Cohomology of group number 932 of order 128

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

General information on the group

  • The group is also known as Syl2(G2(3):2), the Sylow 2-subgroup of exceptional group G_2(3):2.
  • The group has 3 minimal generators and exponent 8.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 1.
  • It has 5 conjugacy classes of maximal elementary abelian subgroups, which are of rank 3, 3, 3, 3 and 4, respectively.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 2.
  • The depth exceeds the Duflot bound, which is 1.
  • The Poincaré series is
    ( − 1) · (t8  −  t7  +  t5  −  2·t4  +  2·t3  −  2·t2  +  t  −  1)
    (t  −  1)4 · (t2  +  1)2 · (t4  +  1)
  • The a-invariants are -∞,-∞,-6,-4,-4. They were obtained using the filter regular HSOP of the Benson test.

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring generators

The cohomology ring has 16 minimal generators of maximal degree 8:

  1. b_1_0, an element of degree 1
  2. b_1_1, an element of degree 1
  3. b_1_2, an element of degree 1
  4. b_2_4, an element of degree 2
  5. b_2_5, an element of degree 2
  6. b_3_8, an element of degree 3
  7. b_3_9, an element of degree 3
  8. b_4_11, an element of degree 4
  9. b_4_14, an element of degree 4
  10. b_5_17, an element of degree 5
  11. b_5_20, an element of degree 5
  12. b_5_21, an element of degree 5
  13. b_6_29, an element of degree 6
  14. b_7_38, an element of degree 7
  15. b_8_46, an element of degree 8
  16. c_8_50, a Duflot regular element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring relations

There are 76 minimal relations of maximal degree 16:

