Mod-2-Cohomology of J3.2, a group of order 100465920

About the group Ring generators Ring relations Completion information Restriction maps


General information on the group

  • J3.2 is a group of order 100465920.
  • The group order factors as 28 · 35 · 5 · 17 · 19.
  • The group is defined by 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  • It is non-abelian.
  • It has 2-Rank 4.
  • The centre of a Sylow 2-subgroup has rank 1.
  • Its Sylow 2-subgroup has 4 conjugacy classes of maximal elementary abelian subgroups, which are of rank 3, 3, 3 and 4, respectively.


Structure of the cohomology ring

The computation was based on 4 stability conditions for H*(Normalizer(J3.2,Centre(SylowSubgroup(J3.2,2))); GF(2)).

General information

  • The cohomology ring is of dimension 4 and depth 3.
  • The depth exceeds the Duflot bound, which is 1.
  • The Poincaré series is
    ( − 1)·( − 1  +  t  −  t2  +  t3  −  t4  −  t6  −  t8  +  t9  −  t10  −  t11  −  t14  +  t15  −  t17  +  t19  −  t20  +  t21  +  t22  −  t23  +  t25  +  t28  −  t29  +  t30)

    (1  +  t) · ( − 1  +  t)4 · (1  −  t  +  t2) · (1  +  t2)2 · (1  +  t  +  t2)2 · (1  −  t2  +  t4) · (1  +  t4) · (1  +  t  +  t2  +  t3  +  t4) · (1  −  t  +  t3  −  t4  +  t5  −  t7  +  t8)
  • The a-invariants are -∞,-∞,-∞,-4,-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 16 minimal generators of maximal degree 15:

  1. b_1_0, an element of degree 1
  2. b_5_0, an element of degree 5
  3. b_6_2, an element of degree 6
  4. b_7_0, an element of degree 7
  5. c_8_4, a Duflot element of degree 8
  6. b_8_3, an element of degree 8
  7. b_9_0, an element of degree 9
  8. b_10_5, an element of degree 10
  9. b_11_4, an element of degree 11
  10. b_11_3, an element of degree 11
  11. b_12_6, an element of degree 12
  12. b_12_0, an element of degree 12
  13. b_13_3, an element of degree 13
  14. b_14_6, an element of degree 14
  15. b_15_9, an element of degree 15
  16. b_15_5, an element of degree 15

About the group Ring generators Ring relations Completion information Restriction maps

Ring relations

There are 74 minimal relations of maximal degree 30:

