_2⁴
       + c_1_0·c_1_1²·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2² + c_1_0²·c_1_1·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_3 + c_1_0²·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1·c_1_3²
       + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_3 + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
14. b_8_10 → c_1_1·c_1_3⁷ + c_1_1·c_1_2·c_1_3⁶ + c_1_1·c_1_2²·c_1_3⁵
       + c_1_1·c_1_2³·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3³ + c_1_1·c_1_2⁵·c_1_3²
       + c_1_1·c_1_2⁶·c_1_3 + c_1_1·c_1_2⁷ + c_1_1²·c_1_3⁶ + c_1_1²·c_1_2⁶
       + c_1_1³·c_1_3⁵ + c_1_1³·c_1_2²·c_1_3³ + c_1_1³·c_1_2³·c_1_3²
       + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2·c_1_3³
       + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁷·c_1_3
       + c_1_1⁷·c_1_2 + c_1_1⁸ + c_1_0·c_1_1²·c_1_3⁵ + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1²·c_1_2⁵ + c_1_0·c_1_1³·c_1_3⁴
       + c_1_0·c_1_1³·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_3³ + c_1_0·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0·c_1_1⁴·c_1_2³ + c_1_0·c_1_1⁵·c_1_3²
       + c_1_0·c_1_1⁵·c_1_2² + c_1_0²·c_1_1·c_1_3⁵ + c_1_0²·c_1_1·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2⁴·c_1_3 + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1²·c_1_3⁴
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2²
       + c_1_0²·c_1_1⁵·c_1_3 + c_1_0²·c_1_1⁵·c_1_2 + c_1_0⁴·c_1_1·c_1_3³
       + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3 + c_1_0⁴·c_1_1·c_1_2³
       + c_1_0⁴·c_1_1³·c_1_3 + c_1_0⁴·c_1_1³·c_1_2, an element of degree 8
15. c_8_5 → c_1_2²·c_1_3⁶ + c_1_2⁶·c_1_3² + c_1_1·c_1_3⁷ + c_1_1·c_1_2³·c_1_3⁴
       + c_1_1·c_1_2⁴·c_1_3³ + c_1_1·c_1_2⁷ + c_1_1²·c_1_2·c_1_3⁵
       + c_1_1²·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2⁴·c_1_3² + c_1_1²·c_1_2⁵·c_1_3
       + c_1_1³·c_1_3⁵ + c_1_1³·c_1_2²·c_1_3³ + c_1_1³·c_1_2³·c_1_3²
       + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2·c_1_3³
       + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_3³ + c_1_1⁵·c_1_2³ + c_1_1⁶·c_1_3² + c_1_1⁶·c_1_2·c_1_3
       + c_1_1⁶·c_1_2² + c_1_0·c_1_1·c_1_2²·c_1_3⁴ + c_1_0·c_1_1·c_1_2⁴·c_1_3²
       + c_1_0·c_1_1²·c_1_3⁵ + c_1_0·c_1_1²·c_1_2⁵ + c_1_0·c_1_1³·c_1_3⁴
       + c_1_0·c_1_1³·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_3³ + c_1_0·c_1_1⁴·c_1_2³
       + c_1_0·c_1_1⁵·c_1_3² + c_1_0·c_1_1⁵·c_1_2² + c_1_0²·c_1_2²·c_1_3⁴
       + c_1_0²·c_1_2⁴·c_1_3² + c_1_0²·c_1_1·c_1_3⁵ + c_1_0²·c_1_1·c_1_2⁵
       + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
       + c_1_0²·c_1_1⁵·c_1_3 + c_1_0²·c_1_1⁵·c_1_2 + c_1_0⁴·c_1_3⁴
       + c_1_0⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_3³
       + c_1_0⁴·c_1_1·c_1_2³ + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3
       + c_1_0⁴·c_1_1²·c_1_2² + c_1_0⁴·c_1_1³·c_1_3 + c_1_0⁴·c_1_1³·c_1_2
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_1, an element of degree 1
