Cohomology of group number 559 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 has 3 minimal generators and exponent 8.
  • It is non-abelian.
  • It has p-Rank 3.
  • Its center has rank 1.
  • It has 3 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 3.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 3 and depth 1.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 2) · (t6  +  1/2·t4  +  1/2·t2  +  1/2·t  +  1/2)
    (t  +  1) · (t  −  1)3 · (t2  +  1) · (t4  +  1)
  • The a-invariants are -∞,-4,-3,-3. 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 18 minimal generators of maximal degree 8:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_2, a nilpotent element of degree 1
  3. b_1_1, an element of degree 1
  4. a_2_3, a nilpotent element of degree 2
  5. b_2_4, an element of degree 2
  6. b_2_5, an element of degree 2
  7. a_3_7, a nilpotent element of degree 3
  8. a_4_6, a nilpotent element of degree 4
  9. b_4_11, an element of degree 4
  10. b_4_12, an element of degree 4
  11. b_5_15, an element of degree 5
  12. b_5_16, an element of degree 5
  13. a_6_13, a nilpotent element of degree 6
  14. b_6_22, an element of degree 6
  15. b_7_27, an element of degree 7
  16. b_7_28, an element of degree 7
  17. a_8_23, a nilpotent element of degree 8
  18. c_8_35, 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 111 minimal relations of maximal degree 16:

  1. a_1_02
  2. a_1_0·a_1_2
  3. a_1_0·b_1_1 + a_1_22
  4. a_1_22·b_1_1
  5. a_2_3·a_1_0
  6. b_2_4·a_1_0 + a_2_3·a_1_2
  7. b_2_4·a_1_2 + a_2_3·b_1_1 + a_2_3·a_1_2
  8. a_2_32
  9. a_2_3·b_1_12 + a_2_3·b_2_4
  10. b_2_5·b_1_12 + b_2_42
  11. b_2_5·a_1_2·b_1_1 + a_2_3·b_1_12
  12. b_2_5·a_1_22
  13. a_1_0·a_3_7
  14. b_2_4·b_1_12 + b_2_42 + a_2_3·b_1_12 + a_1_2·a_3_7 + a_2_3·a_1_2·b_1_1
  15. a_2_3·b_2_5·b_1_1 + a_2_3·b_2_4·b_1_1 + a_2_3·b_2_5·a_1_2
  16. b_2_4·b_2_5·b_1_1 + b_2_42·b_1_1 + a_2_3·b_2_4·b_1_1 + a_2_3·a_3_7
  17. b_1_12·a_3_7 + a_4_6·b_1_1 + b_2_4·a_3_7 + a_2_3·b_2_5·b_1_1 + a_1_2·b_1_1·a_3_7
  18. a_4_6·a_1_0
  19. b_2_4·b_2_5·b_1_1 + b_2_42·b_1_1 + a_2_3·b_2_5·b_1_1 + a_1_2·b_1_1·a_3_7 + a_4_6·a_1_2
  20. b_4_11·b_1_1 + b_2_4·b_2_5·b_1_1 + b_2_5·a_3_7 + a_2_3·b_2_5·b_1_1 + a_1_2·b_1_1·a_3_7
  21. b_2_52·b_1_1 + b_2_42·b_1_1 + b_4_11·a_1_0 + b_2_52·a_1_2 + a_2_3·b_2_4·b_1_1
  22. b_2_52·b_1_1 + b_2_42·b_1_1 + b_4_11·a_1_2 + b_2_5·a_3_7 + b_2_52·a_1_2 + b_2_4·a_3_7
       + a_2_3·b_2_5·b_1_1 + a_2_3·b_2_4·b_1_1
  23. b_4_12·a_1_0