  1. b_1_04·b_5_0 + b_8_3·b_1_0
  2. b_1_0·b_9_0 + b_6_2·b_1_04
  3. b_5_02 + b_6_2·b_1_04 + c_8_4·b_1_02
  4. b_10_5·b_1_0 + b_6_2·b_5_0
  5. b_1_0·b_11_3
  6. b_5_0·b_7_0 + b_1_0·b_11_4 + b_6_2·b_1_06 + c_8_4·b_1_04
  7. b_6_2·b_7_0 + b_6_2·b_1_02·b_5_0
  8. b_8_3·b_5_0 + b_6_2·b_1_07 + c_8_4·b_1_05
  9. b_12_6·b_1_0 + b_6_2·b_1_02·b_5_0 + b_6_22·b_1_0
  10. b_1_0·b_13_3
  11. b_5_0·b_9_0 + b_6_2·b_1_03·b_5_0
  12. b_7_02 + b_12_0·b_1_02 + b_6_2·b_1_08 + c_8_4·b_1_06
  13. b_10_5·b_5_0 + b_6_22·b_1_03 + b_6_2·c_8_4·b_1_0
  14. b_14_6·b_1_0 + b_6_22·b_1_03 + b_6_2·c_8_4·b_1_0
  15. b_1_04·b_11_4 + b_8_3·b_7_0 + b_6_2·b_1_09 + c_8_4·b_1_07
  16. b_1_0·b_15_5
  17. b_1_0·b_15_9 + b_6_2·c_8_4·b_1_02
  18. b_5_0·b_11_3
  19. b_5_0·b_11_4 + c_8_4·b_1_0·b_7_0 + c_8_4·b_1_03·b_5_0
  20. b_7_0·b_9_0 + b_6_2·b_8_3·b_1_02
  21. b_6_2·b_11_4
  22. b_10_5·b_7_0 + b_6_22·b_1_05 + b_6_2·c_8_4·b_1_03
  23. b_12_6·b_5_0 + b_6_22·b_5_0 + b_6_22·b_1_05 + b_6_2·c_8_4·b_1_03
  24. b_5_0·b_13_3
  25. b_7_0·b_11_3
  26. b_7_0·b_11_4 + b_12_0·b_1_0·b_5_0 + c_8_4·b_1_03·b_7_0 + b_8_3·c_8_4·b_1_02
  27. b_9_02 + b_8_3·b_10_5 + b_6_2·b_12_6 + b_6_22·b_1_0·b_5_0 + b_6_23
       + b_6_2·c_8_4·b_1_04
  28. b_6_2·b_12_0·b_1_0
  29. b_8_3·b_11_4 + c_8_4·b_1_04·b_7_0 + b_8_3·c_8_4·b_1_03
  30. b_10_5·b_9_0 + b_8_3·b_11_3 + b_6_2·b_13_3 + b_6_22·b_1_02·b_5_0
  31. b_12_6·b_7_0 + b_6_22·b_1_02·b_5_0 + b_6_22·b_1_07 + b_6_2·c_8_4·b_1_05
  32. b_14_6·b_5_0 + b_6_22·b_1_02·b_5_0 + b_6_2·c_8_4·b_5_0
  33. b_10_52 + b_8_3·b_12_6 + b_6_2·b_14_6 + b_6_22·b_1_03·b_5_0 + b_6_22·b_1_08
       + b_6_2·c_8_4·b_1_06
  34. b_5_0·b_15_5
  35. b_5_0·b_15_9 + b_6_2·c_8_4·b_1_0·b_5_0
  36. b_7_0·b_13_3
  37. b_9_0·b_11_3 + b_8_3·b_12_6 + b_6_2·b_14_6 + b_6_22·b_1_08 + b_6_22·b_8_3
       + b_6_23·b_1_02 + b_6_2·c_8_4·b_1_06 + b_6_22·c_8_4
  38. b_9_0·b_11_4
  39. b_10_5·b_11_3 + b_8_3·b_13_3 + b_6_2·b_15_9 + b_6_22·b_9_0 + b_6_23·b_1_03
       + b_6_22·c_8_4·b_1_0
  40. b_10_5·b_11_4
  41. b_12_6·b_9_0 + b_8_3·b_13_3 + b_6_2·b_15_5 + b_6_22·b_9_0 + b_6_22·b_8_3·b_1_0
  42. b_14_6·b_7_0 + b_6_22·b_8_3·b_1_0 + b_6_2·c_8_4·b_1_02·b_5_0
  43. b_10_5·b_12_0 + b_6_2·b_8_32 + b_6_22·b_1_010 + c_8_4·b_14_6
       + b_6_2·c_8_4·b_1_03·b_5_0 + b_6_2·c_8_4·b_1_08 + b_6_2·b_8_3·c_8_4
       + b_6_22·c_8_4·b_1_02 + b_6_2·c_8_42
  44. b_7_0·b_15_5
  45. b_7_0·b_15_9 + b_6_2·c_8_4·b_1_03·b_5_0
  46. b_9_0·b_13_3 + b_10_5·b_12_6 + b_6_2·b_8_32 + b_6_22·b_1_010 + b_6_22·b_10_5
       + b_6_23·b_1_04 + b_6_2·c_8_4·b_1_03·b_5_0 + b_6_2·c_8_4·b_1_08
       + b_6_2·b_8_3·c_8_4 + b_6_22·c_8_4·b_1_02
  47. b_11_32 + b_10_5·b_12_6 + b_6_22·b_10_5 + b_6_23·b_1_04
       + b_6_2·c_8_4·b_1_03·b_5_0 + b_6_2·b_8_3·c_8_4 + b_6_22·c_8_4·b_1_02
  48. b_11_3·b_11_4
  49. b_11_42 + c_8_4·b_12_0·b_1_02
  50. b_12_0·b_11_3 + b_8_3·b_15_9 + b_8_3·b_15_5 + b_6_2·b_8_3·b_9_0 + b_6_22·b_8_3·b_1_03
       + c_8_4·b_15_5 + b_6_2·b_8_3·c_8_4·b_1_0
  51. b_12_6·b_11_3 + b_10_5·b_13_3 + b_6_2·b_8_3·b_9_0 + b_6_22·b_11_3
       + b_6_22·b_8_3·b_1_03 + b_6_2·c_8_4·b_9_0 + b_6_22·c_8_4·b_1_03
  52. b_12_6·b_11_4
  53. b_14_6·b_9_0 + b_10_5·b_13_3 + b_8_3·b_15_9 + b_8_3·b_15_5 + b_6_23·b_1_05
       + b_6_2·b_8_3·c_8_4·b_1_0 + b_6_22·c_8_4·b_1_03
  54. b_12_62 + b_10_5·b_14_6 + b_6_2·b_8_3·b_10_5 + b_6_22·b_12_0 + b_6_23·b_1_0·b_5_0
       + b_6_24 + b_8_32·c_8_4 + b_6_2·c_8_4·b_1_010 + b_6_2·c_8_4·b_10_5
       + c_8_42·b_1_08
  55. b_9_0·b_15_5 + b_10_5·b_14_6 + b_8_33 + b_6_2·b_8_3·b_1_010 + b_6_2·b_8_3·b_10_5
       + b_6_22·b_12_0 + b_6_23·b_1_0·b_5_0 + b_6_23·b_1_06 + b_8_3·c_8_4·b_1_08
       + b_6_2·c_8_4·b_10_5 + b_6_22·c_8_4·b_1_04
  56. b_9_0·b_15_9 + b_10_5·b_14_6 + b_8_33 + b_6_2·b_8_3·b_1_010 + b_6_2·b_8_3·b_10_5
       + b_6_22·b_12_6 + b_6_23·b_1_06 + b_6_24 + b_8_3·c_8_4·b_1_08 + b_8_32·c_8_4
       + b_6_2·c_8_4·b_1_010 + b_6_2·c_8_4·b_10_5 + c_8_42·b_1_08
  57. b_11_3·b_13_3 + b_10_5·b_14_6 + b_6_23·b_1_0·b_5_0 + b_8_32·c_8_4
       + b_6_2·c_8_4·b_1_010 + b_6_2·c_8_4·b_10_5 + c_8_42·b_1_08
  58. b_11_4·b_13_3
  59. b_10_5·b_15_9 + b_10_5·b_15_5 + b_6_22·b_13_3 + b_8_3·c_8_4·b_9_0 + b_6_2·c_8_4·b_11_3
       + b_6_2·b_8_3·c_8_4·b_1_03 + b_6_22·c_8_4·b_5_0
  60. b_12_6·b_13_3 + b_10_5·b_15_5 + b_8_32·b_9_0 + b_6_22·b_13_3 + b_6_22·b_1_013
       + b_8_3·c_8_4·b_9_0 + b_6_2·c_8_4·b_1_011 + b_6_2·b_8_3·c_8_4·b_1_03
  61. b_14_6·b_11_3 + b_10_5·b_15_5 + b_8_32·b_9_0 + b_6_22·b_1_013 + b_6_2·c_8_4·b_11_3
       + b_6_2·c_8_4·b_1_011
  62. b_14_6·b_11_4
  63. b_11_3·b_15_5 + b_12_6·b_14_6 + b_8_32·b_10_5 + b_6_2·b_8_3·b_12_0 + b_6_22·b_14_6
       + b_6_22·b_8_3·b_1_06 + b_6_23·b_1_03·b_5_0 + b_6_2·c_8_4·b_12_6
       + b_6_2·b_8_3·c_8_4·b_1_04 + b_6_23·c_8_4
  64. b_11_3·b_15_9 + b_12_6·b_14_6 + b_8_32·b_10_5 + b_6_2·b_8_3·b_12_0
       + b_6_22·b_8_3·b_1_06 + b_6_23·b_1_03·b_5_0 + b_6_24·b_1_02
       + b_8_3·c_8_4·b_10_5 + b_6_2·b_8_3·c_8_4·b_1_04 + b_6_22·c_8_4·b_1_0·b_5_0
       + b_6_22·c_8_4·b_1_06 + b_6_23·c_8_4 + b_6_2·c_8_42·b_1_04
  65. b_11_4·b_15_5
  66. b_11_4·b_15_9
  67. b_13_32 + b_12_6·b_14_6 + b_6_2·b_8_3·b_12_6 + b_6_2·b_8_3·b_12_0 + b_6_22·b_14_6
       + b_6_23·b_1_03·b_5_0 + b_6_23·b_1_08 + b_6_23·b_8_3 + b_8_3·c_8_4·b_10_5
       + b_6_22·c_8_4·b_1_0·b_5_0 + b_6_2·c_8_42·b_1_04
  68. b_12_6·b_15_9 + b_12_6·b_15_5 + b_6_2·b_12_0·b_9_0 + b_6_22·b_15_9 + b_8_3·c_8_4·b_11_3
       + b_6_22·c_8_4·b_1_02·b_5_0
  69. b_14_6·b_13_3 + b_12_6·b_15_5 + b_8_32·b_11_3 + b_6_2·b_12_0·b_9_0 + b_6_2·b_8_3·b_13_3
       + b_6_22·b_15_5 + b_6_2·c_8_4·b_13_3
  70. b_13_3·b_15_5 + b_14_62 + b_8_32·b_12_6 + b_8_32·b_12_0 + b_6_22·b_8_3·b_1_08
       + b_6_22·b_8_32 + b_6_24·b_1_04 + c_8_4·b_12_0·b_1_08
       + b_6_2·b_8_3·c_8_4·b_1_06 + b_6_22·c_8_42
  71. b_13_3·b_15_9 + b_14_62 + b_8_32·b_12_6 + b_8_32·b_12_0 + b_6_2·b_10_5·b_12_6
       + b_6_2·b_8_3·b_14_6 + b_6_22·b_8_3·b_1_08 + b_6_23·b_1_010 + b_6_23·b_10_5
       + b_6_23·b_8_3·b_1_02 + c_8_4·b_12_0·b_1_08 + b_8_3·c_8_4·b_12_6
       + b_6_2·c_8_4·b_14_6 + b_6_2·b_8_3·c_8_4·b_1_06 + b_6_22·c_8_4·b_1_03·b_5_0
       + b_6_22·b_8_3·c_8_4 + b_6_2·c_8_42·b_1_06
  72. b_14_6·b_15_9 + b_14_6·b_15_5 + b_8_3·b_12_0·b_9_0 + b_6_2·b_10_5·b_13_3
       + b_6_2·b_8_3·b_15_9 + b_6_2·c_8_4·b_15_9 + b_6_22·c_8_4·b_9_0
       + b_6_22·b_8_3·c_8_4·b_1_0
  73. b_15_5·b_15_9 + b_15_52 + b_8_3·b_10_5·b_12_6 + b_8_32·b_14_6 + b_6_2·b_12_0·b_12_6
       + b_6_2·b_10_5·b_14_6 + b_6_2·b_8_33 + b_6_22·b_8_3·b_1_010 + b_6_23·b_1_012
       + b_6_23·b_8_3·b_1_04 + b_6_24·b_1_0·b_5_0 + b_6_24·b_1_06 + b_8_3·c_8_4·b_14_6
       + b_6_2·b_8_3·c_8_4·b_1_08 + b_6_2·b_8_32·c_8_4 + b_6_22·c_8_4·b_1_010
       + b_6_22·c_8_4·b_10_5 + b_6_23·c_8_4·b_1_04 + b_6_2·b_8_3·c_8_42
  74. b_15_92 + b_15_52 + b_6_2·b_12_0·b_12_6 + b_6_22·b_8_3·b_10_5 + b_6_23·b_12_6
       + b_6_23·b_12_0 + b_6_24·b_1_0·b_5_0 + b_6_24·b_1_06 + b_6_25
       + c_8_4·b_10_5·b_12_6 + b_8_3·c_8_4·b_14_6 + b_6_2·b_8_32·c_8_4
       + b_6_22·c_8_4·b_1_010 + b_6_22·c_8_4·b_10_5 + b_6_22·b_8_3·c_8_4·b_1_02
       + b_6_2·c_8_42·b_1_03·b_5_0 + b_6_2·c_8_42·b_1_08


About the group Ring generators Ring relations Completion information Restriction maps

Data used for the Hilbert-Poincaré test

  • We proved completion in degree 38 using the Hilbert-Poincaré criterion.
  • However, the last relation was already found in degree 30 and the last generator in degree 15.
  • The following is a filter regular homogeneous system of parameters:
    1. b_1_03·b_5_0 + b_1_08 + b_8_3 + b_6_2·b_1_02 + c_8_4, an element of degree 8
    2. b_12_6 + b_12_0 + b_6_2·b_1_0·b_5_0 + b_6_2·b_1_06 + c_8_4·b_1_04, an element of degree 12
    3. b_14_6 + b_12_0·b_1_02 + b_6_2·c_8_4, an element of degree 14
    4. b_15_5, an element of degree 15
  • A Duflot regular sequence is given by c_8_4.
  • The Raw Filter Degree Type of the filter regular HSOP is [-1, -1, -1, 30, 45].
  • Modifying the above filter regular HSOP, we obtained the following parameters:
    1. b_1_03·b_5_0 + b_1_08 + b_8_3 + b_6_2·b_1_02 + c_8_4, an element of degree 8
    2. b_12_6 + b_12_0 + b_6_2·b_1_0·b_5_0 + b_6_2·b_1_06 + c_8_4·b_1_04, an element of degree 12
    3. b_6_2·b_1_02 + c_8_4, an element of degree 8
    4. b_15_5, an element of degree 15
  • We found that there exists some HSOP over a finite extension field, in degrees 8,12,15,6.