  1. b_1_0·b_1_1
  2. b_1_0·b_1_2
  3. b_1_1·b_1_22 + b_1_13
  4. b_1_12·b_1_2 + b_1_13 + b_2_4·b_1_2
  5. b_1_12·b_1_2 + b_1_13 + b_2_5·b_1_1
  6. b_2_4·b_2_5
  7. b_1_0·b_3_8 + b_2_4·b_1_1·b_1_2 + b_2_4·b_1_12
  8. b_1_0·b_3_9 + b_2_4·b_1_1·b_1_2 + b_2_4·b_1_12
  9. b_1_2·b_3_8 + b_1_1·b_3_9 + b_1_1·b_3_8
  10. b_1_1·b_1_2·b_3_9 + b_2_5·b_3_8
  11. b_2_5·b_3_8 + b_2_4·b_3_9 + b_2_4·b_3_8
  12. b_1_12·b_3_9 + b_2_5·b_3_8
  13. b_4_11·b_1_0
  14. b_4_11·b_1_1
  15. b_4_14·b_1_0
  16. b_2_4·b_4_11 + b_2_42·b_1_12
  17. b_1_2·b_5_17 + b_1_23·b_3_9 + b_4_14·b_1_22 + b_4_14·b_1_1·b_1_2 + b_4_11·b_1_22
       + b_2_4·b_1_1·b_3_9 + b_2_4·b_1_1·b_3_8
  18. b_1_1·b_5_17 + b_4_14·b_1_1·b_1_2 + b_4_14·b_1_12 + b_2_42·b_1_12
  19. b_3_92 + b_3_82 + b_1_2·b_5_20 + b_1_23·b_3_9 + b_1_16 + b_4_14·b_1_22
       + b_4_11·b_1_22 + b_2_5·b_4_14 + b_2_5·b_4_11 + b_2_4·b_1_1·b_3_9 + b_2_4·b_1_1·b_3_8
       + b_2_4·b_1_14
  20. b_1_0·b_5_20
  21. b_3_8·b_3_9 + b_3_82 + b_1_1·b_5_20 + b_1_16 + b_4_14·b_1_12
  22. b_3_92 + b_3_8·b_3_9 + b_1_2·b_5_21 + b_1_23·b_3_9 + b_1_13·b_3_8 + b_1_16
       + b_4_14·b_1_1·b_1_2 + b_4_14·b_1_12 + b_2_5·b_4_14 + b_2_5·b_4_11 + b_2_4·b_1_1·b_3_9
       + b_2_4·b_1_1·b_3_8 + b_2_4·b_1_14
  23. b_1_0·b_5_21 + b_2_42·b_1_12
  24. b_3_8·b_3_9 + b_1_1·b_5_21 + b_1_13·b_3_8 + b_1_16 + b_4_14·b_1_1·b_1_2
       + b_4_14·b_1_12 + b_2_4·b_1_1·b_3_8 + b_2_4·b_4_14
  25. b_4_11·b_3_8
  26. b_1_1·b_1_2·b_5_20 + b_1_12·b_5_20 + b_2_4·b_5_20
  27. b_2_5·b_5_21 + b_2_5·b_5_20 + b_2_5·b_4_14·b_1_2 + b_2_5·b_4_11·b_1_2 + b_2_4·b_5_20
       + b_2_4·b_1_12·b_3_8 + b_2_4·b_1_15 + b_2_4·b_4_14·b_1_2
  28. b_1_12·b_5_21 + b_1_14·b_3_8 + b_1_17 + b_2_4·b_5_20 + b_2_4·b_1_12·b_3_8
       + b_2_4·b_1_15 + b_2_4·b_4_14·b_1_2
  29. b_1_14·b_3_8 + b_6_29·b_1_2 + b_4_14·b_1_23 + b_4_14·b_1_13 + b_4_11·b_3_9
       + b_2_5·b_5_20 + b_2_5·b_4_14·b_1_2 + b_2_4·b_1_12·b_3_8 + b_2_4·b_1_15
       + b_2_4·b_4_14·b_1_2
  30. b_1_02·b_5_17 + b_6_29·b_1_0 + b_2_5·b_5_17 + b_2_5·b_1_22·b_3_9 + b_2_5·b_4_14·b_1_2
       + b_2_5·b_4_11·b_1_2 + b_2_4·b_4_14·b_1_2 + b_2_43·b_1_0
  31. b_1_14·b_3_8 + b_6_29·b_1_1 + b_2_4·b_5_20 + b_2_4·b_1_15 + b_2_4·b_4_14·b_1_1
       + b_2_43·b_1_1
  32. b_1_25·b_3_9 + b_4_14·b_1_24 + b_4_14·b_1_14 + b_4_11·b_1_24 + b_4_112
       + b_2_5·b_4_11·b_1_22 + b_2_52·b_4_14 + b_2_52·b_4_11 + b_2_4·b_1_13·b_3_8
  33. b_3_9·b_5_17 + b_3_8·b_5_17 + b_1_23·b_5_20 + b_1_25·b_3_9 + b_1_13·b_5_20
       + b_4_14·b_1_2·b_3_9 + b_4_14·b_1_24 + b_4_14·b_1_14 + b_4_11·b_1_2·b_3_9
       + b_4_11·b_1_24 + b_2_5·b_4_14·b_1_22 + b_2_5·b_4_11·b_1_22 + b_2_4·b_1_1·b_5_20
       + b_2_4·b_1_13·b_3_8 + b_2_4·b_4_14·b_1_12
  34. b_3_8·b_5_17 + b_4_14·b_1_1·b_3_9 + b_2_4·b_1_1·b_5_21 + b_2_4·b_1_13·b_3_8
       + b_2_4·b_1_16
  35. b_2_4·b_1_13·b_3_8 + b_2_4·b_1_0·b_5_17 + b_2_4·b_6_29 + b_2_42·b_4_14 + b_2_44
  36. b_3_9·b_5_21 + b_3_9·b_5_20 + b_3_8·b_5_21 + b_1_13·b_5_20 + b_1_18 + b_6_29·b_1_12
       + b_4_14·b_1_2·b_3_9 + b_4_14·b_1_14 + b_4_11·b_1_2·b_3_9 + b_2_43·b_1_12
  37. b_3_9·b_5_21 + b_3_9·b_5_17 + b_3_8·b_5_21 + b_3_8·b_5_20 + b_3_8·b_5_17 + b_1_2·b_7_38
       + b_1_18 + b_4_14·b_1_1·b_3_9 + b_4_14·b_1_1·b_3_8 + b_4_11·b_1_24 + b_4_11·b_4_14
       + b_4_112 + b_2_5·b_1_23·b_3_9
  38. b_1_0·b_7_38 + b_2_4·b_1_0·b_5_17
  39. b_3_9·b_5_21 + b_3_9·b_5_20 + b_3_9·b_5_17 + b_3_8·b_5_21 + b_3_8·b_5_20 + b_1_23·b_5_20
       + b_1_25·b_3_9 + b_1_1·b_7_38 + b_1_13·b_5_20 + b_1_18 + b_4_14·b_1_24
       + b_4_14·b_1_1·b_3_9 + b_4_14·b_1_1·b_3_8 + b_4_14·b_1_14 + b_4_11·b_1_24
       + b_2_5·b_4_14·b_1_22 + b_2_5·b_4_11·b_1_22 + b_2_42·b_1_1·b_3_8
  40. b_4_11·b_5_17 + b_4_11·b_1_22·b_3_9 + b_4_11·b_4_14·b_1_2 + b_4_112·b_1_2
  41. b_4_11·b_5_21 + b_4_11·b_5_20 + b_4_11·b_4_14·b_1_2 + b_4_112·b_1_2
  42. b_1_1·b_3_8·b_5_21 + b_6_29·b_3_8 + b_6_29·b_1_13 + b_4_14·b_5_17
       + b_4_14·b_1_22·b_3_9 + b_4_142·b_1_2 + b_4_142·b_1_1 + b_4_11·b_4_14·b_1_2
       + b_2_4·b_4_14·b_3_8 + b_2_43·b_3_8
  43. b_1_1·b_3_8·b_5_21 + b_1_14·b_5_20 + b_1_19 + b_6_29·b_3_9 + b_6_29·b_1_13
       + b_4_14·b_5_17 + b_4_14·b_1_15 + b_4_142·b_1_2 + b_4_142·b_1_1 + b_4_11·b_5_20
       + b_4_11·b_1_22·b_3_9 + b_4_112·b_1_2 + b_2_5·b_7_38 + b_2_5·b_1_22·b_5_20
       + b_2_5·b_1_24·b_3_9 + b_2_5·b_4_14·b_3_9 + b_2_5·b_4_14·b_1_23
       + b_2_52·b_1_22·b_3_9 + b_2_52·b_4_14·b_1_2 + b_2_52·b_4_11·b_1_2
       + b_2_4·b_4_14·b_3_9 + b_2_43·b_3_8
  44. b_1_1·b_3_8·b_5_21 + b_1_14·b_5_20 + b_1_19 + b_6_29·b_1_13 + b_4_14·b_1_15
       + b_2_4·b_7_38 + b_2_4·b_1_17 + b_2_4·b_4_14·b_3_9 + b_2_42·b_5_21 + b_2_42·b_5_17
       + b_2_43·b_3_8 + b_2_44·b_1_1
  45. b_1_1·b_3_8·b_5_21 + b_1_1·b_1_2·b_7_38 + b_1_12·b_7_38 + b_1_14·b_5_20 + b_1_19
       + b_6_29·b_1_13 + b_4_14·b_5_17 + b_4_14·b_1_22·b_3_9 + b_4_14·b_1_15
       + b_4_142·b_1_2 + b_4_142·b_1_1 + b_4_11·b_4_14·b_1_2 + b_2_4·b_1_17
       + b_2_4·b_4_14·b_3_9 + b_2_4·b_4_14·b_3_8
  46. b_1_22·b_7_38 + b_1_1·b_3_8·b_5_21 + b_1_1·b_1_2·b_7_38 + b_1_19 + b_8_46·b_1_2
       + b_4_14·b_5_17 + b_4_14·b_1_22·b_3_9 + b_4_14·b_1_12·b_3_8 + b_4_142·b_1_2
       + b_4_142·b_1_1 + b_4_11·b_5_20 + b_4_112·b_1_2 + b_2_5·b_1_24·b_3_9
       + b_2_5·b_4_14·b_3_9 + b_2_5·b_4_14·b_1_23 + b_2_5·b_4_11·b_3_9
       + b_2_5·b_4_11·b_1_23 + b_2_52·b_4_14·b_1_2 + b_2_4·b_1_12·b_5_20
       + b_2_4·b_4_14·b_1_13
  47. b_8_46·b_1_0 + b_6_29·b_1_03 + b_2_5·b_6_29·b_1_0 + b_2_52·b_5_17
       + b_2_52·b_1_22·b_3_9 + b_2_52·b_4_14·b_1_2 + b_2_52·b_4_11·b_1_2
       + b_2_43·b_1_03 + b_2_44·b_1_0
  48. b_1_14·b_5_20 + b_8_46·b_1_1 + b_6_29·b_1_13 + b_4_14·b_5_17 + b_4_14·b_1_22·b_3_9
       + b_4_14·b_1_12·b_3_8 + b_4_14·b_1_15 + b_4_142·b_1_2 + b_4_142·b_1_1
       + b_4_11·b_4_14·b_1_2 + b_2_4·b_1_17 + b_2_4·b_6_29·b_1_1 + b_2_4·b_4_14·b_3_9
       + b_2_4·b_4_14·b_3_8 + b_2_4·b_4_14·b_1_13
  49. b_5_17·b_5_21 + b_5_17·b_5_20 + b_4_14·b_1_23·b_3_9 + b_4_14·b_1_1·b_5_21
       + b_4_14·b_1_13·b_3_8 + b_4_14·b_1_16 + b_4_142·b_1_22 + b_4_142·b_1_1·b_1_2
       + b_4_11·b_1_23·b_3_9 + b_4_112·b_1_22 + b_2_4·b_4_14·b_1_1·b_3_8