  24. a_3_72
  25. b_2_4·a_4_6 + a_2_3·b_2_42
  26. a_2_3·a_4_6
  27. b_2_5·a_4_6 + a_2_3·b_4_11 + a_2_3·b_2_52 + a_2_3·b_2_42 + a_2_3·b_1_1·a_3_7
  28. a_1_0·b_5_15
  29. a_1_2·b_5_15 + b_4_12·a_1_2·b_1_1 + a_2_3·b_4_12 + a_2_3·b_2_42
  30. a_1_0·b_5_16
  31. b_1_1·b_5_15 + b_4_12·b_1_12 + b_2_4·b_4_12 + b_2_43 + a_1_2·b_5_16 + a_2_3·b_2_42
       + a_4_6·a_1_2·b_1_1 + a_2_3·b_1_1·a_3_7
  32. a_4_6·a_3_7 + a_2_3·b_2_4·a_3_7
  33. b_4_11·a_3_7 + b_2_5·b_4_12·a_1_2 + b_2_52·a_3_7 + a_2_3·b_4_12·b_1_1
       + a_2_3·b_2_5·a_3_7 + a_2_3·b_2_4·a_3_7
  34. b_4_11·a_3_7 + b_2_52·a_3_7 + a_2_3·b_5_15 + a_2_3·b_2_42·b_1_1 + a_2_3·b_2_5·a_3_7
       + a_2_3·b_2_4·a_3_7
  35. b_2_5·b_4_12·b_1_1 + b_2_4·b_4_12·b_1_1 + a_1_2·b_1_1·b_5_16 + b_4_12·a_1_2·b_1_12
       + b_2_5·b_4_12·a_1_2 + a_2_3·b_2_42·b_1_1
  36. b_2_5·b_4_12·b_1_1 + b_2_4·b_5_15 + b_2_4·b_4_12·b_1_1 + b_2_43·b_1_1 + a_2_3·b_5_16
       + a_2_3·b_2_5·a_3_7 + a_2_3·b_2_52·a_1_2 + a_2_3·b_2_4·a_3_7
  37. b_2_5·b_4_12·b_1_1 + b_2_4·b_5_16 + b_2_43·b_1_1 + a_6_13·b_1_1 + b_4_12·a_1_2·b_1_12
       + a_4_6·b_1_13 + b_2_5·b_4_12·a_1_2 + a_2_3·b_2_5·a_3_7 + a_2_3·b_2_52·a_1_2
  38. a_6_13·a_1_0
  39. b_2_5·b_4_12·b_1_1 + b_2_4·b_5_15 + b_2_4·b_4_12·b_1_1 + b_2_43·b_1_1
       + b_2_5·b_4_12·a_1_2 + a_2_3·b_2_42·b_1_1 + a_6_13·a_1_2 + a_4_6·a_1_2·b_1_12
       + a_2_3·b_2_52·a_1_2
  40. b_6_22·a_1_0 + b_2_5·b_4_11·a_1_0
  41. b_1_12·b_5_16 + b_4_12·b_1_13 + b_2_4·b_5_15 + b_6_22·a_1_2 + b_4_12·a_3_7
       + b_4_11·a_3_7 + b_2_5·b_4_12·a_1_2 + b_2_5·b_4_11·a_1_0 + b_2_42·a_3_7
       + a_2_3·b_2_42·b_1_1 + a_2_3·b_2_5·a_3_7
  42. a_4_62
  43. b_4_112 + b_2_52·b_4_12 + b_2_52·b_4_11 + b_2_42·b_4_12 + b_2_42·b_1_1·a_3_7
       + a_2_3·b_2_53 + a_2_3·b_2_43
  44. a_4_6·b_4_11 + a_2_3·b_2_5·b_4_12 + a_2_3·b_2_4·b_4_12 + a_2_3·b_2_43
       + a_2_3·b_2_4·b_1_1·a_3_7
  45. a_3_7·b_5_15 + a_4_6·b_4_12 + b_2_42·b_1_1·a_3_7 + a_2_3·b_2_5·b_4_12
       + a_2_3·b_2_4·b_1_1·a_3_7
  46. b_4_112 + b_2_52·b_4_12 + b_2_52·b_4_11 + b_2_4·b_2_5·b_4_12 + a_4_6·b_4_11
       + b_2_5·a_1_2·b_5_16 + b_2_42·b_1_1·a_3_7 + a_2_3·b_2_53 + a_2_3·b_2_43
       + a_2_3·b_2_4·b_1_1·a_3_7
  47. b_2_5·b_1_1·b_5_16 + b_2_4·b_2_5·b_4_12 + b_2_44 + a_6_13·b_1_12
       + b_4_12·a_1_2·b_1_13 + a_4_6·b_1_14 + a_2_3·b_2_5·b_4_12 + b_4_12·a_1_2·a_3_7
       + a_2_3·b_2_4·b_1_1·a_3_7
  48. b_2_5·b_1_1·b_5_16 + b_2_4·b_2_5·b_4_12 + b_2_44 + a_4_6·b_4_11 + b_2_4·a_6_13
  49. b_4_112 + b_2_52·b_4_12 + b_2_52·b_4_11 + b_2_4·b_2_5·b_4_12 + a_4_6·b_4_11