About the group Ring generators Ring relations Completion information Restriction maps

Restriction maps

Expressing the generators as elements of H*(Normalizer(J3.2,Centre(SylowSubgroup(J3.2,2))); GF(2))

  1. b_1_0b_1_0
  2. b_5_0b_5_0 + b_4_2·b_1_0 + b_2_12·b_1_0
  3. b_6_2b_6_4 + b_2_1·b_4_4 + b_2_1·b_4_2
  4. b_7_0b_7_6 + b_7_0 + b_4_4·b_3_3 + b_4_2·b_3_3 + b_4_2·b_1_03 + b_2_12·b_1_03
  5. c_8_4b_4_42 + b_4_2·b_4_4 + b_4_22 + b_2_1·b_6_4 + b_2_12·b_4_2 + b_2_14 + c_8_4
  6. b_8_3b_8_0 + b_4_42 + b_4_2·b_1_04 + b_4_2·b_4_4 + b_2_1·b_3_32 + b_2_12·b_1_04
       + b_2_12·b_4_4 + b_2_12·b_4_2
  7. b_9_0b_9_9 + b_3_33 + b_4_4·b_5_4 + b_2_1·b_7_0 + b_2_1·b_4_4·b_3_3 + b_2_1·b_4_2·b_3_3
  8. b_10_5b_2_1·b_4_42 + b_2_1·b_4_2·b_4_4 + b_2_1·b_4_22 + b_2_12·b_1_0·b_5_0
       + b_2_13·b_4_4 + b_2_1·c_8_4
  9. b_11_4b_4_2·b_7_6 + b_4_2·b_7_0 + b_4_2·b_1_02·b_5_0 + b_4_2·b_4_4·b_3_3 + b_4_22·b_3_3
       + c_8_4·b_3_0
  10. b_11_3b_4_42·b_3_3 + b_4_2·b_4_4·b_3_3 + b_4_22·b_3_3 + b_2_1·b_9_9 + b_2_1·b_3_33
       + b_2_12·b_4_4·b_3_3 + b_2_12·b_4_2·b_3_3 + c_8_4·b_3_3
  11. b_12_6b_4_2·b_1_03·b_5_0 + b_4_2·b_8_0 + b_4_2·b_4_42 + b_4_22·b_4_4
       + b_2_1·b_4_2·b_3_32 + b_2_1·b_4_2·b_6_4 + b_2_12·b_8_0 + b_2_12·b_4_42
       + b_2_12·b_4_22 + b_2_13·b_3_32 + b_2_13·b_1_0·b_5_0 + b_2_13·b_6_4
       + b_2_14·b_4_4 + b_4_4·c_8_4 + b_2_1·c_8_4·b_1_02 + b_2_12·c_8_4
  12. b_12_0b_3_34 + b_4_2·b_4_42 + b_4_22·b_4_4 + b_2_12·b_4_42 + b_2_12·b_4_2·b_4_4
       + b_4_4·c_8_4 + b_4_2·c_8_4
  13. b_13_3b_4_4·b_9_9 + b_4_4·b_3_33 + b_4_2·b_9_9 + b_4_2·b_3_33 + b_4_2·b_4_4·b_5_4
       + b_2_1·b_4_22·b_3_3 + b_2_12·b_4_4·b_5_4 + b_2_13·b_4_4·b_3_3 + c_8_4·b_5_4
       + b_2_1·c_8_4·b_3_3
  14. b_14_6b_4_2·b_4_4·b_6_4 + b_4_22·b_3_32 + b_4_22·b_6_4 + b_2_1·b_4_2·b_8_0
       + b_2_1·b_4_23 + b_2_12·b_4_4·b_3_32 + b_2_12·b_4_4·b_6_4
       + b_2_12·b_4_2·b_3_32 + b_2_13·b_8_0 + b_2_13·b_4_42 + b_2_13·b_4_2·b_4_4
       + b_2_13·b_4_22 + b_2_14·b_3_32 + b_2_15·b_4_2 + c_8_4·b_3_32 + b_6_4·c_8_4
       + b_2_1·b_4_4·c_8_4 + b_2_12·c_8_4·b_1_02 + b_2_13·c_8_4
  15. b_15_9b_4_23·b_3_3 + b_2_1·b_4_4·b_9_9 + b_2_1·b_4_4·b_3_33 + b_2_1·b_4_42·b_5_4
       + b_2_1·b_4_2·b_9_9 + b_2_1·b_4_2·b_3_33 + b_2_1·b_4_2·b_4_4·b_5_4
       + b_2_1·b_4_22·b_5_4 + b_2_12·b_4_2·b_7_0 + b_2_13·b_9_9 + b_2_13·b_3_33
       + b_2_13·b_4_4·b_5_4 + b_2_14·b_7_0 + b_2_14·b_4_4·b_3_3 + b_2_14·b_4_2·b_3_3
       + c_8_4·b_7_6 + b_4_2·c_8_4·b_3_3 + b_2_1·c_8_4·b_5_0 + b_2_13·c_8_4·b_1_0
  16. b_15_5b_4_2·b_4_4·b_7_0 + b_2_1·b_4_2·b_4_4·b_5_4 + b_2_1·b_4_22·b_5_4
       + b_2_12·b_4_2·b_7_0 + b_2_12·b_4_22·b_3_3 + b_4_2·c_8_4·b_3_3

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

  1. b_1_00, an element of degree 1
  2. b_5_00, an element of degree 5
  3. b_6_20, an element of degree 6
  4. b_7_00, an element of degree 7
  5. c_8_4c_1_08, an element of degree 8
  6. b_8_30, an element of degree 8
  7. b_9_00, an element of degree 9
  8. b_10_50, an element of degree 10
  9. b_11_40, an element of degree 11
  10. b_11_30, an element of degree 11
  11. b_12_60, an element of degree 12
  12. b_12_00, an element of degree 12
  13. b_13_30, an element of degree 13
  14. b_14_60, an element of degree 14
  15. b_15_90, an element of degree 15
  16. b_15_50, an element of degree 15

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

  1. b_1_0c_1_2, an element of degree 1
  2. b_5_0c_1_12·c_1_23 + c_1_14·c_1_2 + c_1_0·c_1_1·c_1_23 + c_1_0·c_1_12·c_1_22
       + c_1_02·c_1_23 + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_2, an element of degree 5
  3. b_6_20, an element of degree 6
  4. b_7_0c_1_12·c_1_25 + c_1_14·c_1_23 + c_1_0·c_1_1·c_1_25 + c_1_0·c_1_14·c_1_22
       + c_1_02·c_1_25 + c_1_02·c_1_12·c_1_23 + c_1_02·c_1_14·c_1_2
       + c_1_04·c_1_23 + c_1_04·c_1_1·c_1_22 + c_1_04·c_1_12·c_1_2, an element of degree 7
  5. c_8_4c_1_14·c_1_24 + c_1_18 + 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
  6. b_8_3c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_0·c_1_1·c_1_26 + c_1_0·c_1_12·c_1_25
       + c_1_02·c_1_26 + c_1_02·c_1_1·c_1_25 + c_1_02·c_1_12·c_1_24
       + c_1_04·c_1_24, an element of degree 8
  7. b_9_00, an element of degree 9
  8. b_10_50, an element of degree 10
  9. b_11_4c_1_0·c_1_14·c_1_26 + c_1_0·c_1_18·c_1_22 + c_1_02·c_1_14·c_1_25
       + c_1_02·c_1_18·c_1_2 + c_1_04·c_1_1·c_1_26 + c_1_04·c_1_12·c_1_25
       + c_1_08·c_1_1·c_1_22 + c_1_08·c_1_12·c_1_2, an element of degree 11
  10. b_11_30, an element of degree 11
  11. b_12_60, an element of degree 12
  12. b_12_0c_1_02·c_1_14·c_1_26 + c_1_02·c_1_18·c_1_22 + c_1_04·c_1_12·c_1_26
       + c_1_04·c_1_18 + c_1_08·c_1_12·c_1_22 + c_1_08·c_1_14, an element of degree 12
  13. b_13_30, an element of degree 13
  14. b_14_60, an element of degree 14
  15. b_15_90, an element of degree 15
  16. b_15_50, an element of degree 15