2. b_2_0 → c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → 0, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2² + c_1_1⁴, an element of degree 4
9. b_4_5 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2², an element of degree 4
10. b_5_11 → c_1_1·c_1_3⁴ + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2⁴ + c_1_1²·c_1_2·c_1_3²
       + c_1_1²·c_1_2²·c_1_3 + c_1_1³·c_1_3² + c_1_1³·c_1_2·c_1_3 + c_1_1³·c_1_2², an element of degree 5
11. b_6_13 → c_1_2²·c_1_3⁴ + c_1_2⁴·c_1_3² + c_1_1·c_1_2·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3
       + c_1_1²·c_1_3⁴ + c_1_1²·c_1_2²·c_1_3² + c_1_1²·c_1_2⁴ + c_1_1⁴·c_1_3²
       + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁴·c_1_2² + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_1³·c_1_3⁴ + c_1_1³·c_1_2²·c_1_3² + c_1_1³·c_1_2⁴
       + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁴·c_1_2²·c_1_3 + c_1_1⁵·c_1_3²
       + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁵·c_1_2² + c_1_1⁷, an element of degree 7
13. b_7_0 → 0, an element of degree 7
14. b_8_10 → c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_1⁸, an element of degree 8
15. c_8_5 → c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1·c_1_2⁴·c_1_3² + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1·c_1_2·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
       + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_3 + c_1_2 + c_1_1, an element of degree 1
2. b_2_0 → c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → c_1_1·c_1_3² + c_1_1·c_1_2², an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_2²·c_1_3² + c_1_1·c_1_3³ + c_1_1·c_1_2³ + c_1_1²·c_1_2·c_1_3 + c_1_1⁴, an element of degree 4
9. b_4_5 → c_1_2²·c_1_3² + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3 + c_1_1²·c_1_2·c_1_3, an element of degree 4
10. b_5_11 → c_1_2²·c_1_3³ + c_1_2³·c_1_3² + c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2²·c_1_3²
       + c_1_1·c_1_2³·c_1_3 + c_1_1³·c_1_2·c_1_3, an element of degree 5
11. b_6_13 → c_1_1·c_1_2²·c_1_3³ + c_1_1·c_1_2³·c_1_3² + c_1_1²·c_1_3⁴
       + c_1_1²·c_1_2·c_1_3³ + c_1_1²·c_1_2²·c_1_3² + c_1_1²·c_1_2³·c_1_3
       + c_1_1²·c_1_2⁴ + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_1·c_1_3⁶ + c_1_1·c_1_2⁶ + c_1_1²·c_1_3⁵ + c_1_1²·c_1_2²·c_1_3³
       + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁵ + c_1_1³·c_1_2·c_1_3³
       + c_1_1³·c_1_2²·c_1_3² + c_1_1³·c_1_2³·c_1_3 + c_1_1⁴·c_1_2·c_1_3²
       + c_1_1⁴·c_1_2²·c_1_3 + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁶·c_1_3 + c_1_1⁶·c_1_2 + c_1_1⁷, an element of degree 7
13. b_7_0 → c_1_1²·c_1_3⁵ + c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2²·c_1_3³
       + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁴·c_1_3 + c_1_1²·c_1_2⁵
       + c_1_1³·c_1_3⁴ + c_1_1³·c_1_2·c_1_3³ + c_1_1³·c_1_2³·c_1_3 + c_1_1³·c_1_2⁴
       + c_1_1⁴·c_1_3³ + c_1_1⁴·c_1_2³ + c_1_1⁵·c_1_3² + c_1_1⁵·c_1_2², an element of degree 7