       + b_2_43·b_1_1·b_3_8
  50. b_5_20·b_5_21 + b_5_202 + b_3_8·b_7_38 + b_6_29·b_1_1·b_3_8 + b_4_14·b_1_2·b_5_20
       + b_4_14·b_1_1·b_5_20 + b_4_14·b_1_13·b_3_8 + b_4_14·b_1_16 + b_4_142·b_1_12
       + b_4_11·b_1_2·b_5_20 + b_2_4·b_3_8·b_5_21 + b_2_4·b_6_29·b_1_12
       + b_2_4·b_4_14·b_1_1·b_3_8 + b_2_4·b_4_14·b_1_14 + b_2_4·b_4_142
       + b_2_43·b_1_1·b_3_8 + b_2_43·b_4_14 + b_2_44·b_1_12
  51. b_5_20·b_5_21 + b_5_202 + b_3_9·b_7_38 + b_1_13·b_7_38 + b_4_14·b_1_2·b_5_20
       + b_4_14·b_1_16 + b_4_14·b_6_29 + b_4_142·b_1_1·b_1_2 + b_4_11·b_1_2·b_5_20
       + b_4_11·b_1_23·b_3_9 + b_4_11·b_6_29 + b_4_11·b_4_14·b_1_22
       + b_2_5·b_4_14·b_1_2·b_3_9 + b_2_5·b_4_11·b_1_2·b_3_9 + b_2_5·b_4_11·b_4_14
       + b_2_5·b_4_112 + b_2_52·b_1_23·b_3_9 + b_2_4·b_3_8·b_5_21 + b_2_4·b_1_1·b_7_38
       + b_2_4·b_1_13·b_5_20 + b_2_4·b_1_18 + b_2_4·b_6_29·b_1_12
       + b_2_4·b_4_14·b_1_1·b_3_8 + b_2_4·b_4_14·b_1_14 + b_2_42·b_1_1·b_5_21
       + b_2_43·b_1_1·b_3_8 + c_8_50·b_1_22
  52. b_5_20·b_5_21 + b_5_202 + b_1_13·b_7_38 + b_4_14·b_1_2·b_5_20 + b_4_14·b_1_13·b_3_8
       + b_4_14·b_1_16 + b_4_142·b_1_12 + b_4_11·b_1_2·b_5_20 + b_2_4·b_1_13·b_5_20
       + b_2_4·b_1_18 + b_2_4·b_4_14·b_1_1·b_3_9 + b_2_4·b_4_14·b_1_1·b_3_8
       + c_8_50·b_1_1·b_1_2
  53. b_5_20·b_5_21 + b_5_172 + b_3_9·b_7_38 + b_1_13·b_7_38 + b_6_29·b_1_14
       + b_4_14·b_1_23·b_3_9 + b_4_14·b_1_16 + b_4_14·b_6_29 + b_4_142·b_1_1·b_1_2
       + b_4_142·b_1_12 + b_4_11·b_6_29 + b_4_11·b_4_14·b_1_22 + b_4_112·b_1_22
       + b_2_5·b_1_23·b_5_20 + b_2_5·b_4_14·b_1_2·b_3_9 + b_2_5·b_4_142
       + b_2_5·b_4_11·b_1_2·b_3_9 + b_2_5·b_4_11·b_4_14 + b_2_5·b_4_112
       + b_2_52·b_4_14·b_1_22 + b_2_53·b_4_14 + b_2_53·b_4_11 + b_2_4·b_3_8·b_5_21
       + b_2_4·b_6_29·b_1_02 + b_2_4·b_4_14·b_1_14 + c_8_50·b_1_02
  54. b_5_212 + b_5_20·b_5_21 + b_5_202 + b_5_17·b_5_21 + b_5_17·b_5_20 + b_3_9·b_7_38
       + b_1_25·b_5_20 + b_1_13·b_7_38 + b_4_14·b_1_1·b_5_20 + b_4_14·b_6_29
       + b_4_142·b_1_22 + b_4_142·b_1_1·b_1_2 + b_4_142·b_1_12 + b_4_11·b_1_23·b_3_9
       + b_4_11·b_6_29 + b_4_11·b_4_14·b_1_22 + b_4_112·b_1_22 + b_2_5·b_1_23·b_5_20
       + b_2_5·b_4_14·b_1_2·b_3_9 + b_2_5·b_4_14·b_1_24 + b_2_5·b_4_142
       + b_2_5·b_4_11·b_1_2·b_3_9 + b_2_5·b_4_11·b_4_14 + b_2_5·b_4_112
       + b_2_52·b_4_11·b_1_22 + b_2_53·b_4_14 + b_2_53·b_4_11 + b_2_4·b_3_8·b_5_21
       + b_2_4·b_1_1·b_7_38 + b_2_4·b_6_29·b_1_12 + b_2_4·b_4_14·b_1_1·b_3_9
       + b_2_4·b_4_142 + b_2_43·b_1_1·b_3_8 + b_2_43·b_4_14 + b_2_44·b_1_12
       + c_8_50·b_1_12
  55. b_5_20·b_5_21 + b_3_9·b_7_38 + b_1_13·b_7_38 + b_6_29·b_1_14 + b_4_14·b_1_16
       + b_4_14·b_6_29 + b_4_142·b_1_22 + b_4_142·b_1_1·b_1_2 + b_4_11·b_1_23·b_3_9
       + b_2_5·b_1_2·b_7_38 + b_2_5·b_1_23·b_5_20 + b_2_5·b_8_46 + b_2_5·b_6_29·b_1_02
       + b_2_5·b_4_14·b_1_2·b_3_9 + b_2_5·b_4_142 + b_2_5·b_4_11·b_4_14
       + b_2_52·b_1_23·b_3_9 + b_2_52·b_1_0·b_5_17 + b_2_52·b_4_11·b_1_22
       + b_2_53·b_4_11 + b_2_4·b_3_8·b_5_21 + b_2_4·b_1_1·b_7_38 + b_2_4·b_1_13·b_5_20
       + b_2_4·b_6_29·b_1_12 + b_2_4·b_4_14·b_1_1·b_3_9 + b_2_42·b_1_1·b_5_21
       + b_2_43·b_1_1·b_3_8 + b_2_44·b_1_12
  56. b_5_17·b_5_20 + b_1_25·b_5_20 + b_8_46·b_1_22 + b_6_29·b_1_14 + b_4_14·b_1_2·b_5_20
       + b_4_14·b_1_1·b_5_20 + b_4_14·b_1_13·b_3_8 + b_4_14·b_1_16 + b_4_11·b_1_26
       + b_4_112·b_1_22 + b_2_5·b_4_14·b_1_2·b_3_9 + b_2_5·b_4_11·b_1_2·b_3_9
       + b_2_5·b_4_11·b_1_24 + b_2_52·b_4_11·b_1_22 + b_2_4·b_1_13·b_5_20
       + b_2_4·b_1_18 + b_2_4·b_6_29·b_1_12 + b_2_4·b_4_14·b_1_14 + b_2_44·b_1_12
  57. b_2_4·b_3_8·b_5_21 + b_2_4·b_1_18 + b_2_4·b_8_46 + b_2_4·b_6_29·b_1_02
       + b_2_4·b_4_14·b_1_1·b_3_8 + b_2_42·b_1_1·b_5_21 + b_2_43·b_4_14 + b_2_44·b_1_02
       + b_2_45
  58. b_5_20·b_5_21 + b_3_9·b_7_38 + b_1_25·b_5_20 + b_1_13·b_7_38 + b_8_46·b_1_12
       + b_4_14·b_1_23·b_3_9 + b_4_14·b_1_13·b_3_8 + b_4_14·b_6_29 + b_4_142·b_1_22
       + b_4_142·b_1_1·b_1_2 + b_4_11·b_6_29 + b_4_11·b_4_14·b_1_22 + b_4_112·b_1_22
       + b_2_5·b_1_23·b_5_20 + b_2_5·b_4_14·b_1_2·b_3_9 + b_2_5·b_4_14·b_1_24
       + b_2_5·b_4_142 + b_2_5·b_4_11·b_1_2·b_3_9 + b_2_5·b_4_11·b_4_14 + b_2_5·b_4_112
       + b_2_52·b_4_11·b_1_22 + b_2_53·b_4_14 + b_2_53·b_4_11 + b_2_4·b_3_8·b_5_21
       + b_2_4·b_1_13·b_5_20 + b_2_4·b_1_18 + b_2_4·b_6_29·b_1_12 + b_2_4·b_4_14·b_1_14
       + b_2_44·b_1_12
  59. b_6_29·b_5_21 + b_6_29·b_1_12·b_3_8 + b_6_29·b_1_15 + b_4_14·b_1_22·b_5_20
       + b_4_14·b_1_24·b_3_9 + b_4_14·b_1_12·b_5_20 + b_4_11·b_7_38 + b_4_11·b_1_22·b_5_20
       + b_4_11·b_4_14·b_3_9 + b_4_112·b_3_9 + b_4_112·b_1_23 + b_2_5·b_1_24·b_5_20
       + b_2_5·b_4_14·b_5_20 + b_2_5·b_4_14·b_1_22·b_3_9 + b_2_5·b_4_11·b_4_14·b_1_2
       + b_2_5·b_4_112·b_1_2 + b_2_52·b_1_22·b_5_20 + b_2_52·b_1_24·b_3_9
       + b_2_52·b_4_11·b_1_23 + b_2_53·b_1_22·b_3_9 + b_2_4·b_1_12·b_7_38
       + b_2_4·b_6_29·b_3_8 + b_2_4·b_4_14·b_5_21 + b_2_4·b_4_14·b_5_20 + b_2_42·b_4_14·b_3_8
       + b_2_43·b_5_21 + b_2_44·b_3_8 + b_2_5·c_8_50·b_1_2 + b_2_4·c_8_50·b_1_2
  60. b_1_14·b_7_38 + b_8_46·b_1_13 + b_6_29·b_5_20 + b_4_14·b_1_22·b_5_20
       + b_4_14·b_1_24·b_3_9 + b_4_14·b_1_12·b_5_20 + b_4_142·b_1_23 + b_4_142·b_1_13
       + b_4_11·b_7_38 + b_4_11·b_1_22·b_5_20 + b_4_11·b_4_14·b_1_23 + b_4_112·b_1_23
       + b_2_5·b_1_24·b_5_20 + b_2_5·b_4_14·b_1_22·b_3_9 + b_2_5·b_4_142·b_1_2
       + b_2_5·b_4_11·b_5_20 + b_2_5·b_4_112·b_1_2 + b_2_52·b_1_22·b_5_20
       + b_2_52·b_1_24·b_3_9 + b_2_52·b_4_11·b_1_23 + b_2_53·b_1_22·b_3_9
       + b_2_4·b_6_29·b_3_8 + b_2_4·b_6_29·b_1_13 + b_2_4·b_4_14·b_1_12·b_3_8
       + b_2_4·b_4_14·b_1_15 + b_2_4·b_4_142·b_1_2 + b_2_42·b_4_14·b_3_8 + b_2_44·b_3_8
       + b_2_5·c_8_50·b_1_2
  61. b_6_29·b_5_17 + b_4_14·b_1_24·b_3_9 + b_4_142·b_1_23 + b_4_142·b_1_13
       + b_4_11·b_1_22·b_5_20 + b_4_11·b_1_24·b_3_9 + b_4_11·b_4_14·b_3_9 + b_4_112·b_3_9
       + b_4_112·b_1_23 + b_2_5·b_1_24·b_5_20 + b_2_5·b_8_46·b_1_2 + b_2_5·b_4_14·b_5_20
       + b_2_5·b_4_14·b_1_22·b_3_9 + b_2_5·b_4_142·b_1_2 + b_2_5·b_4_11·b_1_25