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

  1. b_1_0c_1_2, an element of degree 1
  2. b_5_0c_1_12·c_1_23 + c_1_14·c_1_2 + c_1_0·c_1_1·c_1_23 + c_1_0·c_1_12·c_1_22
       + c_1_02·c_1_23 + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_2, an element of degree 5
  3. b_6_2c_1_0·c_1_12·c_1_23 + c_1_0·c_1_14·c_1_2 + c_1_02·c_1_1·c_1_23
       + c_1_02·c_1_14 + c_1_04·c_1_1·c_1_2 + c_1_04·c_1_12, an element of degree 6
  4. b_7_0c_1_12·c_1_25 + c_1_14·c_1_23 + c_1_0·c_1_1·c_1_25 + c_1_0·c_1_12·c_1_24
       + c_1_02·c_1_25 + c_1_02·c_1_1·c_1_24 + c_1_02·c_1_12·c_1_23
       + c_1_04·c_1_23, an element of degree 7
  5. c_8_4c_1_14·c_1_24 + c_1_18 + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_23
       + c_1_02·c_1_1·c_1_25 + c_1_02·c_1_12·c_1_24 + c_1_04·c_1_24
       + c_1_04·c_1_1·c_1_23 + c_1_04·c_1_14 + c_1_08, an element of degree 8
  6. b_8_3c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_0·c_1_1·c_1_26 + c_1_0·c_1_12·c_1_25
       + c_1_02·c_1_26 + c_1_02·c_1_1·c_1_25 + c_1_02·c_1_12·c_1_24
       + c_1_04·c_1_24, an element of degree 8
  7. b_9_0c_1_0·c_1_12·c_1_26 + c_1_0·c_1_14·c_1_24 + c_1_02·c_1_1·c_1_26
       + c_1_02·c_1_14·c_1_23 + c_1_04·c_1_1·c_1_24 + c_1_04·c_1_12·c_1_23, an element of degree 9
  8. b_10_5c_1_0·c_1_14·c_1_25 + c_1_0·c_1_18·c_1_2 + c_1_02·c_1_14·c_1_24
       + c_1_02·c_1_18 + c_1_04·c_1_1·c_1_25 + c_1_04·c_1_12·c_1_24
       + c_1_08·c_1_1·c_1_2 + c_1_08·c_1_12, an element of degree 10
  9. b_11_40, an element of degree 11
  10. b_11_30, an element of degree 11
  11. b_12_6c_1_0·c_1_14·c_1_27 + c_1_0·c_1_18·c_1_23 + c_1_04·c_1_1·c_1_27
       + c_1_04·c_1_18 + c_1_08·c_1_1·c_1_23 + c_1_08·c_1_14, an element of degree 12
  12. b_12_00, an element of degree 12
  13. b_13_30, an element of degree 13
  14. b_14_6c_1_0·c_1_16·c_1_27 + c_1_0·c_1_18·c_1_25 + c_1_0·c_1_110·c_1_23
       + c_1_0·c_1_112·c_1_2 + c_1_02·c_1_15·c_1_27 + c_1_02·c_1_18·c_1_24
       + c_1_02·c_1_19·c_1_23 + c_1_02·c_1_112 + c_1_03·c_1_14·c_1_27
       + c_1_03·c_1_18·c_1_23 + c_1_04·c_1_13·c_1_27 + c_1_04·c_1_18·c_1_22
       + c_1_04·c_1_19·c_1_2 + c_1_04·c_1_110 + c_1_05·c_1_12·c_1_27
       + c_1_05·c_1_18·c_1_2 + c_1_06·c_1_1·c_1_27 + c_1_06·c_1_18
       + c_1_08·c_1_1·c_1_25 + c_1_08·c_1_12·c_1_24 + c_1_08·c_1_13·c_1_23
       + c_1_08·c_1_14·c_1_22 + c_1_08·c_1_15·c_1_2 + c_1_08·c_1_16
       + c_1_09·c_1_12·c_1_23 + c_1_09·c_1_14·c_1_2 + c_1_010·c_1_1·c_1_23
       + c_1_010·c_1_14 + c_1_012·c_1_1·c_1_2 + c_1_012·c_1_12, an element of degree 14
  15. b_15_9c_1_0·c_1_16·c_1_28 + c_1_0·c_1_18·c_1_26 + c_1_0·c_1_110·c_1_24
       + c_1_0·c_1_112·c_1_22 + c_1_02·c_1_14·c_1_29 + c_1_02·c_1_15·c_1_28
       + c_1_02·c_1_19·c_1_24 + c_1_02·c_1_112·c_1_2 + c_1_03·c_1_14·c_1_28
       + c_1_03·c_1_18·c_1_24 + c_1_04·c_1_12·c_1_29 + c_1_04·c_1_13·c_1_28
       + c_1_04·c_1_19·c_1_22 + c_1_04·c_1_110·c_1_2 + c_1_05·c_1_12·c_1_28
       + c_1_05·c_1_18·c_1_22 + c_1_06·c_1_1·c_1_28 + c_1_06·c_1_18·c_1_2
       + c_1_08·c_1_1·c_1_26 + c_1_08·c_1_13·c_1_24 + c_1_08·c_1_15·c_1_22
       + c_1_08·c_1_16·c_1_2 + c_1_09·c_1_12·c_1_24 + c_1_09·c_1_14·c_1_22
       + c_1_010·c_1_1·c_1_24 + c_1_010·c_1_14·c_1_2 + c_1_012·c_1_1·c_1_22
       + c_1_012·c_1_12·c_1_2, an element of degree 15
  16. b_15_50, an element of degree 15

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

  1. b_1_0c_1_2, an element of degree 1
  2. b_5_0c_1_12·c_1_23 + c_1_14·c_1_2 + c_1_0·c_1_1·c_1_23 + c_1_0·c_1_12·c_1_22
       + c_1_02·c_1_23 + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_2, an element of degree 5
  3. b_6_20, an element of degree 6
  4. b_7_0c_1_12·c_1_25 + c_1_14·c_1_23 + c_1_0·c_1_1·c_1_25 + c_1_0·c_1_14·c_1_22
       + c_1_02·c_1_25 + c_1_02·c_1_12·c_1_23 + c_1_02·c_1_14·c_1_2
       + c_1_04·c_1_23 + c_1_04·c_1_1·c_1_22 + c_1_04·c_1_12·c_1_2, an element of degree 7
  5. c_8_4c_1_14·c_1_24 + c_1_18 + 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
  6. b_8_3c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_0·c_1_1·c_1_26 + c_1_0·c_1_12·c_1_25
       + c_1_02·c_1_26 + c_1_02·c_1_1·c_1_25 + c_1_02·c_1_12·c_1_24
       + c_1_04·c_1_24, an element of degree 8
  7. b_9_00, an element of degree 9
  8. b_10_50, an element of degree 10
  9. b_11_4c_1_0·c_1_14·c_1_26 + c_1_0·c_1_18·c_1_22 + c_1_02·c_1_14·c_1_25
       + c_1_02·c_1_18·c_1_2 + c_1_04·c_1_1·c_1_26 + c_1_04·c_1_12·c_1_25
       + c_1_08·c_1_1·c_1_22 + c_1_08·c_1_12·c_1_2, an element of degree 11
  10. b_11_30, an element of degree 11
  11. b_12_60, an element of degree 12
  12. b_12_0c_1_02·c_1_14·c_1_26 + c_1_02·c_1_18·c_1_22 + c_1_04·c_1_12·c_1_26
       + c_1_04·c_1_18 + c_1_08·c_1_12·c_1_22 + c_1_08·c_1_14, an element of degree 12
  13. b_13_30, an element of degree 13
  14. b_14_60, an element of degree 14
  15. b_15_90, an element of degree 15
  16. b_15_50, an element of degree 15