14. b_8_10 → c_1_1²·c_1_3⁶ + c_1_1²·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2⁴·c_1_3²
       + c_1_1²·c_1_2⁶ + c_1_1³·c_1_2²·c_1_3³ + c_1_1³·c_1_2³·c_1_3²
       + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2·c_1_3³ + c_1_1⁴·c_1_2²·c_1_3²
       + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁴·c_1_2⁴ + c_1_1⁶·c_1_3² + c_1_1⁶·c_1_2·c_1_3
       + c_1_1⁶·c_1_2² + c_1_1⁸, an element of degree 8
15. c_8_5 → c_1_2²·c_1_3⁶ + c_1_2⁶·c_1_3² + c_1_1·c_1_2·c_1_3⁶ + c_1_1·c_1_2²·c_1_3⁵
       + c_1_1·c_1_2⁵·c_1_3² + c_1_1·c_1_2⁶·c_1_3 + c_1_1²·c_1_3⁶
       + c_1_1²·c_1_2·c_1_3⁵ + c_1_1²·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2⁴·c_1_3²
       + c_1_1²·c_1_2⁵·c_1_3 + c_1_1²·c_1_2⁶ + c_1_1³·c_1_3⁵ + c_1_1³·c_1_2·c_1_3⁴
       + c_1_1³·c_1_2²·c_1_3³ + c_1_1³·c_1_2³·c_1_3² + c_1_1³·c_1_2⁴·c_1_3
       + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_2·c_1_3³ + c_1_1⁴·c_1_2²·c_1_3²
       + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁶·c_1_2·c_1_3 + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1·c_1_2⁴·c_1_3² + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1·c_1_2·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
       + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_2, an element of degree 1
2. b_2_0 → c_1_3² + c_1_2² + c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → c_1_3³ + c_1_2³ + c_1_1·c_1_3² + c_1_1²·c_1_3 + c_1_1³, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_2·c_1_3³ + c_1_2²·c_1_3² + c_1_1·c_1_2²·c_1_3 + c_1_1²·c_1_3²
      + c_1_1²·c_1_2² + c_1_1³·c_1_2, an element of degree 4
9. b_4_5 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2², an element of degree 4
10. b_5_11 → c_1_2³·c_1_3² + c_1_2⁵ + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2³·c_1_3
       + c_1_1²·c_1_2·c_1_3² + c_1_1²·c_1_2²·c_1_3 + c_1_1²·c_1_2³, an element of degree 5
11. b_6_13 → c_1_2⁴·c_1_3² + c_1_2⁶ + c_1_1·c_1_2²·c_1_3³ + c_1_1·c_1_2⁴·c_1_3
       + c_1_1²·c_1_2·c_1_3³ + c_1_1²·c_1_2²·c_1_3² + c_1_1²·c_1_2⁴
       + c_1_1³·c_1_2·c_1_3² + c_1_1³·c_1_2²·c_1_3, an element of degree 6
12. b_7_1 → c_1_2²·c_1_3⁵ + c_1_2⁷ + c_1_1·c_1_2³·c_1_3³ + c_1_1·c_1_2⁴·c_1_3²
       + c_1_1·c_1_2⁵·c_1_3 + c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2²·c_1_3³
       + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁴·c_1_3 + c_1_1³·c_1_2²·c_1_3²
       + c_1_1³·c_1_2³·c_1_3 + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁵·c_1_2², an element of degree 7
13. b_7_0 → c_1_2³·c_1_3⁴ + c_1_2⁵·c_1_3² + c_1_1·c_1_2·c_1_3⁵ + c_1_1·c_1_2²·c_1_3⁴
       + c_1_1·c_1_2³·c_1_3³ + c_1_1·c_1_2⁴·c_1_3² + c_1_1²·c_1_3⁵
       + c_1_1²·c_1_2⁴·c_1_3 + c_1_1²·c_1_2⁵ + c_1_1³·c_1_3⁴ + c_1_1³·c_1_2³·c_1_3
       + c_1_1⁴·c_1_3³ + c_1_1⁴·c_1_2²·c_1_3 + c_1_1⁴·c_1_2³ + c_1_1⁵·c_1_3²
       + c_1_1⁵·c_1_2·c_1_3, an element of degree 7
14. b_8_10 → c_1_2⁴·c_1_3⁴ + c_1_2⁶·c_1_3² + c_1_1²·c_1_2⁶ + c_1_1⁴·c_1_2⁴, an element of degree 8