       + b_2_52·b_4_14·b_3_9 + b_2_52·b_4_11·b_3_9 + b_2_52·b_4_11·b_1_23
       + b_2_53·b_4_11·b_1_2 + b_2_4·b_6_29·b_1_13 + b_2_4·b_6_29·b_1_03
       + b_2_4·b_4_14·b_5_20 + b_2_4·b_4_14·b_1_12·b_3_8 + b_2_4·b_4_14·b_1_15
       + b_2_4·b_4_142·b_1_2 + b_2_4·b_4_142·b_1_1 + b_2_42·b_7_38 + b_2_42·b_4_14·b_3_8
       + b_2_43·b_5_21 + b_2_44·b_3_8 + b_2_45·b_1_1 + c_8_50·b_1_03 + b_2_5·c_8_50·b_1_0
  62. b_8_46·b_3_8 + b_6_29·b_5_20 + b_6_29·b_1_12·b_3_8 + b_4_14·b_1_22·b_5_20
       + b_4_14·b_1_24·b_3_9 + b_4_14·b_1_17 + b_4_14·b_6_29·b_1_1 + b_4_142·b_1_23
       + b_4_11·b_7_38 + b_4_11·b_1_22·b_5_20 + b_4_11·b_4_14·b_1_23 + b_4_112·b_1_23
       + b_2_5·b_1_24·b_5_20 + b_2_5·b_4_14·b_1_22·b_3_9 + b_2_5·b_4_142·b_1_2
       + b_2_5·b_4_11·b_5_20 + b_2_5·b_4_112·b_1_2 + b_2_52·b_1_22·b_5_20
       + b_2_52·b_1_24·b_3_9 + b_2_52·b_4_11·b_1_23 + b_2_53·b_1_22·b_3_9
       + b_2_4·b_6_29·b_3_8 + b_2_4·b_4_14·b_5_21 + b_2_4·b_4_14·b_1_12·b_3_8
       + b_2_4·b_4_14·b_1_15 + b_2_4·b_4_142·b_1_1 + b_2_5·c_8_50·b_1_2
  63. b_8_46·b_3_9 + b_6_29·b_5_21 + b_6_29·b_1_12·b_3_8 + b_6_29·b_1_15
       + b_4_14·b_1_22·b_5_20 + b_4_14·b_1_12·b_5_20 + b_4_11·b_1_24·b_3_9
       + b_4_11·b_4_14·b_3_9 + b_4_11·b_4_14·b_1_23 + b_4_112·b_3_9 + b_2_5·b_4_14·b_5_20
       + b_2_5·b_4_11·b_4_14·b_1_2 + b_2_52·b_1_22·b_5_20 + b_2_52·b_4_14·b_3_9
       + b_2_52·b_4_14·b_1_23 + b_2_52·b_4_11·b_1_23 + b_2_53·b_1_22·b_3_9
       + b_2_53·b_4_14·b_1_2 + b_2_53·b_4_11·b_1_2 + b_2_4·b_6_29·b_1_13
       + b_2_4·b_4_14·b_1_15 + b_2_4·b_4_142·b_1_2 + b_2_42·b_4_14·b_3_8 + b_2_43·b_5_21
       + b_2_43·b_4_14·b_1_1 + b_2_44·b_3_8 + c_8_50·b_1_23 + c_8_50·b_1_13
       + b_2_5·c_8_50·b_1_2
  64. b_5_17·b_7_38 + b_4_14·b_1_2·b_7_38 + b_4_14·b_1_1·b_7_38 + b_4_142·b_1_24
       + b_4_142·b_1_14 + b_4_11·b_1_2·b_7_38 + b_4_11·b_4_14·b_1_2·b_3_9
       + b_4_11·b_4_14·b_1_24 + b_4_112·b_1_2·b_3_9 + b_4_112·b_1_24 + b_4_113
       + b_2_5·b_4_14·b_1_2·b_5_20 + b_2_5·b_4_14·b_1_23·b_3_9 + b_2_5·b_4_142·b_1_22
       + b_2_5·b_4_11·b_1_2·b_5_20 + b_2_5·b_4_11·b_1_23·b_3_9 + b_2_52·b_4_14·b_1_24
       + b_2_52·b_4_11·b_1_24 + b_2_52·b_4_11·b_4_14 + b_2_53·b_4_11·b_1_22
       + b_2_54·b_4_14 + b_2_54·b_4_11 + b_2_4·b_4_14·b_1_1·b_5_21
       + b_2_4·b_4_14·b_1_1·b_5_20 + b_2_4·b_4_14·b_1_16 + b_2_4·b_4_14·b_6_29
       + b_2_4·b_4_142·b_1_12 + b_2_42·b_6_29·b_1_02 + b_2_42·b_4_14·b_1_1·b_3_8
       + b_2_42·b_4_142 + b_2_43·b_1_1·b_5_21 + b_2_44·b_1_1·b_3_8 + b_2_44·b_4_14
       + c_8_50·b_1_24 + c_8_50·b_1_14 + b_2_4·c_8_50·b_1_02
  65. b_5_21·b_7_38 + b_5_20·b_7_38 + b_8_46·b_1_24 + b_8_46·b_1_14 + b_6_29·b_1_1·b_5_20
       + b_6_29·b_1_13·b_3_8 + b_6_29·b_1_16 + b_6_292 + b_4_14·b_3_8·b_5_21
       + b_4_14·b_1_2·b_7_38 + b_4_14·b_1_23·b_5_20 + b_4_14·b_1_1·b_7_38
       + b_4_14·b_1_13·b_5_20 + b_4_14·b_1_18 + b_4_14·b_6_29·b_1_12
       + b_4_142·b_1_1·b_3_9 + b_4_142·b_1_1·b_3_8 + b_4_11·b_1_2·b_7_38 + b_4_11·b_1_28
       + b_4_112·b_1_24 + b_2_5·b_4_14·b_1_26 + b_2_5·b_4_142·b_1_22
       + b_2_5·b_4_11·b_1_2·b_5_20 + b_2_5·b_4_11·b_1_23·b_3_9 + b_2_5·b_4_11·b_1_26
       + b_2_5·b_4_11·b_4_14·b_1_22 + b_2_52·b_1_23·b_5_20 + b_2_52·b_4_14·b_1_24
       + b_2_52·b_4_142 + b_2_52·b_4_11·b_4_14 + b_2_52·b_4_112 + b_2_53·b_1_2·b_5_20
       + b_2_53·b_1_23·b_3_9 + b_2_53·b_4_11·b_1_22 + b_2_54·b_1_2·b_3_9
       + b_2_4·b_1_13·b_7_38 + b_2_4·b_6_29·b_1_1·b_3_8 + b_2_4·b_6_29·b_1_04
       + b_2_4·b_4_14·b_1_1·b_5_21 + b_2_4·b_4_14·b_1_1·b_5_20 + b_2_4·b_4_14·b_1_16
       + b_2_42·b_8_46 + b_2_42·b_6_29·b_1_02 + b_2_43·b_1_1·b_5_21 + b_2_44·b_1_1·b_3_8
       + b_2_45·b_1_12 + b_2_45·b_1_02 + c_8_50·b_1_1·b_3_9 + c_8_50·b_1_1·b_3_8
       + c_8_50·b_1_04 + b_2_52·c_8_50 + b_2_4·c_8_50·b_1_12
  66. b_8_46·b_1_24 + b_8_46·b_1_14 + b_6_29·b_1_13·b_3_8 + b_6_292
       + b_4_14·b_1_23·b_5_20 + b_4_14·b_1_13·b_5_20 + b_4_11·b_1_28 + b_4_112·b_1_24
       + b_2_5·b_4_14·b_1_26 + b_2_5·b_4_142·b_1_22 + b_2_5·b_4_11·b_1_2·b_5_20
       + b_2_5·b_4_11·b_1_23·b_3_9 + b_2_5·b_4_11·b_1_26 + b_2_5·b_4_11·b_4_14·b_1_22
       + b_2_52·b_1_23·b_5_20 + b_2_52·b_4_14·b_1_24 + b_2_52·b_4_142
       + b_2_52·b_4_11·b_4_14 + b_2_52·b_4_112 + b_2_53·b_1_2·b_5_20
       + b_2_53·b_1_23·b_3_9 + b_2_53·b_4_11·b_1_22 + b_2_54·b_1_2·b_3_9
       + b_2_4·b_1_13·b_7_38 + b_2_4·b_8_46·b_1_12 + b_2_4·b_6_29·b_1_14
       + b_2_4·b_6_29·b_1_04 + b_2_4·b_4_14·b_1_1·b_5_20 + b_2_4·b_4_14·b_1_16
       + b_2_4·b_4_14·b_6_29 + b_2_4·b_4_142·b_1_12 + b_2_44·b_4_14 + b_2_45·b_1_12
       + b_2_46 + c_8_50·b_1_04 + b_2_52·c_8_50
  67. b_8_46·b_1_24 + b_8_46·b_1_14 + b_4_14·b_1_23·b_5_20 + b_4_14·b_1_13·b_5_20
       + b_4_142·b_1_24 + b_4_142·b_1_14 + b_4_11·b_1_2·b_7_38 + b_4_11·b_1_28
       + b_4_11·b_8_46 + b_4_112·b_1_2·b_3_9 + b_4_112·b_1_24 + b_2_5·b_4_14·b_1_23·b_3_9
       + b_2_5·b_4_14·b_1_26 + b_2_5·b_4_14·b_6_29 + b_2_5·b_4_142·b_1_22
       + b_2_5·b_4_11·b_1_2·b_5_20 + b_2_5·b_4_11·b_1_23·b_3_9 + b_2_5·b_4_11·b_1_26
       + b_2_5·b_4_11·b_6_29 + b_2_5·b_4_11·b_4_14·b_1_22 + b_2_52·b_4_14·b_1_2·b_3_9
       + b_2_52·b_4_14·b_1_24 + b_2_52·b_4_11·b_1_2·b_3_9 + b_2_52·b_4_112
       + b_2_4·b_4_14·b_1_1·b_5_20 + b_2_4·b_4_14·b_1_16 + b_2_4·b_4_14·b_6_29
       + b_2_4·b_4_142·b_1_12 + b_2_42·b_4_142 + b_2_44·b_4_14 + b_2_45·b_1_12
  68. b_5_20·b_7_38 + b_8_46·b_1_24 + b_8_46·b_1_14 + b_6_29·b_1_1·b_5_20
       + b_6_29·b_1_13·b_3_8 + b_6_29·b_1_16 + b_4_14·b_3_8·b_5_21 + b_4_14·b_1_23·b_5_20
       + b_4_14·b_1_13·b_5_20 + b_4_14·b_1_18 + b_4_14·b_8_46 + b_4_142·b_1_2·b_3_9
       + b_4_142·b_1_1·b_3_9 + b_4_142·b_1_14 + b_4_11·b_1_2·b_7_38
       + b_4_11·b_1_23·b_5_20 + b_4_11·b_1_28 + b_4_11·b_4_14·b_1_24
       + b_4_112·b_1_2·b_3_9 + b_2_5·b_4_14·b_1_2·b_5_20 + b_2_5·b_4_14·b_1_23·b_3_9
       + b_2_5·b_4_14·b_1_26 + b_2_5·b_4_14·b_6_29 + b_2_5·b_4_142·b_1_22
       + b_2_5·b_4_11·b_1_23·b_3_9 + b_2_5·b_4_11·b_1_26 + b_2_5·b_4_11·b_6_29
       + b_2_5·b_4_11·b_4_14·b_1_22 + b_2_52·b_1_23·b_5_20 + b_2_52·b_4_142
       + b_2_52·b_4_11·b_1_24 + b_2_52·b_4_11·b_4_14 + b_2_52·b_4_112