       + b_2_42·b_1_1·a_3_7 + a_2_3·b_2_5·b_4_12 + a_2_3·b_2_53 + a_2_3·a_6_13
       + a_2_3·b_2_4·b_1_1·a_3_7
  50. b_4_11·b_4_12 + b_2_5·b_6_22 + b_2_52·b_4_11 + b_2_4·b_6_22 + b_2_4·b_2_5·b_4_12
       + b_2_4·b_2_5·b_4_11 + a_3_7·b_5_16 + b_4_12·b_1_1·a_3_7 + a_4_6·b_4_11 + b_2_5·a_6_13
       + b_2_42·b_1_1·a_3_7 + a_2_3·b_2_5·b_4_12 + a_2_3·b_2_5·b_4_11 + a_2_3·b_2_43
       + a_6_13·a_1_2·b_1_1 + b_4_12·a_1_2·a_3_7 + a_4_6·a_1_2·b_1_13
  51. b_4_112 + b_2_5·b_1_1·b_5_16 + b_2_52·b_4_12 + b_2_52·b_4_11 + b_2_44
       + b_4_12·b_1_1·a_3_7 + a_4_6·b_4_12 + b_2_42·b_1_1·a_3_7 + a_2_3·b_6_22
       + a_2_3·b_2_5·b_4_11 + a_2_3·b_2_53 + a_2_3·b_2_43 + a_6_13·a_1_2·b_1_1
       + b_4_12·a_1_2·a_3_7 + a_4_6·a_1_2·b_1_13 + a_2_3·b_2_4·b_1_1·a_3_7
  52. b_1_1·b_7_27 + b_4_11·b_4_12 + b_4_112 + b_2_5·b_1_1·b_5_16 + b_2_5·b_6_22
       + b_2_52·b_4_12 + b_6_22·a_1_2·b_1_1 + b_4_12·b_1_1·a_3_7 + b_2_5·a_6_13
       + a_2_3·b_2_5·b_4_11 + a_2_3·b_2_53 + a_2_3·b_2_43 + a_4_6·a_1_2·b_1_13
       + a_2_3·b_2_4·b_1_1·a_3_7
  53. a_1_0·b_7_27
  54. b_2_5·b_1_1·b_5_16 + b_2_4·b_2_5·b_4_12 + b_2_44 + a_1_2·b_7_27 + b_4_12·b_1_1·a_3_7
       + a_4_6·b_4_12 + a_4_6·b_4_11 + a_6_13·a_1_2·b_1_1 + a_4_6·a_1_2·b_1_13
       + a_2_3·b_2_4·b_1_1·a_3_7
  55. a_1_0·b_7_28
  56. a_3_7·b_5_16 + a_1_2·b_7_28 + b_6_22·a_1_2·b_1_1 + b_4_12·b_1_1·a_3_7
       + b_4_12·a_1_2·b_1_13 + a_4_6·b_4_11 + b_2_42·b_1_1·a_3_7 + a_2_3·b_2_5·b_4_12
       + a_6_13·a_1_2·b_1_1 + b_4_12·a_1_2·a_3_7 + a_4_6·a_1_2·b_1_13
  57. a_4_6·b_5_15 + a_4_6·b_4_12·b_1_1 + b_2_5·b_4_12·a_3_7 + b_2_4·b_4_12·a_3_7
       + a_2_3·b_2_5·b_5_15 + a_2_3·b_2_4·b_4_12·b_1_1 + a_4_6·b_4_12·a_1_2
       + a_2_3·b_4_12·a_3_7
  58. b_2_5·a_6_13·b_1_1 + b_2_4·b_4_12·a_3_7 + a_2_3·b_6_22·b_1_1 + b_2_5·a_6_13·a_1_2
       + a_2_3·b_2_52·a_3_7
  59. b_4_11·b_5_15 + b_2_5·b_7_27 + b_2_52·b_5_15 + b_2_4·b_6_22·b_1_1
       + b_2_42·b_4_12·b_1_1 + a_4_6·b_5_16 + a_4_6·b_4_12·b_1_1 + b_2_54·a_1_2
       + b_2_43·a_3_7 + a_2_3·b_2_5·b_5_15 + a_2_3·b_2_4·b_4_12·b_1_1 + a_2_3·b_2_43·b_1_1
       + a_6_13·a_3_7 + b_2_5·a_6_13·a_1_2 + a_2_3·b_2_53·a_1_2 + a_2_3·b_2_42·a_3_7
  60. b_2_4·b_7_27 + b_2_4·b_6_22·b_1_1 + b_2_42·b_4_12·b_1_1 + a_4_6·b_5_16
       + a_4_6·b_4_12·b_1_1 + b_2_5·a_6_13·b_1_1 + b_2_5·b_4_12·a_3_7 + a_2_3·b_2_5·b_5_15
       + b_2_5·a_6_13·a_1_2 + a_2_3·b_4_12·a_3_7 + a_2_3·b_2_53·a_1_2
  61. b_2_5·a_6_13·b_1_1 + b_2_5·b_4_12·a_3_7 + a_2_3·b_7_27 + a_2_3·b_2_5·b_5_15