15. c_8_5 → c_1_2·c_1_3⁷ + c_1_2²·c_1_3⁶ + c_1_2³·c_1_3⁵ + c_1_2⁴·c_1_3⁴
       + c_1_2⁶·c_1_3² + c_1_2⁸ + c_1_1·c_1_2²·c_1_3⁵ + c_1_1·c_1_2⁴·c_1_3³
       + c_1_1·c_1_2⁵·c_1_3² + c_1_1·c_1_2⁶·c_1_3 + c_1_1²·c_1_3⁶
       + c_1_1²·c_1_2³·c_1_3³ + c_1_1²·c_1_2⁴·c_1_3² + c_1_1²·c_1_2⁵·c_1_3
       + c_1_1²·c_1_2⁶ + c_1_1³·c_1_2·c_1_3⁴ + c_1_1³·c_1_2³·c_1_3²
       + c_1_1³·c_1_2⁴·c_1_3 + c_1_1⁴·c_1_2·c_1_3³ + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁵·c_1_2³ + c_1_1⁶·c_1_3² + c_1_1⁶·c_1_2²
       + c_1_1⁷·c_1_2 + c_1_0·c_1_1·c_1_2²·c_1_3⁴ + c_1_0·c_1_1·c_1_2⁴·c_1_3²
       + c_1_0·c_1_1²·c_1_2·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁴·c_1_3
       + c_1_0·c_1_1⁴·c_1_2·c_1_3² + c_1_0·c_1_1⁴·c_1_2²·c_1_3
       + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3² + c_1_0²·c_1_1·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2⁴·c_1_3 + c_1_0²·c_1_1²·c_1_3⁴
       + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0²·c_1_1²·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3 + c_1_0²·c_1_1⁴·c_1_2²
       + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_2⁴
       + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_3 + c_1_2 + c_1_1, an element of degree 1
2. b_2_0 → c_1_3² + c_1_2² + c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → c_1_3³ + c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_2³ + c_1_1·c_1_3² + c_1_1·c_1_2²
      + c_1_1²·c_1_3 + c_1_1²·c_1_2 + c_1_1³, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_2²·c_1_3² + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3 + c_1_1²·c_1_3²
      + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2², an element of degree 4
9. b_4_5 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2² + c_1_1⁴, an element of degree 4
10. b_5_11 → c_1_3⁵ + c_1_2·c_1_3⁴ + c_1_2²·c_1_3³ + c_1_2³·c_1_3² + c_1_2⁴·c_1_3 + c_1_2⁵
       + c_1_1·c_1_3⁴ + c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2³·c_1_3
       + c_1_1·c_1_2⁴ + c_1_1²·c_1_3³ + c_1_1²·c_1_2·c_1_3² + c_1_1²·c_1_2²·c_1_3
       + c_1_1²·c_1_2³ + c_1_1³·c_1_3² + c_1_1³·c_1_2·c_1_3 + c_1_1³·c_1_2²
       + c_1_1⁴·c_1_3 + c_1_1⁴·c_1_2 + c_1_1⁵, an element of degree 5
11. b_6_13 → c_1_3⁶ + c_1_2⁶ + c_1_1·c_1_2·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3
       + c_1_1²·c_1_2²·c_1_3² + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_3⁷ + c_1_2·c_1_3⁶ + c_1_2⁶·c_1_3 + c_1_2⁷ + c_1_1·c_1_3⁶
       + c_1_1·c_1_2·c_1_3⁵ + c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3²
       + c_1_1·c_1_2⁵·c_1_3 + c_1_1·c_1_2⁶ + c_1_1²·c_1_2·c_1_3⁴
       + c_1_1²·c_1_2²·c_1_3³ + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁴·c_1_3
       + c_1_1³·c_1_2²·c_1_3² + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁴·c_1_2²·c_1_3
       + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁶·c_1_3 + c_1_1⁶·c_1_2 + c_1_1⁷, an element of degree 7
13. b_7_0 → 0, an element of degree 7