       + b_2_53·b_4_14·b_1_22 + b_2_53·b_4_11·b_1_22 + b_2_4·b_1_13·b_7_38
       + b_2_4·b_6_29·b_1_1·b_3_8 + b_2_4·b_4_14·b_1_1·b_5_21 + b_2_4·b_4_14·b_1_1·b_5_20
       + b_2_4·b_4_14·b_6_29 + b_2_4·b_4_142·b_1_12 + b_2_42·b_4_14·b_1_1·b_3_8
       + b_2_44·b_1_1·b_3_8 + c_8_50·b_1_2·b_3_9 + c_8_50·b_1_24 + c_8_50·b_1_1·b_3_9
       + c_8_50·b_1_1·b_3_8
  69. b_8_46·b_5_17 + b_8_46·b_1_15 + b_6_29·b_7_38 + b_6_29·b_1_12·b_5_20 + b_6_292·b_1_1
       + b_4_14·b_1_24·b_5_20 + b_4_142·b_5_17 + b_4_142·b_1_25 + b_4_142·b_1_15
       + b_4_143·b_1_2 + b_4_143·b_1_1 + b_4_11·b_4_14·b_5_20 + b_4_11·b_4_14·b_1_25
       + b_4_11·b_4_142·b_1_2 + b_4_112·b_5_20 + b_4_113·b_1_2 + b_2_5·b_4_14·b_1_24·b_3_9
       + b_2_5·b_4_142·b_1_23 + b_2_5·b_4_11·b_7_38 + b_2_5·b_4_11·b_1_22·b_5_20
       + b_2_5·b_4_11·b_4_14·b_1_23 + b_2_5·b_4_112·b_1_23 + b_2_52·b_4_14·b_5_20
       + b_2_52·b_4_14·b_1_25 + b_2_52·b_4_11·b_5_20 + b_2_52·b_4_11·b_1_22·b_3_9
       + b_2_52·b_4_11·b_1_25 + b_2_52·b_4_11·b_4_14·b_1_2 + b_2_53·b_1_22·b_5_20
       + b_2_53·b_4_14·b_1_23 + b_2_4·b_6_29·b_5_20 + b_2_4·b_6_29·b_1_05
       + b_2_4·b_4_14·b_7_38 + b_2_4·b_4_14·b_1_12·b_5_20 + b_2_4·b_4_14·b_6_29·b_1_1
       + b_2_42·b_6_29·b_1_03 + b_2_43·b_4_14·b_3_8 + b_2_44·b_5_21 + b_2_45·b_3_8
       + c_8_50·b_1_25 + c_8_50·b_1_05 + b_4_11·c_8_50·b_1_2 + b_2_5·c_8_50·b_3_9
       + b_2_5·c_8_50·b_1_23 + b_2_4·c_8_50·b_3_9 + b_2_4·c_8_50·b_3_8
       + b_2_4·c_8_50·b_1_13 + b_2_4·c_8_50·b_1_03
  70. b_8_46·b_5_21 + b_8_46·b_1_15 + b_6_29·b_1_12·b_5_20 + b_6_292·b_1_1
       + b_4_14·b_6_29·b_3_8 + b_4_14·b_6_29·b_1_13 + b_4_142·b_5_17 + b_4_142·b_1_25
       + b_4_142·b_1_15 + b_4_143·b_1_2 + b_4_143·b_1_1 + b_4_11·b_4_14·b_1_22·b_3_9
       + b_4_11·b_4_14·b_1_25 + b_4_112·b_1_22·b_3_9 + b_4_112·b_1_25 + b_4_113·b_1_2
       + b_2_5·b_8_46·b_1_23 + b_2_5·b_4_14·b_7_38 + b_2_5·b_4_14·b_1_22·b_5_20
       + b_2_5·b_4_142·b_1_23 + b_2_5·b_4_11·b_7_38 + b_2_5·b_4_11·b_1_22·b_5_20
       + b_2_5·b_4_11·b_1_24·b_3_9 + b_2_5·b_4_11·b_1_27 + b_2_5·b_4_11·b_4_14·b_1_23
       + b_2_5·b_4_112·b_3_9 + b_2_5·b_4_112·b_1_23 + b_2_52·b_1_24·b_5_20
       + b_2_52·b_4_14·b_5_20 + b_2_52·b_4_14·b_1_22·b_3_9 + b_2_52·b_4_11·b_1_22·b_3_9
       + b_2_52·b_4_11·b_4_14·b_1_2 + b_2_52·b_4_112·b_1_2 + b_2_53·b_4_14·b_3_9
       + b_2_53·b_4_11·b_3_9 + b_2_53·b_4_11·b_1_23 + b_2_4·b_8_46·b_1_13
       + b_2_4·b_6_29·b_5_20 + b_2_4·b_6_29·b_1_15 + b_2_4·b_4_14·b_7_38
       + b_2_4·b_4_14·b_1_17 + b_2_4·b_4_142·b_3_9 + b_2_4·b_4_142·b_1_13
       + b_2_43·b_4_14·b_3_8 + b_2_44·b_5_21 + b_2_44·b_4_14·b_1_1 + b_2_46·b_1_1
       + c_8_50·b_1_22·b_3_9 + c_8_50·b_1_25 + c_8_50·b_1_15 + b_4_11·c_8_50·b_1_2
       + b_2_4·c_8_50·b_3_9 + b_2_4·c_8_50·b_3_8 + b_2_4·c_8_50·b_1_13
  71. b_8_46·b_5_20 + b_6_29·b_1_12·b_5_20 + b_6_29·b_1_17 + b_4_14·b_1_12·b_7_38
       + b_4_14·b_8_46·b_1_2 + b_4_142·b_5_17 + b_4_142·b_1_25 + b_4_143·b_1_2
       + b_4_143·b_1_1 + b_4_11·b_8_46·b_1_2 + b_4_11·b_4_14·b_1_22·b_3_9
       + b_4_11·b_4_14·b_1_25 + b_4_112·b_1_22·b_3_9 + b_4_112·b_1_25 + b_4_113·b_1_2
       + b_2_5·b_8_46·b_1_23 + b_2_5·b_4_14·b_7_38 + b_2_5·b_4_14·b_1_22·b_5_20
       + b_2_5·b_4_142·b_1_23 + b_2_5·b_4_11·b_7_38 + b_2_5·b_4_11·b_1_22·b_5_20
       + b_2_5·b_4_11·b_1_24·b_3_9 + b_2_5·b_4_11·b_1_27 + b_2_5·b_4_11·b_4_14·b_1_23
       + b_2_5·b_4_112·b_3_9 + b_2_5·b_4_112·b_1_23 + b_2_52·b_1_24·b_5_20
       + b_2_52·b_4_14·b_5_20 + b_2_52·b_4_14·b_1_22·b_3_9 + b_2_52·b_4_11·b_1_22·b_3_9
       + b_2_52·b_4_11·b_4_14·b_1_2 + b_2_52·b_4_112·b_1_2 + b_2_53·b_4_14·b_3_9
       + b_2_53·b_4_11·b_3_9 + b_2_53·b_4_11·b_1_23 + b_2_4·b_6_29·b_1_12·b_3_8
       + b_2_4·b_6_29·b_1_15 + b_2_4·b_4_14·b_7_38 + b_2_4·b_4_14·b_1_12·b_5_20
       + b_2_4·b_4_14·b_6_29·b_1_1 + b_2_4·b_4_142·b_3_8 + b_2_42·b_4_14·b_5_21
       + b_2_43·b_7_38 + b_2_44·b_5_21 + b_2_44·b_5_17 + b_2_45·b_3_8 + b_2_46·b_1_1
       + c_8_50·b_1_22·b_3_9 + c_8_50·b_1_25 + b_4_11·c_8_50·b_1_2 + b_2_4·c_8_50·b_3_9
       + b_2_4·c_8_50·b_3_8 + b_2_4·c_8_50·b_1_13
  72. b_8_46·b_5_20 + b_8_46·b_1_15 + b_6_29·b_7_38 + b_6_29·b_1_17 + b_6_292·b_1_1
       + b_4_14·b_1_24·b_5_20 + b_4_14·b_1_12·b_7_38 + b_4_14·b_8_46·b_1_1
       + b_4_142·b_1_25 + b_4_11·b_1_24·b_5_20 + b_4_11·b_8_46·b_1_2
       + b_4_11·b_4_14·b_5_20 + b_4_11·b_4_14·b_1_22·b_3_9 + b_4_11·b_4_14·b_1_25
       + b_4_11·b_4_142·b_1_2 + b_4_112·b_1_22·b_3_9 + b_4_112·b_1_25
       + b_2_5·b_8_46·b_1_23 + b_2_5·b_4_14·b_7_38 + b_2_5·b_4_14·b_1_22·b_5_20
       + b_2_5·b_4_14·b_1_24·b_3_9 + b_2_5·b_4_11·b_1_24·b_3_9 + b_2_5·b_4_11·b_1_27
       + b_2_5·b_4_11·b_4_14·b_3_9 + b_2_5·b_4_112·b_3_9 + b_2_52·b_1_24·b_5_20
       + b_2_52·b_4_142·b_1_2 + b_2_52·b_4_11·b_5_20 + b_2_52·b_4_11·b_1_22·b_3_9
       + b_2_52·b_4_11·b_4_14·b_1_2 + b_2_52·b_4_112·b_1_2 + b_2_53·b_1_22·b_5_20
       + b_2_53·b_4_14·b_1_23 + b_2_54·b_4_14·b_1_2 + b_2_54·b_4_11·b_1_2
       + b_2_4·b_6_29·b_5_20 + b_2_4·b_6_29·b_1_12·b_3_8 + b_2_4·b_6_29·b_1_15
       + b_2_4·b_4_142·b_3_8 + b_2_4·b_4_142·b_1_13 + b_2_42·b_6_29·b_1_03
       + b_2_42·b_4_14·b_5_21 + b_2_42·b_4_142·b_1_1 + b_2_44·b_5_21 + b_2_44·b_5_17
       + b_2_45·b_3_8 + c_8_50·b_1_22·b_3_9 + c_8_50·b_1_25 + c_8_50·b_1_15
       + b_2_5·c_8_50·b_3_9 + b_2_5·c_8_50·b_1_23 + b_2_4·c_8_50·b_1_13
       + b_2_4·c_8_50·b_1_03
  73. b_7_382 + b_6_29·b_1_13·b_5_20 + b_6_292·b_1_12 + b_4_142·b_1_2·b_5_20
       + b_4_142·b_1_1·b_5_21 + b_4_142·b_1_1·b_5_20 + b_4_142·b_1_13·b_3_8
       + b_4_142·b_1_16 + b_4_143·b_1_22 + b_4_143·b_1_1·b_1_2 + b_4_143·b_1_12
       + b_4_11·b_4_142·b_1_22 + b_4_112·b_1_23·b_3_9 + b_4_112·b_1_26
       + b_4_112·b_4_14·b_1_22 + b_4_113·b_1_22 + b_2_5·b_4_142·b_1_24
       + b_2_5·b_4_143 + b_2_5·b_4_113 + b_2_52·b_8_46·b_1_22
       + b_2_52·b_4_11·b_1_2·b_5_20 + b_2_52·b_4_11·b_1_26 + b_2_53·b_4_142
       + b_2_54·b_4_14·b_1_22 + b_2_54·b_4_11·b_1_22 + b_2_55·b_4_14 + b_2_55·b_4_11
       + b_2_4·b_8_46·b_1_14 + b_2_4·b_6_29·b_1_1·b_5_20 + b_2_4·b_6_29·b_1_16