       + a_2_3·b_2_4·b_4_12·b_1_1 + a_2_3·b_2_43·b_1_1 + b_2_5·a_6_13·a_1_2
       + a_2_3·b_4_12·a_3_7 + a_2_3·b_2_53·a_1_2 + a_2_3·b_2_42·a_3_7
  62. b_1_12·b_7_28 + b_6_22·b_1_13 + b_4_12·b_1_15 + b_2_42·b_4_12·b_1_1
       + b_2_44·b_1_1 + b_6_22·a_3_7 + b_4_122·a_1_2 + a_4_6·b_5_16 + b_2_5·a_6_13·b_1_1
       + b_2_53·a_3_7 + b_2_43·a_3_7 + a_2_3·b_2_4·b_4_12·b_1_1 + a_4_6·b_4_12·a_1_2
       + a_2_3·b_2_42·a_3_7
  63. a_1_2·b_1_1·b_7_28 + b_6_22·a_1_2·b_1_12 + b_4_12·a_1_2·b_1_14 + a_4_6·b_5_16
       + a_4_6·b_4_12·b_1_1 + b_2_5·b_4_12·a_3_7 + b_2_4·b_4_12·a_3_7 + a_2_3·b_2_5·b_5_15
       + a_2_3·b_2_4·b_4_12·b_1_1 + a_2_3·b_2_43·b_1_1 + a_6_13·a_3_7 + b_2_5·a_6_13·a_1_2
  64. b_4_11·b_5_16 + b_2_5·b_7_28 + b_2_4·b_7_28 + b_2_42·b_4_12·b_1_1 + b_2_44·b_1_1
       + a_4_6·b_5_16 + a_4_6·b_4_12·b_1_1 + b_2_53·a_3_7 + a_2_3·b_2_5·b_5_15
       + a_2_3·b_2_4·b_4_12·b_1_1 + a_6_13·a_3_7 + a_4_6·b_4_12·a_1_2 + b_2_5·a_6_13·a_1_2
  65. b_2_5·a_6_13·b_1_1 + b_2_5·b_4_12·a_3_7 + a_2_3·b_7_28 + a_2_3·b_2_43·b_1_1
       + a_6_13·a_3_7 + a_4_6·b_4_12·a_1_2 + b_2_5·a_6_13·a_1_2 + a_2_3·b_2_42·a_3_7
  66. b_4_11·b_5_16 + b_2_5·b_7_28 + b_2_4·b_6_22·b_1_1 + b_2_42·b_4_12·b_1_1 + a_8_23·b_1_1
       + b_6_22·a_3_7 + b_6_22·a_1_2·b_1_12 + b_4_122·a_1_2 + b_2_43·a_3_7
       + a_2_3·b_2_5·b_5_15 + a_2_3·b_2_43·b_1_1 + a_6_13·a_3_7 + a_4_6·a_1_2·b_1_14
       + a_2_3·b_4_12·a_3_7 + a_2_3·b_2_52·a_3_7 + a_2_3·b_2_53·a_1_2
  67. a_8_23·a_1_0 + a_2_3·b_2_53·a_1_2
  68. a_4_6·b_5_16 + a_4_6·b_4_12·b_1_1 + b_2_5·b_4_12·a_3_7 + b_2_4·b_4_12·a_3_7
       + a_2_3·b_2_5·b_5_15 + a_8_23·a_1_2 + b_2_5·a_6_13·a_1_2 + a_2_3·b_2_53·a_1_2
  69. b_5_152 + b_4_122·b_1_12 + b_2_5·b_4_122 + b_2_45 + a_2_3·b_2_44
       + a_2_3·b_2_42·b_1_1·a_3_7
  70. b_5_15·b_5_16 + b_4_12·b_1_1·b_5_16 + b_2_5·b_4_122 + b_2_45 + b_4_12·a_6_13
       + a_4_6·b_4_12·b_1_12 + b_2_42·a_6_13 + a_2_3·b_4_122 + a_2_3·b_2_5·b_6_22
       + a_2_3·b_2_52·b_4_11 + a_2_3·b_2_4·b_6_22 + a_4_6·b_4_12·a_1_2·b_1_1
       + a_2_3·b_2_5·a_6_13 + a_2_3·b_2_4·a_6_13 + a_2_3·b_2_42·b_1_1·a_3_7
  71. b_5_15·b_5_16 + b_4_12·b_1_1·b_5_16 + b_4_11·b_6_22 + b_2_52·b_6_22 + b_2_53·b_4_12
       + b_2_4·b_4_122 + b_2_43·b_4_12 + b_2_45 + b_6_22·b_1_1·a_3_7 + b_4_12·a_1_2·b_5_16
       + b_4_12·a_6_13 + b_4_122·a_1_2·b_1_1 + b_4_11·a_6_13 + a_4_6·b_6_22
       + a_4_6·b_4_12·b_1_12 + b_2_52·a_6_13 + b_2_42·a_6_13 + a_2_3·b_2_5·b_6_22
       + a_2_3·b_2_52·b_4_12 + a_2_3·b_2_52·b_4_11 + a_2_3·b_2_54 + a_2_3·b_2_42·b_4_12