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

  1. b_1_00, an element of degree 1
  2. b_5_00, an element of degree 5
  3. b_6_2c_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_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
       + 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_0·c_1_23·c_1_32 + c_1_0·c_1_24·c_1_3
       + c_1_0·c_1_1·c_1_34 + c_1_0·c_1_1·c_1_22·c_1_32 + c_1_0·c_1_1·c_1_24
       + c_1_0·c_1_12·c_1_33 + c_1_0·c_1_12·c_1_2·c_1_32 + c_1_0·c_1_12·c_1_23
       + c_1_02·c_1_34 + c_1_02·c_1_23·c_1_3 + c_1_02·c_1_24 + c_1_02·c_1_1·c_1_33
       + c_1_02·c_1_1·c_1_22·c_1_3 + c_1_02·c_1_1·c_1_23 + c_1_02·c_1_12·c_1_32
       + c_1_02·c_1_12·c_1_2·c_1_3 + c_1_02·c_1_12·c_1_22 + c_1_03·c_1_2·c_1_32
       + c_1_03·c_1_22·c_1_3 + c_1_04·c_1_32 + c_1_04·c_1_2·c_1_3 + c_1_04·c_1_22, an element of degree 6
  4. b_7_00, an element of degree 7
  5. c_8_4c_1_38 + c_1_24·c_1_34 + c_1_28 + 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_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_2·c_1_34 + c_1_13·c_1_24·c_1_3 + 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_18
       + c_1_0·c_1_23·c_1_34 + c_1_0·c_1_25·c_1_32 + c_1_0·c_1_12·c_1_35
       + 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_14·c_1_33
       + c_1_0·c_1_14·c_1_22·c_1_3 + c_1_0·c_1_14·c_1_23 + c_1_02·c_1_22·c_1_34
       + c_1_02·c_1_25·c_1_3 + 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_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_12·c_1_24
       + c_1_03·c_1_2·c_1_34 + c_1_03·c_1_24·c_1_3 + c_1_04·c_1_34
       + c_1_04·c_1_23·c_1_3 + c_1_04·c_1_24 + 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_23 + c_1_04·c_1_14
       + c_1_05·c_1_2·c_1_32 + c_1_05·c_1_22·c_1_3 + c_1_08, an element of degree 8
  6. b_8_3c_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_12·c_1_2·c_1_35 + c_1_12·c_1_25·c_1_3
       + c_1_13·c_1_2·c_1_34 + c_1_13·c_1_24·c_1_3 + c_1_14·c_1_2·c_1_33
       + 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_0·c_1_23·c_1_34 + c_1_0·c_1_25·c_1_32 + 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_2·c_1_34 + c_1_0·c_1_12·c_1_25 + 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_23 + c_1_02·c_1_24·c_1_32
       + c_1_02·c_1_25·c_1_3 + c_1_02·c_1_1·c_1_35 + 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_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_03·c_1_2·c_1_34 + c_1_03·c_1_24·c_1_3
       + c_1_04·c_1_22·c_1_32 + c_1_04·c_1_23·c_1_3 + c_1_04·c_1_1·c_1_33
       + 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_05·c_1_2·c_1_32
       + c_1_05·c_1_22·c_1_3, an element of degree 8
  7. b_9_0c_1_1·c_1_22·c_1_36 + c_1_1·c_1_26·c_1_32 + c_1_12·c_1_2·c_1_36
       + c_1_12·c_1_23·c_1_34 + c_1_12·c_1_24·c_1_33 + c_1_12·c_1_26·c_1_3
       + c_1_13·c_1_22·c_1_34 + c_1_13·c_1_24·c_1_32 + c_1_14·c_1_22·c_1_33
       + c_1_14·c_1_23·c_1_32 + c_1_16·c_1_2·c_1_32 + c_1_16·c_1_22·c_1_3
       + c_1_0·c_1_24·c_1_34 + c_1_0·c_1_26·c_1_32 + c_1_0·c_1_12·c_1_36
       + c_1_0·c_1_12·c_1_24·c_1_32 + c_1_0·c_1_12·c_1_26 + c_1_0·c_1_14·c_1_34
       + c_1_0·c_1_14·c_1_22·c_1_32 + c_1_0·c_1_14·c_1_24 + c_1_02·c_1_23·c_1_34
       + c_1_02·c_1_26·c_1_3 + c_1_02·c_1_1·c_1_36 + c_1_02·c_1_1·c_1_22·c_1_34
       + c_1_02·c_1_1·c_1_26 + c_1_02·c_1_12·c_1_2·c_1_34
       + c_1_02·c_1_12·c_1_24·c_1_3 + c_1_02·c_1_14·c_1_33
       + c_1_02·c_1_14·c_1_22·c_1_3 + c_1_02·c_1_14·c_1_23 + c_1_03·c_1_22·c_1_34
       + c_1_03·c_1_24·c_1_32 + c_1_04·c_1_2·c_1_34 + c_1_04·c_1_23·c_1_32
       + c_1_04·c_1_1·c_1_34 + c_1_04·c_1_1·c_1_22·c_1_32 + c_1_04·c_1_1·c_1_24
       + c_1_04·c_1_12·c_1_33 + c_1_04·c_1_12·c_1_2·c_1_32
       + c_1_04·c_1_12·c_1_23 + c_1_06·c_1_2·c_1_32 + c_1_06·c_1_22·c_1_3, an element of degree 9
  8. b_10_5c_1_22·c_1_38 + c_1_28·c_1_32 + c_1_1·c_1_2·c_1_38 + c_1_1·c_1_24·c_1_35
       + c_1_1·c_1_25·c_1_34 + c_1_1·c_1_28·c_1_3 + c_1_12·c_1_38
       + c_1_12·c_1_24·c_1_34 + c_1_12·c_1_28 + c_1_14·c_1_2·c_1_35
       + c_1_14·c_1_22·c_1_34 + c_1_14·c_1_24·c_1_32 + c_1_14·c_1_25·c_1_3
       + c_1_15·c_1_2·c_1_34 + c_1_15·c_1_24·c_1_3 + c_1_18·c_1_32
       + c_1_18·c_1_2·c_1_3 + c_1_18·c_1_22 + c_1_0·c_1_25·c_1_34 + c_1_0·c_1_28·c_1_3
       + c_1_0·c_1_1·c_1_38 + c_1_0·c_1_1·c_1_24·c_1_34 + c_1_0·c_1_1·c_1_28
       + c_1_0·c_1_14·c_1_35 + c_1_0·c_1_14·c_1_2·c_1_34 + c_1_0·c_1_14·c_1_25
       + c_1_02·c_1_38 + c_1_02·c_1_24·c_1_34 + c_1_02·c_1_28
       + c_1_04·c_1_22·c_1_34 + c_1_04·c_1_25·c_1_3 + c_1_04·c_1_1·c_1_35
       + c_1_04·c_1_1·c_1_24·c_1_3 + c_1_04·c_1_1·c_1_25 + c_1_04·c_1_14·c_1_32
       + c_1_04·c_1_14·c_1_2·c_1_3 + c_1_04·c_1_14·c_1_22 + c_1_05·c_1_2·c_1_34
       + c_1_05·c_1_24·c_1_3 + c_1_08·c_1_32 + c_1_08·c_1_2·c_1_3 + c_1_08·c_1_22, an element of degree 10
  9. b_11_40, an element of degree 11
  10. b_11_3c_1_1·c_1_22·c_1_38 + c_1_1·c_1_24·c_1_36 + c_1_1·c_1_26·c_1_34
       + c_1_1·c_1_28·c_1_32 + c_1_12·c_1_2·c_1_38 + c_1_12·c_1_24·c_1_35
       + c_1_12·c_1_25·c_1_34 + c_1_12·c_1_28·c_1_3 + c_1_14·c_1_2·c_1_36
       + c_1_14·c_1_22·c_1_35 + c_1_14·c_1_25·c_1_32 + c_1_14·c_1_26·c_1_3
       + c_1_15·c_1_22·c_1_34 + c_1_15·c_1_24·c_1_32 + c_1_16·c_1_2·c_1_34
       + c_1_16·c_1_24·c_1_3 + c_1_18·c_1_2·c_1_32 + c_1_18·c_1_22·c_1_3
       + c_1_0·c_1_26·c_1_34 + c_1_0·c_1_28·c_1_32 + c_1_0·c_1_12·c_1_38
       + c_1_0·c_1_12·c_1_24·c_1_34 + c_1_0·c_1_12·c_1_28 + c_1_0·c_1_14·c_1_36
       + c_1_0·c_1_14·c_1_22·c_1_34 + c_1_0·c_1_14·c_1_26 + c_1_02·c_1_25·c_1_34
       + c_1_02·c_1_28·c_1_3 + c_1_02·c_1_1·c_1_38 + c_1_02·c_1_1·c_1_24·c_1_34
       + c_1_02·c_1_1·c_1_28 + c_1_02·c_1_14·c_1_35 + c_1_02·c_1_14·c_1_2·c_1_34
       + c_1_02·c_1_14·c_1_25 + c_1_04·c_1_25·c_1_32 + c_1_04·c_1_26·c_1_3