       + b_2_4·b_6_292 + b_2_4·b_4_14·b_1_13·b_5_20 + b_2_4·b_4_14·b_1_18
       + b_2_4·b_4_142·b_1_1·b_3_9 + b_2_4·b_4_142·b_1_14 + b_2_4·b_4_143
       + b_2_42·b_6_29·b_1_04 + b_2_42·b_4_14·b_1_1·b_5_21 + b_2_43·b_6_29·b_1_02
       + b_2_43·b_4_14·b_1_1·b_3_8 + b_2_47 + c_8_50·b_1_2·b_5_20 + c_8_50·b_1_23·b_3_9
       + b_2_5·c_8_50·b_1_24 + b_2_5·b_4_14·c_8_50 + b_2_5·b_4_11·c_8_50
       + b_2_4·c_8_50·b_1_14 + b_2_4·c_8_50·b_1_04 + b_2_42·c_8_50·b_1_12
       + b_2_42·c_8_50·b_1_02
  74. b_6_29·b_1_13·b_5_20 + b_6_29·b_8_46 + b_6_292·b_1_12 + b_4_14·b_6_29·b_1_1·b_3_8
       + b_4_14·b_6_29·b_1_14 + b_4_142·b_1_26 + b_4_142·b_1_16
       + b_4_11·b_8_46·b_1_22 + b_4_11·b_4_14·b_1_2·b_5_20 + b_4_11·b_4_14·b_1_26
       + b_4_11·b_4_142·b_1_22 + b_4_112·b_1_26 + b_4_112·b_4_14·b_1_22
       + b_4_113·b_1_22 + b_2_5·b_4_14·b_1_23·b_5_20 + b_2_5·b_4_142·b_1_24
       + b_2_5·b_4_11·b_1_2·b_7_38 + b_2_5·b_4_11·b_8_46 + b_2_5·b_4_11·b_4_14·b_1_24
       + b_2_5·b_4_11·b_4_142 + b_2_52·b_8_46·b_1_22 + b_2_52·b_4_14·b_1_2·b_5_20
       + b_2_52·b_4_14·b_1_26 + b_2_52·b_4_14·b_6_29 + b_2_52·b_4_142·b_1_22
       + b_2_52·b_4_11·b_1_2·b_5_20 + b_2_52·b_4_11·b_6_29
       + b_2_52·b_4_11·b_4_14·b_1_22 + b_2_52·b_4_112·b_1_22 + b_2_53·b_1_2·b_7_38
       + b_2_53·b_1_23·b_5_20 + b_2_53·b_8_46 + b_2_53·b_6_29·b_1_02
       + b_2_53·b_4_14·b_1_2·b_3_9 + b_2_53·b_4_142 + b_2_53·b_4_11·b_1_2·b_3_9
       + b_2_53·b_4_11·b_1_24 + b_2_53·b_4_112 + b_2_54·b_1_23·b_3_9
       + b_2_54·b_1_0·b_5_17 + b_2_54·b_4_11·b_1_22 + b_2_55·b_4_14
       + b_2_4·b_6_29·b_1_16 + b_2_4·b_6_29·b_1_06 + b_2_4·b_6_292 + b_2_4·b_4_14·b_8_46
       + b_2_4·b_4_142·b_1_1·b_3_8 + b_2_42·b_6_29·b_1_04 + b_2_43·b_8_46
       + b_2_43·b_4_14·b_1_1·b_3_8 + b_2_43·b_4_142 + b_2_44·b_6_29 + b_2_45·b_4_14
       + b_2_46·b_1_12 + c_8_50·b_1_26 + c_8_50·b_1_16 + c_8_50·b_1_06
       + b_4_11·c_8_50·b_1_22 + b_2_5·c_8_50·b_1_2·b_3_9 + b_2_5·c_8_50·b_1_24
       + b_2_5·c_8_50·b_1_04 + b_2_5·b_4_11·c_8_50 + b_2_4·c_8_50·b_1_14
       + b_2_4·c_8_50·b_1_04
  75. b_8_46·b_7_38 + b_6_29·b_1_12·b_7_38 + b_6_292·b_3_8 + b_6_292·b_1_13
       + b_4_14·b_6_29·b_1_12·b_3_8 + b_4_14·b_6_29·b_1_15 + b_4_142·b_1_27
       + b_4_142·b_1_12·b_5_20 + b_4_142·b_6_29·b_1_1 + b_4_11·b_4_14·b_1_24·b_3_9
       + b_4_11·b_4_142·b_3_9 + b_4_112·b_7_38 + b_4_112·b_1_27 + b_4_112·b_4_14·b_3_9
       + b_4_112·b_4_14·b_1_23 + b_4_113·b_3_9 + b_4_113·b_1_23
       + b_2_5·b_4_14·b_1_24·b_5_20 + b_2_5·b_4_14·b_8_46·b_1_2 + b_2_5·b_4_142·b_1_25
       + b_2_5·b_4_11·b_1_24·b_5_20 + b_2_5·b_4_11·b_4_14·b_5_20
       + b_2_5·b_4_11·b_4_14·b_1_25 + b_2_5·b_4_112·b_1_25
       + b_2_5·b_4_112·b_4_14·b_1_2 + b_2_52·b_8_46·b_1_23
       + b_2_52·b_4_14·b_1_22·b_5_20 + b_2_52·b_4_14·b_1_27 + b_2_52·b_4_142·b_3_9
       + b_2_52·b_4_11·b_7_38 + b_2_52·b_4_11·b_1_22·b_5_20
       + b_2_52·b_4_11·b_1_24·b_3_9 + b_2_52·b_4_11·b_4_14·b_1_23
       + b_2_52·b_4_112·b_3_9 + b_2_52·b_4_112·b_1_23 + b_2_53·b_4_14·b_1_22·b_3_9
       + b_2_53·b_4_14·b_1_25 + b_2_53·b_4_11·b_1_22·b_3_9 + b_2_53·b_4_112·b_1_2
       + b_2_54·b_4_11·b_1_23 + b_2_4·b_6_29·b_1_12·b_5_20 + b_2_4·b_6_292·b_1_1
       + b_2_4·b_4_14·b_8_46·b_1_1 + b_2_4·b_4_14·b_6_29·b_1_13 + b_2_4·b_4_142·b_5_21
       + b_2_4·b_4_142·b_5_20 + b_2_4·b_4_142·b_1_12·b_3_8 + b_2_4·b_4_142·b_1_15
       + b_2_42·b_6_29·b_1_05 + b_2_42·b_4_14·b_7_38 + b_2_43·b_4_14·b_5_21
       + b_2_44·b_7_38 + b_2_44·b_4_14·b_3_8 + b_2_45·b_4_14·b_1_1 + b_2_46·b_3_8
       + b_2_47·b_1_1 + c_8_50·b_1_22·b_5_20 + c_8_50·b_1_24·b_3_9 + c_8_50·b_1_27
       + c_8_50·b_1_12·b_5_20 + b_6_29·c_8_50·b_1_1 + b_4_14·c_8_50·b_1_13
       + b_4_11·c_8_50·b_3_9 + b_4_11·c_8_50·b_1_23 + b_2_4·c_8_50·b_5_20
       + b_2_4·c_8_50·b_1_12·b_3_8 + b_2_4·c_8_50·b_1_05 + b_2_4·b_4_14·c_8_50·b_1_2
       + b_2_4·b_4_14·c_8_50·b_1_1 + b_2_43·c_8_50·b_1_1
  76. b_8_462 + b_6_29·b_8_46·b_1_12 + b_6_292·b_1_1·b_3_8 + b_4_14·b_8_46·b_1_14
       + b_4_14·b_6_29·b_1_16 + b_4_14·b_6_292 + b_4_142·b_1_28
       + b_4_142·b_1_13·b_5_20 + b_4_142·b_1_18 + b_4_142·b_6_29·b_1_12
       + b_4_143·b_1_24 + b_4_11·b_4_14·b_1_2·b_7_38 + b_4_11·b_4_14·b_8_46
       + b_4_112·b_1_2·b_7_38 + b_4_112·b_1_28 + b_4_112·b_4_14·b_1_2·b_3_9
       + b_4_112·b_4_14·b_1_24 + b_4_112·b_4_142 + b_4_113·b_4_14 + b_4_114
       + b_2_5·b_4_142·b_1_23·b_3_9 + b_2_5·b_4_142·b_6_29 + b_2_5·b_4_11·b_8_46·b_1_22
       + b_2_5·b_4_11·b_4_14·b_1_2·b_5_20 + b_2_5·b_4_11·b_4_14·b_1_23·b_3_9
       + b_2_5·b_4_11·b_4_142·b_1_22 + b_2_5·b_4_112·b_1_2·b_5_20
       + b_2_5·b_4_112·b_6_29 + b_2_5·b_4_112·b_4_14·b_1_22 + b_2_52·b_4_14·b_1_28
       + b_2_52·b_4_14·b_8_46 + b_2_52·b_4_142·b_1_2·b_3_9 + b_2_52·b_4_143
       + b_2_52·b_4_11·b_1_2·b_7_38 + b_2_52·b_4_11·b_1_23·b_5_20
       + b_2_52·b_4_11·b_1_28 + b_2_52·b_4_11·b_4_14·b_1_2·b_3_9
       + b_2_52·b_4_11·b_4_142 + b_2_52·b_4_112·b_1_2·b_3_9 + b_2_52·b_4_112·b_1_24
       + b_2_52·b_4_112·b_4_14 + b_2_53·b_4_14·b_1_2·b_5_20
       + b_2_53·b_4_14·b_1_23·b_3_9 + b_2_53·b_4_14·b_1_26 + b_2_53·b_4_14·b_6_29
       + b_2_53·b_4_11·b_1_2·b_5_20 + b_2_53·b_4_11·b_1_23·b_3_9 + b_2_53·b_4_11·b_6_29
       + b_2_54·b_4_14·b_1_2·b_3_9 + b_2_54·b_4_14·b_1_24 + b_2_54·b_4_142
       + b_2_54·b_4_112 + b_2_55·b_4_14·b_1_22 + b_2_55·b_4_11·b_1_22
       + b_2_4·b_6_29·b_1_1·b_7_38 + b_2_4·b_6_29·b_1_08 + b_2_4·b_6_29·b_8_46
       + b_2_4·b_6_292·b_1_12 + b_2_4·b_4_14·b_1_13·b_7_38
       + b_2_4·b_4_14·b_8_46·b_1_12 + b_2_4·b_4_14·b_6_29·b_1_14
       + b_2_4·b_4_142·b_1_16 + b_2_42·b_6_29·b_1_06 + b_2_42·b_4_14·b_8_46
       + b_2_43·b_4_14·b_1_1·b_5_21 + b_2_44·b_8_46 + b_2_45·b_1_1·b_5_21 + b_2_45·b_6_29
       + c_8_50·b_1_23·b_5_20 + c_8_50·b_1_28 + c_8_50·b_1_13·b_5_20 + c_8_50·b_1_08
       + b_4_14·c_8_50·b_1_24 + b_4_14·c_8_50·b_1_14 + b_4_11·c_8_50·b_1_24
       + b_2_5·c_8_50·b_1_26 + b_2_5·b_4_14·c_8_50·b_1_22 + b_2_52·b_4_11·c_8_50
       + b_2_4·c_8_50·b_1_1·b_5_20 + b_2_4·c_8_50·b_1_16 + b_2_4·c_8_50·b_1_06
       + b_2_4·b_4_14·c_8_50·b_1_12