       + a_2_3·b_2_44 + a_6_13·b_1_1·a_3_7 + a_2_3·b_2_5·a_6_13 + a_2_3·b_2_42·b_1_1·a_3_7
  72. a_3_7·b_7_27 + b_6_22·b_1_1·a_3_7 + a_4_6·b_6_22 + b_2_42·a_6_13 + a_2_3·b_2_52·b_4_12
       + a_2_3·b_2_42·b_4_12 + a_6_13·b_1_1·a_3_7 + a_4_6·a_6_13 + a_2_3·b_2_42·b_1_1·a_3_7
  73. b_5_15·b_5_16 + b_4_12·b_1_1·b_5_16 + b_2_5·b_4_122 + b_2_45 + a_3_7·b_7_28
       + b_6_22·b_1_1·a_3_7 + b_4_12·a_1_2·b_5_16 + b_4_12·a_6_13 + b_4_122·a_1_2·b_1_1
       + b_2_42·a_6_13 + b_2_43·b_1_1·a_3_7 + a_2_3·b_4_122 + a_2_3·b_2_44
       + a_6_13·b_1_1·a_3_7 + a_4_6·a_6_13 + a_2_3·b_2_5·a_6_13
  74. b_2_5·a_1_2·b_7_28 + a_2_3·b_2_5·b_6_22 + a_2_3·b_2_52·b_4_11 + a_6_13·b_1_1·a_3_7
       + a_4_6·a_6_13 + a_2_3·b_2_42·b_1_1·a_3_7
  75. b_5_162 + b_4_122·b_1_12 + b_2_5·b_4_122 + b_2_4·b_4_122 + b_2_45
       + b_4_12·a_1_2·b_5_16 + b_4_122·a_1_2·b_1_1 + a_2_3·b_4_122 + a_2_3·b_2_42·b_4_12
       + a_2_3·b_2_44 + a_2_3·b_2_42·b_1_1·a_3_7 + c_8_35·a_1_22
  76. b_5_15·b_5_16 + b_4_12·b_1_1·b_5_16 + b_2_5·b_4_122 + b_2_45 + a_8_23·b_1_12
       + b_6_22·a_1_2·b_1_13 + b_4_12·a_6_13 + b_4_122·a_1_2·b_1_1 + a_4_6·b_6_22
       + a_4_6·b_4_12·b_1_12 + a_2_3·b_2_5·b_6_22 + a_2_3·b_2_52·b_4_12
       + a_2_3·b_2_52·b_4_11 + a_6_13·b_1_1·a_3_7 + a_4_6·a_1_2·b_1_15 + a_4_6·a_6_13
       + a_4_6·b_4_12·a_1_2·b_1_1 + a_2_3·b_2_5·a_6_13 + a_2_3·b_2_4·a_6_13
  77. b_2_4·b_2_54 + b_2_45 + b_4_11·a_6_13 + b_2_5·a_8_23 + a_2_3·b_2_5·b_6_22
       + a_2_3·b_2_52·b_4_11 + a_2_3·b_2_54 + a_2_3·b_2_42·b_4_12 + a_4_6·a_6_13
       + a_4_6·b_4_12·a_1_2·b_1_1 + a_2_3·b_2_5·a_6_13 + a_2_3·b_2_4·a_6_13
  78. b_5_15·b_5_16 + b_4_12·b_1_1·b_5_16 + b_2_5·b_4_122 + b_2_45 + b_4_12·a_6_13
       + a_4_6·b_4_12·b_1_12 + b_2_4·a_8_23 + a_2_3·b_4_122 + a_2_3·b_2_5·b_6_22
       + a_2_3·b_2_52·b_4_11 + a_2_3·b_2_42·b_4_12 + a_6_13·b_1_1·a_3_7 + a_2_3·b_2_5·a_6_13
       + a_2_3·b_2_4·a_6_13
  79. a_4_6·a_6_13 + a_4_6·b_4_12·a_1_2·b_1_1 + a_2_3·a_8_23 + a_2_3·b_2_5·a_6_13
       + a_2_3·b_2_4·a_6_13
  80. b_2_5·b_4_12·b_5_16 + b_2_5·b_4_12·b_5_15 + b_2_4·b_4_122·b_1_1 + a_6_13·b_5_15
       + b_4_12·a_1_2·b_1_1·b_5_16 + b_4_12·a_6_13·b_1_1 + b_4_122·a_1_2·b_1_12
       + b_2_42·b_4_12·a_3_7 + a_2_3·b_2_5·b_7_27 + a_2_3·b_2_52·b_5_15
       + a_2_3·b_2_44·b_1_1 + a_4_6·b_4_12·a_1_2·b_1_12 + a_2_3·b_2_54·a_1_2
       + a_2_3·b_2_43·a_3_7
  81. b_2_5·b_4_12·b_5_16 + b_2_5·b_4_12·b_5_15 + b_2_4·b_4_122·b_1_1 + a_6_13·b_5_15
       + b_4_12·a_1_2·b_1_1·b_5_16 + b_4_12·a_6_13·b_1_1 + b_4_122·a_1_2·b_1_12