       + c_1_04·c_1_1·c_1_36 + c_1_04·c_1_1·c_1_24·c_1_32 + c_1_04·c_1_1·c_1_26
       + c_1_04·c_1_12·c_1_35 + c_1_04·c_1_12·c_1_24·c_1_3 + c_1_04·c_1_12·c_1_25
       + c_1_04·c_1_14·c_1_2·c_1_32 + c_1_04·c_1_14·c_1_22·c_1_3
       + c_1_05·c_1_22·c_1_34 + c_1_05·c_1_24·c_1_32 + c_1_06·c_1_2·c_1_34
       + c_1_06·c_1_24·c_1_3 + c_1_08·c_1_2·c_1_32 + c_1_08·c_1_22·c_1_3, an element of degree 11
  11. b_12_6c_1_24·c_1_38 + c_1_28·c_1_34 + c_1_1·c_1_22·c_1_39 + c_1_1·c_1_23·c_1_38
       + c_1_1·c_1_28·c_1_33 + c_1_1·c_1_29·c_1_32 + c_1_12·c_1_2·c_1_39
       + c_1_12·c_1_22·c_1_38 + c_1_12·c_1_24·c_1_36 + c_1_12·c_1_26·c_1_34
       + c_1_12·c_1_28·c_1_32 + c_1_12·c_1_29·c_1_3 + c_1_13·c_1_2·c_1_38
       + c_1_13·c_1_28·c_1_3 + c_1_14·c_1_38 + c_1_14·c_1_22·c_1_36
       + c_1_14·c_1_24·c_1_34 + c_1_14·c_1_26·c_1_32 + c_1_14·c_1_28
       + c_1_16·c_1_22·c_1_34 + c_1_16·c_1_24·c_1_32 + c_1_18·c_1_34
       + c_1_18·c_1_2·c_1_33 + c_1_18·c_1_22·c_1_32 + c_1_18·c_1_23·c_1_3
       + c_1_18·c_1_24 + c_1_19·c_1_2·c_1_32 + c_1_19·c_1_22·c_1_3
       + c_1_0·c_1_23·c_1_38 + c_1_0·c_1_29·c_1_32 + c_1_0·c_1_1·c_1_22·c_1_38
       + c_1_0·c_1_1·c_1_28·c_1_32 + c_1_0·c_1_12·c_1_39
       + c_1_0·c_1_12·c_1_2·c_1_38 + c_1_0·c_1_12·c_1_29 + c_1_0·c_1_18·c_1_33
       + c_1_0·c_1_18·c_1_2·c_1_32 + c_1_0·c_1_18·c_1_23 + c_1_02·c_1_26·c_1_34
       + c_1_02·c_1_29·c_1_3 + c_1_02·c_1_1·c_1_39 + c_1_02·c_1_1·c_1_28·c_1_3
       + c_1_02·c_1_1·c_1_29 + c_1_02·c_1_12·c_1_38
       + c_1_02·c_1_12·c_1_24·c_1_34 + c_1_02·c_1_12·c_1_28
       + c_1_02·c_1_14·c_1_36 + c_1_02·c_1_14·c_1_22·c_1_34
       + c_1_02·c_1_14·c_1_26 + c_1_02·c_1_18·c_1_32 + c_1_02·c_1_18·c_1_2·c_1_3
       + c_1_02·c_1_18·c_1_22 + c_1_03·c_1_2·c_1_38 + c_1_03·c_1_28·c_1_3
       + c_1_04·c_1_38 + c_1_04·c_1_26·c_1_32 + c_1_04·c_1_28
       + c_1_04·c_1_12·c_1_36 + c_1_04·c_1_12·c_1_24·c_1_32
       + c_1_04·c_1_12·c_1_26 + c_1_04·c_1_14·c_1_34
       + c_1_04·c_1_14·c_1_22·c_1_32 + c_1_04·c_1_14·c_1_24
       + c_1_06·c_1_22·c_1_34 + c_1_06·c_1_24·c_1_32 + c_1_08·c_1_34
       + c_1_08·c_1_23·c_1_3 + c_1_08·c_1_24 + c_1_08·c_1_1·c_1_33
       + c_1_08·c_1_1·c_1_22·c_1_3 + c_1_08·c_1_1·c_1_23 + c_1_08·c_1_12·c_1_32
       + c_1_08·c_1_12·c_1_2·c_1_3 + c_1_08·c_1_12·c_1_22 + c_1_09·c_1_2·c_1_32
       + c_1_09·c_1_22·c_1_3, an element of degree 12
  12. b_12_0c_1_1·c_1_22·c_1_39 + c_1_1·c_1_23·c_1_38 + c_1_1·c_1_28·c_1_33
       + c_1_1·c_1_29·c_1_32 + c_1_12·c_1_2·c_1_39 + c_1_12·c_1_24·c_1_36
       + c_1_12·c_1_26·c_1_34 + c_1_12·c_1_29·c_1_3 + c_1_13·c_1_2·c_1_38
       + c_1_13·c_1_28·c_1_3 + c_1_14·c_1_22·c_1_36 + c_1_14·c_1_26·c_1_32
       + c_1_16·c_1_22·c_1_34 + c_1_16·c_1_24·c_1_32 + c_1_18·c_1_2·c_1_33
       + c_1_18·c_1_23·c_1_3 + c_1_19·c_1_2·c_1_32 + c_1_19·c_1_22·c_1_3
       + c_1_0·c_1_23·c_1_38 + c_1_0·c_1_29·c_1_32 + c_1_0·c_1_12·c_1_39
       + c_1_0·c_1_12·c_1_28·c_1_3 + c_1_0·c_1_12·c_1_29 + c_1_0·c_1_18·c_1_33
       + c_1_0·c_1_18·c_1_22·c_1_3 + c_1_0·c_1_18·c_1_23 + c_1_02·c_1_22·c_1_38
       + c_1_02·c_1_26·c_1_34 + c_1_02·c_1_28·c_1_32 + c_1_02·c_1_29·c_1_3
       + c_1_02·c_1_1·c_1_39 + c_1_02·c_1_1·c_1_2·c_1_38 + c_1_02·c_1_1·c_1_29
       + c_1_02·c_1_14·c_1_36 + c_1_02·c_1_14·c_1_24·c_1_32
       + c_1_02·c_1_14·c_1_26 + c_1_03·c_1_2·c_1_38 + c_1_03·c_1_28·c_1_3
       + c_1_04·c_1_24·c_1_34 + c_1_04·c_1_26·c_1_32 + c_1_04·c_1_12·c_1_36
       + c_1_04·c_1_12·c_1_22·c_1_34 + c_1_04·c_1_12·c_1_26 + c_1_04·c_1_18
       + c_1_06·c_1_22·c_1_34 + c_1_06·c_1_24·c_1_32 + c_1_08·c_1_22·c_1_32
       + c_1_08·c_1_23·c_1_3 + c_1_08·c_1_1·c_1_33 + c_1_08·c_1_1·c_1_2·c_1_32
       + c_1_08·c_1_1·c_1_23 + c_1_08·c_1_14 + c_1_09·c_1_2·c_1_32
       + c_1_09·c_1_22·c_1_3, an element of degree 12
  13. b_13_3c_1_1·c_1_22·c_1_310 + c_1_1·c_1_24·c_1_38 + c_1_1·c_1_28·c_1_34
       + c_1_1·c_1_210·c_1_32 + c_1_12·c_1_2·c_1_310 + c_1_12·c_1_23·c_1_38
       + c_1_12·c_1_28·c_1_33 + c_1_12·c_1_210·c_1_3 + c_1_13·c_1_22·c_1_38
       + c_1_13·c_1_28·c_1_32 + c_1_14·c_1_2·c_1_38 + c_1_14·c_1_28·c_1_3
       + c_1_18·c_1_2·c_1_34 + c_1_18·c_1_22·c_1_33 + c_1_18·c_1_23·c_1_32
       + c_1_18·c_1_24·c_1_3 + c_1_110·c_1_2·c_1_32 + c_1_110·c_1_22·c_1_3
       + c_1_0·c_1_24·c_1_38 + c_1_0·c_1_210·c_1_32 + c_1_0·c_1_12·c_1_310
       + c_1_0·c_1_12·c_1_28·c_1_32 + c_1_0·c_1_12·c_1_210 + c_1_0·c_1_18·c_1_34
       + c_1_0·c_1_18·c_1_22·c_1_32 + c_1_0·c_1_18·c_1_24 + c_1_02·c_1_23·c_1_38
       + c_1_02·c_1_210·c_1_3 + c_1_02·c_1_1·c_1_310 + c_1_02·c_1_1·c_1_22·c_1_38
       + c_1_02·c_1_1·c_1_210 + c_1_02·c_1_12·c_1_2·c_1_38
       + c_1_02·c_1_12·c_1_28·c_1_3 + c_1_02·c_1_18·c_1_33
       + c_1_02·c_1_18·c_1_22·c_1_3 + c_1_02·c_1_18·c_1_23 + c_1_03·c_1_22·c_1_38
       + c_1_03·c_1_28·c_1_32 + c_1_04·c_1_2·c_1_38 + c_1_04·c_1_28·c_1_3
       + c_1_08·c_1_23·c_1_32 + c_1_08·c_1_24·c_1_3 + c_1_08·c_1_1·c_1_34
       + c_1_08·c_1_1·c_1_22·c_1_32 + c_1_08·c_1_1·c_1_24 + c_1_08·c_1_12·c_1_33
       + c_1_08·c_1_12·c_1_2·c_1_32 + c_1_08·c_1_12·c_1_23 + c_1_010·c_1_2·c_1_32
       + c_1_010·c_1_22·c_1_3, an element of degree 13
  14. b_14_6c_1_22·c_1_312 + c_1_24·c_1_310 + c_1_26·c_1_38 + c_1_28·c_1_36
       + c_1_210·c_1_34 + c_1_212·c_1_32 + c_1_1·c_1_2·c_1_312
       + c_1_1·c_1_22·c_1_311 + c_1_1·c_1_23·c_1_310 + c_1_1·c_1_26·c_1_37
       + c_1_1·c_1_27·c_1_36 + c_1_1·c_1_210·c_1_33 + c_1_1·c_1_211·c_1_32
       + c_1_1·c_1_212·c_1_3 + c_1_12·c_1_312 + c_1_12·c_1_2·c_1_311
       + c_1_12·c_1_22·c_1_310 + c_1_12·c_1_23·c_1_39 + c_1_12·c_1_25·c_1_37
       + c_1_12·c_1_26·c_1_36 + c_1_12·c_1_27·c_1_35 + c_1_12·c_1_29·c_1_33
       + c_1_12·c_1_210·c_1_32 + c_1_12·c_1_211·c_1_3 + c_1_12·c_1_212
       + c_1_13·c_1_2·c_1_310 + c_1_13·c_1_22·c_1_39 + c_1_13·c_1_23·c_1_38