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Data used for Benson′s test

  • Benson′s completion test succeeded in degree 17.
  • 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. c_8_50, a Duflot regular element of degree 8
    2. b_1_2·b_3_9 + b_1_24 + b_1_14 + b_1_04 + b_4_14 + b_4_11 + b_2_52 + b_2_42, an element of degree 4
    3. b_1_23·b_3_9 + b_1_16 + b_4_14·b_1_22 + b_4_14·b_1_1·b_1_2 + b_4_14·b_1_12
         + b_4_11·b_1_22 + b_2_5·b_1_2·b_3_9 + b_2_5·b_4_14 + b_2_5·b_4_11 + b_2_52·b_1_22
         + b_2_52·b_1_02 + b_2_4·b_1_1·b_3_8 + b_2_4·b_1_14 + b_2_4·b_4_14 + b_2_42·b_1_12
         + b_2_42·b_1_02, an element of degree 6
    4. b_2_5·b_1_22·b_3_9 + b_2_5·b_4_14·b_1_2 + b_2_5·b_4_11·b_1_2 + b_2_4·b_1_12·b_3_8
         + b_2_4·b_1_15 + b_2_4·b_4_14·b_1_2 + b_2_43·b_1_1, an element of degree 7
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 6, 14, 21].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].
  • We found that there exists some filter regular HSOP formed by the first term of the above HSOP, together with 3 elements of degree 4.

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 1

  1. b_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_2_4 → 0, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → 0, an element of degree 3
  8. b_4_11 → 0, an element of degree 4
  9. b_4_14 → 0, an element of degree 4
  10. b_5_17 → 0, an element of degree 5
  11. b_5_20 → 0, an element of degree 5
  12. b_5_21 → 0, an element of degree 5
  13. b_6_29 → 0, an element of degree 6
  14. b_7_38 → 0, an element of degree 7
  15. b_8_46 → 0, an element of degree 8
  16. c_8_50 → c_1_08, an element of degree 8

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

  1. b_1_0 → c_1_1, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_2_4 → c_1_22 + c_1_1·c_1_2, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → 0, an element of degree 3
  8. b_4_11 → 0, an element of degree 4
  9. b_4_14 → 0, an element of degree 4
  10. b_5_17 → c_1_0·c_1_12·c_1_22 + c_1_0·c_1_13·c_1_2 + c_1_02·c_1_1·c_1_22
       + c_1_02·c_1_12·c_1_2 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  11. b_5_20 → 0, an element of degree 5
  12. b_5_21 → 0, an element of degree 5
  13. b_6_29 → c_1_26 + c_1_1·c_1_25 + c_1_12·c_1_24 + c_1_13·c_1_23 + c_1_0·c_1_13·c_1_22
       + c_1_0·c_1_14·c_1_2 + c_1_02·c_1_12·c_1_22 + c_1_02·c_1_13·c_1_2
       + c_1_02·c_1_14 + c_1_04·c_1_12, an element of degree 6
  14. b_7_38 → 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
  15. b_8_46 → c_1_28 + c_1_14·c_1_24 + c_1_0·c_1_15·c_1_22 + c_1_0·c_1_16·c_1_2
       + c_1_02·c_1_14·c_1_22 + c_1_02·c_1_15·c_1_2 + c_1_02·c_1_16
       + c_1_04·c_1_14, an element of degree 8
  16. c_8_50 → c_1_28 + c_1_14·c_1_24 + c_1_0·c_1_13·c_1_24 + c_1_0·c_1_15·c_1_22
       + c_1_02·c_1_14·c_1_22 + c_1_02·c_1_15·c_1_2 + c_1_04·c_1_24
       + 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 3

  1. b_1_0 → c_1_1, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_2_4 → 0, an element of degree 2
  5. b_2_5 → c_1_22 + c_1_1·c_1_2, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → 0, an element of degree 3
  8. b_4_11 → 0, an element of degree 4
  9. b_4_14 → 0, an element of degree 4
  10. b_5_17 → c_1_0·c_1_12·c_1_22 + c_1_0·c_1_13·c_1_2 + c_1_02·c_1_1·c_1_22
       + c_1_02·c_1_12·c_1_2 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  11. b_5_20 → 0, an element of degree 5
  12. b_5_21 → 0, an element of degree 5
  13. b_6_29 → c_1_0·c_1_1·c_1_24 + c_1_0·c_1_14·c_1_2 + c_1_02·c_1_24
       + c_1_02·c_1_12·c_1_22 + c_1_02·c_1_14 + c_1_04·c_1_22 + c_1_04·c_1_1·c_1_2
       + c_1_04·c_1_12, an element of degree 6
  14. b_7_38 → 0, an element of degree 7
  15. b_8_46 → c_1_0·c_1_15·c_1_22 + c_1_0·c_1_16·c_1_2 + c_1_02·c_1_14·c_1_22
       + c_1_02·c_1_15·c_1_2 + c_1_02·c_1_16 + c_1_04·c_1_14, an element of degree 8
  16. c_8_50 → 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 3