       + a_4_6·b_7_27 + b_2_42·b_4_12·a_3_7 + a_2_3·b_4_12·b_5_15 + a_2_3·b_2_52·b_5_15
       + a_2_3·b_2_42·b_4_12·b_1_1 + a_2_3·b_2_44·b_1_1 + a_4_6·b_6_22·a_1_2
       + a_4_6·b_4_12·a_1_2·b_1_12 + a_2_3·b_2_53·a_3_7 + a_2_3·b_2_54·a_1_2
  82. b_4_11·b_7_27 + b_2_5·b_4_12·b_5_16 + b_2_4·b_4_122·b_1_1 + b_2_42·b_6_22·b_1_1
       + a_6_13·b_5_15 + b_4_12·a_1_2·b_1_1·b_5_16 + b_4_12·a_6_13·b_1_1
       + b_4_122·a_1_2·b_1_12 + b_2_53·b_4_11·a_1_0 + b_2_54·a_3_7 + b_2_4·b_6_22·a_3_7
       + b_2_44·a_3_7 + a_2_3·b_4_12·b_5_15 + a_2_3·b_2_52·b_5_15 + a_2_3·b_2_44·b_1_1
       + a_4_6·b_4_12·a_1_2·b_1_12 + a_2_3·b_2_54·a_1_2 + a_2_3·b_2_4·b_4_12·a_3_7
  83. b_6_22·b_5_15 + b_4_12·b_7_27 + b_4_12·b_6_22·b_1_1 + b_2_5·b_4_12·b_5_16
       + b_2_52·b_7_27 + b_2_53·b_5_15 + b_2_45·b_1_1 + b_4_12·a_1_2·b_1_1·b_5_16
       + b_4_122·a_3_7 + b_4_122·a_1_2·b_1_12 + b_2_55·a_1_2 + a_2_3·b_2_52·b_5_15
       + a_2_3·b_2_42·b_4_12·b_1_1 + b_4_12·a_6_13·a_1_2 + a_4_6·b_6_22·a_1_2
       + a_2_3·b_2_53·a_3_7 + a_2_3·b_2_54·a_1_2 + a_2_3·b_2_4·b_4_12·a_3_7
       + a_2_3·b_2_43·a_3_7
  84. b_4_12·a_1_2·b_1_1·b_5_16 + b_4_122·a_1_2·b_1_12 + a_4_6·b_7_28
       + a_4_6·b_6_22·b_1_1 + a_4_6·b_4_12·b_1_13 + a_2_3·b_4_12·b_5_15
       + a_2_3·b_2_42·b_4_12·b_1_1 + a_2_3·b_2_44·b_1_1 + b_4_12·a_6_13·a_1_2
       + a_4_6·b_4_12·a_1_2·b_1_12 + a_2_3·b_6_22·a_3_7 + a_2_3·b_2_53·a_3_7
       + a_2_3·b_2_4·b_4_12·a_3_7 + a_2_3·b_2_43·a_3_7
  85. b_4_11·b_7_28 + b_2_5·b_4_12·b_5_16 + b_2_52·b_7_28 + b_2_4·b_4_122·b_1_1
       + b_2_43·b_4_12·b_1_1 + b_4_12·a_6_13·b_1_1 + b_4_122·a_1_2·b_1_12
       + a_4_6·b_4_12·b_1_13 + b_2_4·b_6_22·a_3_7 + b_2_44·a_3_7 + a_2_3·b_4_12·b_5_15
       + a_2_3·b_4_122·b_1_1 + a_4_6·b_6_22·a_1_2 + a_4_6·b_4_12·a_1_2·b_1_12
       + b_2_52·a_6_13·a_1_2 + a_2_3·b_2_53·a_3_7 + a_2_3·b_2_4·b_4_12·a_3_7
  86. b_6_22·b_5_16 + b_4_12·b_7_28 + b_4_122·b_1_13 + b_2_52·b_7_28
       + b_2_4·b_4_122·b_1_1 + b_2_43·b_4_12·b_1_1 + b_2_45·b_1_1 + b_6_22·a_1_2·b_1_14
       + a_6_13·b_5_16 + b_4_12·a_1_2·b_1_1·b_5_16 + b_4_12·b_6_22·a_1_2 + b_4_12·a_6_13·b_1_1
       + b_4_122·a_3_7 + b_2_54·a_3_7 + b_2_4·b_6_22·a_3_7 + b_2_44·a_3_7
       + a_2_3·b_4_122·b_1_1 + b_4_12·a_6_13·a_1_2 + a_4_6·a_1_2·b_1_16
       + a_2_3·b_6_22·a_3_7 + a_2_3·b_2_43·a_3_7 + c_8_35·a_1_2·b_1_12
  87. a_6_13·b_5_16 + a_6_13·b_5_15 + b_4_12·a_6_13·b_1_1 + b_4_122·a_1_2·b_1_12
       + a_4_6·b_4_12·b_1_13 + a_2_3·b_4_122·b_1_1 + a_2_3·b_2_42·b_4_12·b_1_1