       + c_1_13·c_1_24·c_1_37 + c_1_13·c_1_25·c_1_36 + c_1_13·c_1_26·c_1_35
       + c_1_13·c_1_27·c_1_34 + c_1_13·c_1_28·c_1_33 + c_1_13·c_1_29·c_1_32
       + c_1_13·c_1_210·c_1_3 + c_1_14·c_1_310 + c_1_14·c_1_23·c_1_37
       + c_1_14·c_1_24·c_1_36 + c_1_14·c_1_25·c_1_35 + c_1_14·c_1_26·c_1_34
       + c_1_14·c_1_27·c_1_33 + c_1_14·c_1_210 + c_1_15·c_1_22·c_1_37
       + c_1_15·c_1_23·c_1_36 + c_1_15·c_1_24·c_1_35 + c_1_15·c_1_25·c_1_34
       + c_1_15·c_1_26·c_1_33 + c_1_15·c_1_27·c_1_32 + c_1_16·c_1_38
       + c_1_16·c_1_2·c_1_37 + c_1_16·c_1_22·c_1_36 + c_1_16·c_1_23·c_1_35
       + c_1_16·c_1_24·c_1_34 + c_1_16·c_1_25·c_1_33 + c_1_16·c_1_26·c_1_32
       + c_1_16·c_1_27·c_1_3 + c_1_16·c_1_28 + c_1_17·c_1_2·c_1_36
       + c_1_17·c_1_22·c_1_35 + c_1_17·c_1_23·c_1_34 + c_1_17·c_1_24·c_1_33
       + c_1_17·c_1_25·c_1_32 + c_1_17·c_1_26·c_1_3 + c_1_18·c_1_36
       + c_1_18·c_1_23·c_1_33 + c_1_18·c_1_26 + c_1_19·c_1_22·c_1_33
       + c_1_19·c_1_23·c_1_32 + c_1_110·c_1_34 + c_1_110·c_1_2·c_1_33
       + c_1_110·c_1_22·c_1_32 + c_1_110·c_1_23·c_1_3 + c_1_110·c_1_24
       + c_1_111·c_1_2·c_1_32 + c_1_111·c_1_22·c_1_3 + c_1_112·c_1_32
       + c_1_112·c_1_2·c_1_3 + c_1_112·c_1_22 + c_1_0·c_1_23·c_1_310
       + c_1_0·c_1_24·c_1_39 + c_1_0·c_1_25·c_1_38 + c_1_0·c_1_27·c_1_36
       + c_1_0·c_1_28·c_1_35 + c_1_0·c_1_29·c_1_34 + c_1_0·c_1_211·c_1_32
       + c_1_0·c_1_212·c_1_3 + c_1_0·c_1_1·c_1_312 + c_1_0·c_1_1·c_1_22·c_1_310
       + c_1_0·c_1_1·c_1_26·c_1_36 + c_1_0·c_1_1·c_1_210·c_1_32
       + c_1_0·c_1_1·c_1_212 + c_1_0·c_1_12·c_1_311 + c_1_0·c_1_12·c_1_2·c_1_310
       + c_1_0·c_1_12·c_1_23·c_1_38 + c_1_0·c_1_12·c_1_25·c_1_36
       + c_1_0·c_1_12·c_1_27·c_1_34 + c_1_0·c_1_12·c_1_29·c_1_32
       + c_1_0·c_1_12·c_1_211 + c_1_0·c_1_13·c_1_22·c_1_38
       + c_1_0·c_1_13·c_1_24·c_1_36 + c_1_0·c_1_13·c_1_26·c_1_34
       + c_1_0·c_1_13·c_1_28·c_1_32 + c_1_0·c_1_14·c_1_39
       + c_1_0·c_1_14·c_1_23·c_1_36 + c_1_0·c_1_14·c_1_25·c_1_34
       + c_1_0·c_1_14·c_1_27·c_1_32 + c_1_0·c_1_14·c_1_29 + c_1_0·c_1_15·c_1_38
       + c_1_0·c_1_15·c_1_22·c_1_36 + c_1_0·c_1_15·c_1_24·c_1_34
       + c_1_0·c_1_15·c_1_26·c_1_32 + c_1_0·c_1_15·c_1_28 + c_1_0·c_1_16·c_1_37
       + c_1_0·c_1_16·c_1_2·c_1_36 + c_1_0·c_1_16·c_1_23·c_1_34
       + c_1_0·c_1_16·c_1_25·c_1_32 + c_1_0·c_1_16·c_1_27
       + c_1_0·c_1_17·c_1_22·c_1_34 + c_1_0·c_1_17·c_1_24·c_1_32
       + c_1_0·c_1_18·c_1_35 + c_1_0·c_1_18·c_1_23·c_1_32 + c_1_0·c_1_18·c_1_25
       + c_1_0·c_1_19·c_1_34 + c_1_0·c_1_19·c_1_22·c_1_32 + c_1_0·c_1_19·c_1_24
       + c_1_0·c_1_110·c_1_33 + c_1_0·c_1_110·c_1_2·c_1_32 + c_1_0·c_1_110·c_1_23
       + c_1_02·c_1_312 + c_1_02·c_1_23·c_1_39 + c_1_02·c_1_27·c_1_35
       + c_1_02·c_1_211·c_1_3 + c_1_02·c_1_212 + c_1_02·c_1_1·c_1_311
       + c_1_02·c_1_1·c_1_22·c_1_39 + c_1_02·c_1_1·c_1_23·c_1_38
       + c_1_02·c_1_1·c_1_26·c_1_35 + c_1_02·c_1_1·c_1_27·c_1_34
       + c_1_02·c_1_1·c_1_210·c_1_3 + c_1_02·c_1_1·c_1_211 + c_1_02·c_1_12·c_1_310
       + c_1_02·c_1_12·c_1_2·c_1_39 + c_1_02·c_1_12·c_1_25·c_1_35
       + c_1_02·c_1_12·c_1_26·c_1_34 + c_1_02·c_1_12·c_1_28·c_1_32
       + c_1_02·c_1_12·c_1_29·c_1_3 + c_1_02·c_1_12·c_1_210
       + c_1_02·c_1_13·c_1_2·c_1_38 + c_1_02·c_1_13·c_1_24·c_1_35
       + c_1_02·c_1_13·c_1_25·c_1_34 + c_1_02·c_1_13·c_1_28·c_1_3
       + c_1_02·c_1_14·c_1_23·c_1_35 + c_1_02·c_1_14·c_1_27·c_1_3
       + c_1_02·c_1_15·c_1_37 + c_1_02·c_1_15·c_1_22·c_1_35
       + c_1_02·c_1_15·c_1_23·c_1_34 + c_1_02·c_1_15·c_1_26·c_1_3
       + c_1_02·c_1_15·c_1_27 + c_1_02·c_1_16·c_1_36
       + c_1_02·c_1_16·c_1_2·c_1_35 + c_1_02·c_1_16·c_1_22·c_1_34
       + c_1_02·c_1_16·c_1_25·c_1_3 + c_1_02·c_1_16·c_1_26
       + c_1_02·c_1_17·c_1_2·c_1_34 + c_1_02·c_1_17·c_1_24·c_1_3
       + c_1_02·c_1_18·c_1_22·c_1_32 + c_1_02·c_1_18·c_1_23·c_1_3
       + c_1_02·c_1_19·c_1_33 + c_1_02·c_1_19·c_1_22·c_1_3 + c_1_02·c_1_19·c_1_23
       + c_1_02·c_1_110·c_1_32 + c_1_02·c_1_110·c_1_2·c_1_3
       + c_1_02·c_1_110·c_1_22 + c_1_03·c_1_2·c_1_310 + c_1_03·c_1_22·c_1_39
       + c_1_03·c_1_27·c_1_34 + c_1_03·c_1_28·c_1_33 + c_1_03·c_1_29·c_1_32
       + c_1_03·c_1_210·c_1_3 + c_1_03·c_1_1·c_1_26·c_1_34
       + c_1_03·c_1_1·c_1_28·c_1_32 + c_1_03·c_1_12·c_1_25·c_1_34
       + c_1_03·c_1_12·c_1_28·c_1_3 + c_1_03·c_1_13·c_1_38
       + c_1_03·c_1_13·c_1_24·c_1_34 + c_1_03·c_1_13·c_1_28
       + c_1_03·c_1_14·c_1_37 + c_1_03·c_1_14·c_1_23·c_1_34
       + c_1_03·c_1_14·c_1_27 + c_1_03·c_1_15·c_1_36
       + c_1_03·c_1_15·c_1_22·c_1_34 + c_1_03·c_1_15·c_1_26
       + c_1_03·c_1_16·c_1_35 + c_1_03·c_1_16·c_1_2·c_1_34
       + c_1_03·c_1_16·c_1_25 + c_1_03·c_1_18·c_1_2·c_1_32
       + c_1_03·c_1_18·c_1_22·c_1_3 + c_1_04·c_1_310 + c_1_04·c_1_2·c_1_39
       + c_1_04·c_1_27·c_1_33 + c_1_04·c_1_28·c_1_32 + c_1_04·c_1_210
       + c_1_04·c_1_1·c_1_39 + c_1_04·c_1_1·c_1_26·c_1_33
       + c_1_04·c_1_1·c_1_27·c_1_32 + c_1_04·c_1_1·c_1_28·c_1_3
       + c_1_04·c_1_1·c_1_29 + c_1_04·c_1_12·c_1_24·c_1_34
       + c_1_04·c_1_12·c_1_25·c_1_33 + c_1_04·c_1_12·c_1_26·c_1_32
       + c_1_04·c_1_12·c_1_27·c_1_3 + c_1_04·c_1_13·c_1_37
       + c_1_04·c_1_13·c_1_24·c_1_33 + c_1_04·c_1_13·c_1_25·c_1_32
       + c_1_04·c_1_13·c_1_26·c_1_3 + c_1_04·c_1_13·c_1_27 + c_1_04·c_1_14·c_1_36
       + c_1_04·c_1_14·c_1_22·c_1_34 + c_1_04·c_1_14·c_1_23·c_1_33
       + c_1_04·c_1_14·c_1_25·c_1_3 + c_1_04·c_1_14·c_1_26 + c_1_04·c_1_15·c_1_35
       + c_1_04·c_1_15·c_1_22·c_1_33 + c_1_04·c_1_15·c_1_23·c_1_32
       + c_1_04·c_1_15·c_1_24·c_1_3 + c_1_04·c_1_15·c_1_25 + c_1_04·c_1_16·c_1_34
       + c_1_04·c_1_16·c_1_2·c_1_33 + c_1_04·c_1_16·c_1_22·c_1_32
       + c_1_04·c_1_16·c_1_23·c_1_3 + c_1_04·c_1_16·c_1_24
       + c_1_04·c_1_17·c_1_2·c_1_32 + c_1_04·c_1_17·c_1_22·c_1_3