14. b_8_10 → 0, an element of degree 8
15. c_8_5 → c_1_3⁸ + c_1_2²·c_1_3⁶ + c_1_2⁶·c_1_3² + c_1_2⁸ + c_1_1·c_1_2·c_1_3⁶
       + c_1_1·c_1_2²·c_1_3⁵ + c_1_1·c_1_2⁵·c_1_3² + c_1_1·c_1_2⁶·c_1_3
       + c_1_1²·c_1_3⁶ + c_1_1²·c_1_2·c_1_3⁵ + c_1_1²·c_1_2²·c_1_3⁴
       + c_1_1²·c_1_2⁴·c_1_3² + c_1_1²·c_1_2⁵·c_1_3 + c_1_1²·c_1_2⁶
       + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3
       + c_1_1⁶·c_1_3² + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_1⁸
       + c_1_0·c_1_1·c_1_2²·c_1_3⁴ + c_1_0·c_1_1·c_1_2⁴·c_1_3²
       + c_1_0·c_1_1²·c_1_2·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁴·c_1_3
       + c_1_0·c_1_1⁴·c_1_2·c_1_3² + c_1_0·c_1_1⁴·c_1_2²·c_1_3
       + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3² + c_1_0²·c_1_1·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2⁴·c_1_3 + c_1_0²·c_1_1²·c_1_3⁴
       + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0²·c_1_1²·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3 + c_1_0²·c_1_1⁴·c_1_2²
       + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_2⁴
       + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_1, an element of degree 1
2. b_2_0 → c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → c_1_1³, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2², an element of degree 4
9. b_4_5 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3
      + c_1_1²·c_1_3² + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2² + c_1_1⁴, an element of degree 4
10. b_5_11 → c_1_1·c_1_3⁴ + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2⁴ + c_1_1²·c_1_2·c_1_3²
       + c_1_1²·c_1_2²·c_1_3 + c_1_1³·c_1_3² + c_1_1³·c_1_2·c_1_3 + c_1_1³·c_1_2²
       + c_1_1⁵, an element of degree 5
11. b_6_13 → c_1_2²·c_1_3⁴ + c_1_2⁴·c_1_3² + c_1_1·c_1_2·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3
       + c_1_1²·c_1_3⁴ + c_1_1²·c_1_2²·c_1_3² + c_1_1²·c_1_2⁴ + c_1_1⁴·c_1_3²
       + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁴·c_1_2² + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1²·c_1_2·c_1_3⁴
       + c_1_1²·c_1_2⁴·c_1_3 + c_1_1³·c_1_3⁴ + c_1_1³·c_1_2²·c_1_3²
       + c_1_1³·c_1_2⁴ + c_1_1⁵·c_1_3² + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁵·c_1_2² + c_1_1⁷, an element of degree 7
13. b_7_0 → 0, an element of degree 7
14. b_8_10 → 0, an element of degree 8
15. c_8_5 → c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2⁴
       + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_1⁸ + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1·c_1_2⁴·c_1_3² + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1·c_1_2·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
       + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

1. b_1_0 → c_1_3 + c_1_2 + c_1_1, an element of degree 1
2. b_2_0 → c_1_1², an element of degree 2
3. b_3_5 → 0, an element of degree 3
4. b_3_2 → 0, an element of degree 3
5. b_3_1 → c_1_1·c_1_3² + c_1_1·c_1_2² + c_1_1²·c_1_3 + c_1_1²·c_1_2 + c_1_1³, an element of degree 3