       + b_4_12·a_6_13·a_1_2 + a_4_6·b_6_22·a_1_2 + b_2_5·a_6_13·a_3_7 + a_2_3·b_6_22·a_3_7
       + a_2_3·b_2_53·a_3_7 + a_2_3·b_2_54·a_1_2 + a_2_3·b_2_43·a_3_7 + a_2_3·c_8_35·a_1_2
  88. b_4_12·a_1_2·b_1_1·b_5_16 + b_4_122·a_1_2·b_1_12 + a_2_3·b_2_42·b_4_12·b_1_1
       + a_8_23·a_3_7 + b_4_12·a_6_13·a_1_2 + a_4_6·b_6_22·a_1_2 + a_4_6·b_4_12·a_1_2·b_1_12
       + b_2_5·a_6_13·a_3_7 + a_2_3·b_6_22·a_3_7 + a_2_3·b_2_53·a_3_7
       + a_2_3·b_2_4·b_4_12·a_3_7 + a_2_3·b_2_43·a_3_7
  89. a_6_132
  90. b_5_16·b_7_27 + b_5_15·b_7_27 + b_2_4·b_4_12·b_6_22 + b_2_42·b_4_122 + a_6_13·b_6_22
       + b_4_12·b_6_22·a_1_2·b_1_1 + a_4_6·b_6_22·b_1_12 + b_2_5·b_4_12·a_6_13
       + b_2_5·b_4_11·a_6_13 + b_2_43·a_6_13 + a_2_3·b_2_5·b_4_122 + a_2_3·b_2_4·b_4_122
       + a_2_3·b_2_42·b_6_22 + b_4_12·a_6_13·a_1_2·b_1_1 + b_4_122·a_1_2·a_3_7
       + a_4_6·b_4_12·a_1_2·b_1_13 + a_2_3·b_4_12·a_6_13 + a_2_3·b_2_52·a_6_13
  91. b_5_16·b_7_27 + b_6_22·b_1_16 + b_6_222 + b_4_12·b_6_22·b_1_12 + b_4_122·b_1_14
       + b_4_123 + b_2_52·b_4_122 + b_2_54·b_4_12 + b_2_54·b_4_11 + b_2_4·b_4_12·b_6_22
       + b_2_42·b_4_122 + b_2_44·b_4_12 + b_2_46 + a_6_13·b_6_22
       + b_4_12·b_6_22·a_1_2·b_1_1 + b_4_122·a_1_2·b_1_13 + a_4_6·b_1_18
       + a_4_6·b_4_12·b_1_14 + b_2_5·b_4_12·a_6_13 + b_2_5·b_4_11·a_6_13
       + b_2_4·b_4_12·a_6_13 + b_2_43·a_6_13 + b_2_44·b_1_1·a_3_7 + a_2_3·b_4_12·b_6_22
       + a_2_3·b_2_52·b_6_22 + a_2_3·b_2_53·b_4_12 + a_2_3·b_2_53·b_4_11 + a_2_3·b_2_55
       + a_2_3·b_2_4·b_4_122 + a_2_3·b_2_43·b_4_12 + a_4_6·a_1_2·b_1_17
       + a_4_6·b_6_22·a_1_2·b_1_1 + c_8_35·b_1_14
  92. b_5_16·b_7_28 + b_4_12·b_6_22·b_1_12 + b_4_122·b_1_14 + b_2_5·b_4_12·b_6_22
       + b_2_53·b_6_22 + b_2_54·b_4_11 + b_2_4·b_4_12·b_6_22 + b_2_42·b_4_122
       + b_2_44·b_4_12 + b_6_22·a_1_2·b_1_15 + b_4_12·a_1_2·b_7_28
       + b_4_12·b_6_22·a_1_2·b_1_1 + b_2_5·b_4_12·a_6_13 + b_2_53·a_6_13
       + b_2_4·b_6_22·b_1_1·a_3_7 + b_2_43·a_6_13 + b_2_44·b_1_1·a_3_7 + a_2_3·b_4_12·b_6_22
       + a_2_3·b_2_53·b_4_11 + a_2_3·b_2_4·b_4_122 + a_2_3·b_2_45 + a_4_6·a_1_2·b_1_17
       + a_4_6·b_4_12·a_1_2·b_1_13 + a_2_3·b_2_52·a_6_13 + c_8_35·a_1_2·b_1_13
       + c_8_35·a_1_2·a_3_7
  93. b_5_16·b_7_27 + b_5_15·b_7_28 + b_4_12·b_1_1·b_7_28 + b_2_52·b_4_122 + b_2_46
       + b_4_12·a_1_2·b_7_28 + b_4_12·b_6_22·a_1_2·b_1_1 + a_4_6·b_4_122
       + b_2_5·b_4_12·a_6_13 + b_2_4·b_6_22·b_1_1·a_3_7 + b_2_4·b_4_12·a_6_13 + b_2_43·a_6_13