       + c_1_04·c_1_18·c_1_32 + c_1_04·c_1_18·c_1_2·c_1_3 + c_1_04·c_1_18·c_1_22
       + c_1_05·c_1_2·c_1_38 + c_1_05·c_1_27·c_1_32 + c_1_05·c_1_1·c_1_38
       + c_1_05·c_1_1·c_1_26·c_1_32 + c_1_05·c_1_1·c_1_28 + c_1_05·c_1_12·c_1_37
       + c_1_05·c_1_12·c_1_25·c_1_32 + c_1_05·c_1_12·c_1_27
       + c_1_05·c_1_13·c_1_36 + c_1_05·c_1_13·c_1_24·c_1_32
       + c_1_05·c_1_13·c_1_26 + c_1_05·c_1_14·c_1_35
       + c_1_05·c_1_14·c_1_23·c_1_32 + c_1_05·c_1_14·c_1_25
       + c_1_05·c_1_15·c_1_34 + c_1_05·c_1_15·c_1_22·c_1_32
       + c_1_05·c_1_15·c_1_24 + c_1_05·c_1_16·c_1_33
       + c_1_05·c_1_16·c_1_2·c_1_32 + c_1_05·c_1_16·c_1_23 + c_1_06·c_1_38
       + c_1_06·c_1_27·c_1_3 + c_1_06·c_1_28 + c_1_06·c_1_1·c_1_37
       + c_1_06·c_1_1·c_1_26·c_1_3 + c_1_06·c_1_1·c_1_27 + c_1_06·c_1_12·c_1_36
       + c_1_06·c_1_12·c_1_25·c_1_3 + c_1_06·c_1_12·c_1_26 + c_1_06·c_1_13·c_1_35
       + c_1_06·c_1_13·c_1_24·c_1_3 + c_1_06·c_1_13·c_1_25 + c_1_06·c_1_14·c_1_34
       + c_1_06·c_1_14·c_1_23·c_1_3 + c_1_06·c_1_14·c_1_24 + c_1_06·c_1_15·c_1_33
       + c_1_06·c_1_15·c_1_22·c_1_3 + c_1_06·c_1_15·c_1_23 + c_1_06·c_1_16·c_1_32
       + c_1_06·c_1_16·c_1_2·c_1_3 + c_1_06·c_1_16·c_1_22 + c_1_07·c_1_2·c_1_36
       + c_1_07·c_1_22·c_1_35 + c_1_07·c_1_23·c_1_34 + c_1_07·c_1_24·c_1_33
       + c_1_07·c_1_25·c_1_32 + c_1_07·c_1_26·c_1_3 + c_1_07·c_1_1·c_1_22·c_1_34
       + c_1_07·c_1_1·c_1_24·c_1_32 + c_1_07·c_1_12·c_1_2·c_1_34
       + c_1_07·c_1_12·c_1_24·c_1_3 + c_1_07·c_1_14·c_1_2·c_1_32
       + c_1_07·c_1_14·c_1_22·c_1_3 + c_1_08·c_1_36 + c_1_08·c_1_2·c_1_35
       + c_1_08·c_1_23·c_1_33 + c_1_08·c_1_24·c_1_32 + c_1_08·c_1_26
       + c_1_08·c_1_1·c_1_35 + c_1_08·c_1_1·c_1_22·c_1_33
       + c_1_08·c_1_1·c_1_23·c_1_32 + c_1_08·c_1_1·c_1_24·c_1_3
       + c_1_08·c_1_1·c_1_25 + c_1_08·c_1_12·c_1_2·c_1_33
       + c_1_08·c_1_12·c_1_23·c_1_3 + c_1_08·c_1_13·c_1_2·c_1_32
       + c_1_08·c_1_13·c_1_22·c_1_3 + c_1_08·c_1_14·c_1_32
       + c_1_08·c_1_14·c_1_2·c_1_3 + c_1_08·c_1_14·c_1_22 + c_1_09·c_1_2·c_1_34
       + c_1_09·c_1_23·c_1_32 + c_1_09·c_1_1·c_1_34 + c_1_09·c_1_1·c_1_22·c_1_32
       + c_1_09·c_1_1·c_1_24 + c_1_09·c_1_12·c_1_33 + c_1_09·c_1_12·c_1_2·c_1_32
       + c_1_09·c_1_12·c_1_23 + c_1_010·c_1_34 + c_1_010·c_1_23·c_1_3
       + c_1_010·c_1_24 + c_1_010·c_1_1·c_1_33 + c_1_010·c_1_1·c_1_22·c_1_3
       + c_1_010·c_1_1·c_1_23 + c_1_010·c_1_12·c_1_32 + c_1_010·c_1_12·c_1_2·c_1_3
       + c_1_010·c_1_12·c_1_22 + c_1_011·c_1_2·c_1_32 + c_1_011·c_1_22·c_1_3
       + c_1_012·c_1_32 + c_1_012·c_1_2·c_1_3 + c_1_012·c_1_22, an element of degree 14
  15. b_15_9c_1_1·c_1_22·c_1_312 + c_1_1·c_1_24·c_1_310 + c_1_1·c_1_210·c_1_34
       + c_1_1·c_1_212·c_1_32 + c_1_12·c_1_2·c_1_312 + c_1_12·c_1_25·c_1_38
       + c_1_12·c_1_28·c_1_35 + c_1_12·c_1_212·c_1_3 + c_1_13·c_1_24·c_1_38
       + c_1_13·c_1_28·c_1_34 + c_1_14·c_1_2·c_1_310 + c_1_14·c_1_23·c_1_38
       + c_1_14·c_1_28·c_1_33 + c_1_14·c_1_210·c_1_3 + c_1_15·c_1_22·c_1_38
       + c_1_15·c_1_28·c_1_32 + c_1_18·c_1_22·c_1_35 + c_1_18·c_1_23·c_1_34
       + c_1_18·c_1_24·c_1_33 + c_1_18·c_1_25·c_1_32 + c_1_110·c_1_2·c_1_34
       + c_1_110·c_1_24·c_1_3 + c_1_112·c_1_2·c_1_32 + c_1_112·c_1_22·c_1_3
       + c_1_0·c_1_210·c_1_34 + c_1_0·c_1_212·c_1_32 + c_1_0·c_1_12·c_1_312
       + c_1_0·c_1_12·c_1_28·c_1_34 + c_1_0·c_1_12·c_1_212 + c_1_0·c_1_14·c_1_310
       + c_1_0·c_1_14·c_1_28·c_1_32 + c_1_0·c_1_14·c_1_210
       + c_1_0·c_1_18·c_1_22·c_1_34 + c_1_0·c_1_18·c_1_24·c_1_32
       + c_1_02·c_1_25·c_1_38 + c_1_02·c_1_212·c_1_3 + c_1_02·c_1_1·c_1_312
       + c_1_02·c_1_1·c_1_24·c_1_38 + c_1_02·c_1_1·c_1_212
       + c_1_02·c_1_14·c_1_2·c_1_38 + c_1_02·c_1_14·c_1_28·c_1_3
       + c_1_02·c_1_18·c_1_35 + c_1_02·c_1_18·c_1_24·c_1_3 + c_1_02·c_1_18·c_1_25
       + c_1_03·c_1_24·c_1_38 + c_1_03·c_1_28·c_1_34 + c_1_04·c_1_23·c_1_38
       + c_1_04·c_1_210·c_1_3 + c_1_04·c_1_1·c_1_310 + c_1_04·c_1_1·c_1_22·c_1_38
       + c_1_04·c_1_1·c_1_210 + c_1_04·c_1_12·c_1_2·c_1_38
       + c_1_04·c_1_12·c_1_28·c_1_3 + c_1_04·c_1_18·c_1_33
       + c_1_04·c_1_18·c_1_22·c_1_3 + c_1_04·c_1_18·c_1_23 + c_1_05·c_1_22·c_1_38
       + c_1_05·c_1_28·c_1_32 + c_1_08·c_1_23·c_1_34 + c_1_08·c_1_25·c_1_32
       + c_1_08·c_1_1·c_1_22·c_1_34 + c_1_08·c_1_1·c_1_24·c_1_32
       + c_1_08·c_1_12·c_1_35 + c_1_08·c_1_12·c_1_2·c_1_34
       + c_1_08·c_1_12·c_1_25 + c_1_08·c_1_14·c_1_33
       + c_1_08·c_1_14·c_1_2·c_1_32 + c_1_08·c_1_14·c_1_23 + c_1_010·c_1_2·c_1_34
       + c_1_010·c_1_24·c_1_3 + c_1_012·c_1_2·c_1_32 + c_1_012·c_1_22·c_1_3, an element of degree 15
  16. b_15_5c_1_0·c_1_12·c_1_24·c_1_38 + c_1_0·c_1_12·c_1_28·c_1_34
       + c_1_0·c_1_14·c_1_22·c_1_38 + c_1_0·c_1_14·c_1_28·c_1_32
       + c_1_0·c_1_18·c_1_22·c_1_34 + c_1_0·c_1_18·c_1_24·c_1_32
       + c_1_02·c_1_1·c_1_24·c_1_38 + c_1_02·c_1_1·c_1_28·c_1_34
       + c_1_02·c_1_14·c_1_2·c_1_38 + c_1_02·c_1_14·c_1_28·c_1_3
       + c_1_02·c_1_18·c_1_2·c_1_34 + c_1_02·c_1_18·c_1_24·c_1_3
       + c_1_04·c_1_1·c_1_22·c_1_38 + c_1_04·c_1_1·c_1_28·c_1_32
       + c_1_04·c_1_12·c_1_2·c_1_38 + c_1_04·c_1_12·c_1_28·c_1_3
       + c_1_04·c_1_18·c_1_2·c_1_32 + c_1_04·c_1_18·c_1_22·c_1_3
       + c_1_08·c_1_1·c_1_22·c_1_34 + c_1_08·c_1_1·c_1_24·c_1_32
       + c_1_08·c_1_12·c_1_2·c_1_34 + c_1_08·c_1_12·c_1_24·c_1_3
       + c_1_08·c_1_14·c_1_2·c_1_32 + c_1_08·c_1_14·c_1_22·c_1_3, an element of degree 15


About the group Ring generators Ring relations Completion information Restriction maps




Simon King
Department of Mathematics and Computer Science
Friedrich-Schiller-Universität Jena
07737 Jena
GERMANY
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46161
Fax: +49 (0)3641 9-46162
Office: Zi. 3529, Ernst-Abbe-Platz 2



Last change: 14.12.2010