  1. b_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_2_4 → c_1_12, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  7. b_3_9 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  8. b_4_11 → 0, an element of degree 4
  9. b_4_14 → c_1_24 + c_1_12·c_1_22, an element of degree 4
  10. b_5_17 → 0, an element of degree 5
  11. b_5_20 → 0, an element of degree 5
  12. b_5_21 → c_1_1·c_1_24 + c_1_14·c_1_2, an element of degree 5
  13. b_6_29 → c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_16, an element of degree 6
  14. b_7_38 → c_1_1·c_1_26 + c_1_12·c_1_25 + c_1_14·c_1_23 + c_1_15·c_1_22, an element of degree 7
  15. b_8_46 → c_1_12·c_1_26 + c_1_13·c_1_25 + c_1_14·c_1_24 + c_1_15·c_1_23 + c_1_18, an element of degree 8
  16. c_8_50 → c_1_28 + c_1_12·c_1_26 + c_1_13·c_1_25 + c_1_15·c_1_23 + 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

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

  1. b_1_0 → 0, an element of degree 1
  2. b_1_1 → c_1_2, an element of degree 1
  3. b_1_2 → c_1_2, an element of degree 1
  4. b_2_4 → 0, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → c_1_1·c_1_22 + c_1_12·c_1_2 + c_1_0·c_1_22 + c_1_02·c_1_2, an element of degree 3
  7. b_3_9 → 0, an element of degree 3
  8. b_4_11 → 0, an element of degree 4
  9. b_4_14 → c_1_24 + c_1_12·c_1_22 + c_1_14, an element of degree 4
  10. b_5_17 → 0, an element of degree 5
  11. b_5_20 → c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  12. b_5_21 → c_1_25 + c_1_1·c_1_24 + c_1_12·c_1_23 + c_1_0·c_1_24 + c_1_02·c_1_23, an element of degree 5
  13. b_6_29 → c_1_1·c_1_25 + c_1_12·c_1_24 + c_1_0·c_1_25 + c_1_02·c_1_24, an element of degree 6
  14. b_7_38 → c_1_27 + c_1_12·c_1_25 + c_1_13·c_1_24 + c_1_15·c_1_22 + c_1_16·c_1_2
       + c_1_0·c_1_12·c_1_24 + c_1_0·c_1_14·c_1_22 + c_1_02·c_1_25
       + c_1_02·c_1_1·c_1_24 + c_1_02·c_1_14·c_1_2 + c_1_03·c_1_24
       + c_1_04·c_1_1·c_1_22 + c_1_04·c_1_12·c_1_2 + c_1_05·c_1_22 + c_1_06·c_1_2, an element of degree 7
  15. b_8_46 → c_1_28 + c_1_12·c_1_26 + c_1_13·c_1_25 + c_1_15·c_1_23 + c_1_16·c_1_22
       + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_23 + c_1_02·c_1_26
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22 + c_1_04·c_1_24, an element of degree 8
  16. c_8_50 → c_1_28 + c_1_1·c_1_27 + c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_18
       + c_1_0·c_1_27 + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22
       + 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

  1. b_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → c_1_1, an element of degree 1
  4. b_2_4 → 0, an element of degree 2
  5. b_2_5 → c_1_22 + c_1_1·c_1_2, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_12
       + c_1_02·c_1_1, an element of degree 3
  8. b_4_11 → c_1_22·c_1_32 + c_1_23·c_1_3 + c_1_1·c_1_2·c_1_32 + c_1_12·c_1_32
       + c_1_12·c_1_2·c_1_3 + c_1_13·c_1_3 + c_1_0·c_1_1·c_1_22 + c_1_0·c_1_12·c_1_2, an element of degree 4
  9. b_4_14 → c_1_34 + c_1_23·c_1_3 + c_1_1·c_1_2·c_1_32 + c_1_12·c_1_32
       + c_1_0·c_1_1·c_1_22 + c_1_0·c_1_12·c_1_2 + c_1_0·c_1_13 + c_1_02·c_1_12, an element of degree 4
  10. b_5_17 → c_1_1·c_1_34 + 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 + c_1_13·c_1_32 + c_1_13·c_1_2·c_1_3, an element of degree 5
  11. b_5_20 → c_1_2·c_1_34 + c_1_23·c_1_32 + 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_0·c_1_12·c_1_22
       + c_1_0·c_1_13·c_1_2 + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2
       + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  12. b_5_21 → 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_12·c_1_2·c_1_32 + c_1_12·c_1_22·c_1_3 + c_1_13·c_1_2·c_1_3 + c_1_14·c_1_3
       + c_1_0·c_1_12·c_1_22 + c_1_0·c_1_13·c_1_2 + c_1_0·c_1_14
       + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_1, an element of degree 5
  13. b_6_29 → 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_2·c_1_33 + c_1_13·c_1_2·c_1_32
       + 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_22·c_1_32
       + c_1_0·c_1_12·c_1_22·c_1_3 + c_1_0·c_1_13·c_1_32 + c_1_0·c_1_14·c_1_3
       + c_1_0·c_1_15 + c_1_02·c_1_22·c_1_32 + c_1_02·c_1_23·c_1_3 + c_1_02·c_1_24
       + c_1_02·c_1_1·c_1_2·c_1_32 + 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_13·c_1_3 + c_1_02·c_1_13·c_1_2
       + c_1_02·c_1_14 + c_1_03·c_1_1·c_1_22 + c_1_03·c_1_12·c_1_2 + c_1_04·c_1_22
       + c_1_04·c_1_1·c_1_2, an element of degree 6
  14. b_7_38 → c_1_23·c_1_34 + c_1_25·c_1_32 + c_1_1·c_1_36 + 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_12·c_1_23·c_1_32 + c_1_12·c_1_24·c_1_3 + 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_14·c_1_33
       + c_1_14·c_1_22·c_1_3 + c_1_15·c_1_32 + c_1_16·c_1_3 + c_1_0·c_1_22·c_1_34
       + c_1_0·c_1_24·c_1_32 + c_1_0·c_1_1·c_1_23·c_1_32 + c_1_0·c_1_1·c_1_24·c_1_3
       + c_1_0·c_1_13·c_1_2·c_1_32 + c_1_0·c_1_14·c_1_32 + c_1_0·c_1_14·c_1_2·c_1_3
       + c_1_0·c_1_15·c_1_3 + c_1_02·c_1_2·c_1_34 + c_1_02·c_1_24·c_1_3
       + c_1_02·c_1_1·c_1_23·c_1_3 + c_1_02·c_1_12·c_1_22·c_1_3
       + c_1_02·c_1_13·c_1_22 + c_1_02·c_1_14·c_1_2 + c_1_02·c_1_15
       + c_1_03·c_1_12·c_1_22 + c_1_03·c_1_13·c_1_2 + c_1_03·c_1_14
       + c_1_04·c_1_2·c_1_32 + c_1_04·c_1_22·c_1_3 + 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
       + c_1_05·c_1_12 + c_1_06·c_1_1, an element of degree 7
  15. b_8_46 → c_1_26·c_1_32 + c_1_27·c_1_3 + c_1_1·c_1_2·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_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_2·c_1_33 + c_1_17·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_26 + 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_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_25·c_1_3
       + c_1_02·c_1_1·c_1_24·c_1_3 + 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_02·c_1_16
       + c_1_03·c_1_1·c_1_24 + c_1_03·c_1_14·c_1_2 + c_1_03·c_1_15
       + 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_22·c_1_3
       + c_1_04·c_1_12·c_1_2·c_1_3 + c_1_05·c_1_1·c_1_22 + c_1_05·c_1_12·c_1_2
       + c_1_05·c_1_13 + c_1_06·c_1_12, an element of degree 8
  16. c_8_50 → c_1_38 + c_1_22·c_1_36 + c_1_23·c_1_35 + c_1_24·c_1_34 + c_1_25·c_1_33
       + c_1_26·c_1_32 + 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_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_13·c_1_35 + c_1_13·c_1_2·c_1_34 + c_1_13·c_1_23·c_1_32
       + c_1_14·c_1_2·c_1_33 + c_1_14·c_1_22·c_1_32 + 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_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_13·c_1_34 + c_1_0·c_1_13·c_1_24
       + 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_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_15·c_1_3 + c_1_02·c_1_15·c_1_2 + c_1_02·c_1_16 + c_1_03·c_1_15
       + 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_12·c_1_2·c_1_3 + 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_05·c_1_13 + c_1_06·c_1_12 + c_1_08, an element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128


Simon A. King David J. Green
Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik
Friedrich-Schiller-Universität Jena Friedrich-Schiller-Universität Jena
Ernst-Abbe-Platz 2 Ernst-Abbe-Platz 2
D-07743 Jena D-07743 Jena
Germany Germany
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46184
Fax: +49 (0)3641 9-46162
Office: Zi. 3524, Ernst-Abbe-Platz 2
E-mail: david dot green at uni hyphen jena dot de
Tel: +49 3641 9-46166
Fax: +49 3641 9-46162
Office: Zi 3512, Ernst-Abbe-Platz 2

Last change: 25.08.2009