6. b_3_0 → 0, an element of degree 3
7. b_4_9 → 0, an element of degree 4
8. b_4_6 → c_1_2²·c_1_3² + c_1_1·c_1_3³ + c_1_1·c_1_2³ + c_1_1²·c_1_3²
      + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2², an element of degree 4
9. b_4_5 → c_1_2²·c_1_3² + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2²·c_1_3 + c_1_1²·c_1_3²
      + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2² + c_1_1⁴, an element of degree 4
10. b_5_11 → c_1_2²·c_1_3³ + c_1_2³·c_1_3² + c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2²·c_1_3²
       + c_1_1·c_1_2³·c_1_3 + c_1_1²·c_1_3³ + c_1_1²·c_1_2·c_1_3²
       + c_1_1²·c_1_2²·c_1_3 + c_1_1²·c_1_2³ + c_1_1³·c_1_3² + c_1_1³·c_1_2·c_1_3
       + c_1_1³·c_1_2² + c_1_1⁴·c_1_3 + c_1_1⁴·c_1_2 + c_1_1⁵, an element of degree 5
11. b_6_13 → c_1_1·c_1_2²·c_1_3³ + c_1_1·c_1_2³·c_1_3² + c_1_1²·c_1_3⁴
       + c_1_1²·c_1_2·c_1_3³ + c_1_1²·c_1_2²·c_1_3² + c_1_1²·c_1_2³·c_1_3
       + c_1_1²·c_1_2⁴ + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁶, an element of degree 6
12. b_7_1 → c_1_1·c_1_3⁶ + c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1·c_1_2⁶
       + c_1_1²·c_1_2²·c_1_3³ + c_1_1²·c_1_2³·c_1_3² + c_1_1³·c_1_3⁴
       + c_1_1³·c_1_2·c_1_3³ + c_1_1³·c_1_2²·c_1_3² + c_1_1³·c_1_2³·c_1_3
       + c_1_1³·c_1_2⁴ + c_1_1⁴·c_1_3³ + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁴·c_1_2²·c_1_3
       + c_1_1⁴·c_1_2³ + c_1_1⁵·c_1_3² + c_1_1⁵·c_1_2·c_1_3 + c_1_1⁵·c_1_2²
       + c_1_1⁶·c_1_3 + c_1_1⁶·c_1_2 + c_1_1⁷, an element of degree 7
13. b_7_0 → c_1_1²·c_1_3⁵ + c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2²·c_1_3³
       + c_1_1²·c_1_2³·c_1_3² + c_1_1²·c_1_2⁴·c_1_3 + c_1_1²·c_1_2⁵
       + c_1_1³·c_1_3⁴ + c_1_1³·c_1_2·c_1_3³ + c_1_1³·c_1_2³·c_1_3 + c_1_1³·c_1_2⁴
       + c_1_1⁴·c_1_3³ + c_1_1⁴·c_1_2³ + c_1_1⁵·c_1_3² + c_1_1⁵·c_1_2², an element of degree 7
14. b_8_10 → c_1_1²·c_1_3⁶ + c_1_1²·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2⁴·c_1_3²
       + c_1_1²·c_1_2⁶ + c_1_1⁶·c_1_3² + c_1_1⁶·c_1_2², an element of degree 8
15. c_8_5 → c_1_2²·c_1_3⁶ + c_1_2⁶·c_1_3² + c_1_1·c_1_2·c_1_3⁶ + c_1_1·c_1_2²·c_1_3⁵
       + c_1_1·c_1_2⁵·c_1_3² + c_1_1·c_1_2⁶·c_1_3 + c_1_1²·c_1_3⁶
       + c_1_1²·c_1_2·c_1_3⁵ + c_1_1²·c_1_2⁵·c_1_3 + c_1_1²·c_1_2⁶ + c_1_1³·c_1_3⁵
       + c_1_1³·c_1_2²·c_1_3³ + c_1_1³·c_1_2³·c_1_3² + c_1_1³·c_1_2⁵
       + c_1_1⁴·c_1_2·c_1_3³ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2³·c_1_3
       + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_3²
       + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁶·c_1_2² + c_1_1⁸ + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1·c_1_2⁴·c_1_3² + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1·c_1_2·c_1_3⁴ + c_1_0²·c_1_1·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
       + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1²·c_1_3² + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8