       + a_2_3·b_4_12·b_6_22 + a_2_3·b_2_5·b_4_122 + a_2_3·b_2_52·b_6_22
       + a_2_3·b_2_53·b_4_12 + a_2_3·b_2_53·b_4_11 + a_2_3·b_2_4·b_4_122 + a_2_3·b_2_45
       + b_4_12·a_6_13·a_1_2·b_1_1 + a_4_6·b_6_22·a_1_2·b_1_1 + a_4_6·b_4_12·a_1_2·b_1_13
       + a_2_3·b_2_42·a_6_13 + a_2_3·b_2_4·c_8_35 + a_2_3·c_8_35·a_1_2·b_1_1
  94. b_5_16·b_7_27 + b_2_5·b_4_12·b_6_22 + b_2_52·b_4_122 + b_2_53·b_6_22
       + b_2_54·b_4_11 + b_2_44·b_4_12 + b_2_46 + a_6_13·b_6_22 + b_4_12·a_1_2·b_7_28
       + b_4_12·b_6_22·a_1_2·b_1_1 + b_4_122·a_1_2·b_1_13 + a_4_6·b_6_22·b_1_12
       + a_4_6·b_4_122 + b_2_5·b_4_11·a_6_13 + b_2_53·a_6_13 + b_2_4·b_4_12·a_6_13
       + b_2_44·b_1_1·a_3_7 + a_2_3·b_2_53·b_4_12 + a_2_3·b_2_53·b_4_11
       + a_2_3·b_2_42·b_6_22 + a_2_3·b_2_45 + b_4_122·a_1_2·a_3_7
       + a_4_6·b_4_12·a_1_2·b_1_13 + a_2_3·b_2_5·a_8_23 + a_2_3·b_2_42·a_6_13
  95. b_4_122·a_1_2·a_3_7 + a_4_6·a_8_23 + a_4_6·b_6_22·a_1_2·b_1_1 + a_2_3·b_4_12·a_6_13
       + a_2_3·b_2_42·a_6_13
  96. b_2_4·b_2_53·b_4_11 + b_2_46 + b_4_11·a_8_23 + b_2_5·b_4_12·a_6_13
       + b_2_5·b_4_11·a_6_13 + b_2_4·b_4_12·a_6_13 + b_2_44·b_1_1·a_3_7
       + a_2_3·b_2_5·b_4_122 + a_2_3·b_2_52·b_6_22 + a_2_3·b_2_4·b_4_122
       + a_2_3·b_2_43·b_4_12 + a_2_3·b_2_45 + a_2_3·b_4_12·a_6_13
       + a_2_3·b_2_43·b_1_1·a_3_7
  97. b_5_15·b_7_28 + b_4_12·b_6_22·b_1_12 + b_4_122·b_1_14 + b_2_5·b_4_12·b_6_22
       + b_2_53·b_6_22 + b_2_54·b_4_11 + b_2_42·b_4_122 + b_4_12·a_1_2·b_7_28
       + b_4_12·a_8_23 + b_4_12·b_6_22·a_1_2·b_1_1 + a_4_6·b_4_122 + b_2_5·b_4_12·a_6_13
       + b_2_53·a_6_13 + b_2_4·b_6_22·b_1_1·a_3_7 + b_2_44·b_1_1·a_3_7 + a_2_3·b_4_12·b_6_22
       + a_2_3·b_2_52·b_6_22 + a_2_3·b_2_53·b_4_12 + a_2_3·b_2_4·b_4_122
       + b_4_122·a_1_2·a_3_7 + a_4_6·b_6_22·a_1_2·b_1_1 + a_2_3·b_4_12·a_6_13
       + a_2_3·b_2_52·a_6_13
  98. a_6_13·b_7_28 + a_6_13·b_7_27 + b_4_12·b_6_22·a_1_2·b_1_12 + b_4_122·a_1_2·b_1_14
       + a_4_6·b_6_22·b_1_13 + a_4_6·b_4_12·b_1_15 + b_2_5·a_6_13·b_5_15
       + b_2_4·b_4_122·a_3_7 + a_2_3·b_2_4·b_4_122·b_1_1 + a_2_3·b_2_42·b_6_22·b_1_1
       + a_2_3·b_2_43·b_4_12·b_1_1 + a_4_6·b_6_22·a_1_2·b_1_12 + b_2_53·a_6_13·a_1_2
       + a_2_3·a_6_13·b_5_15 + a_2_3·b_2_54·a_3_7 + a_2_3·b_2_44·a_3_7 + a_2_3·c_8_35·a_3_7
  99. b_2_5·b_4_12·b_7_28 + b_2_5·b_4_12·b_7_27 + b_2_52·b_4_12·b_5_15
       + b_2_42·b_4_122·b_1_1 + a_6_13·b_7_27 + b_2_5·a_6_13·b_5_15 + b_2_43·b_4_12·a_3_7
       + a_2_3·b_2_5·b_4_12·b_5_15 + a_2_3·b_2_53·b_5_15 + a_2_3·b_2_4·b_4_122·b_1_1
       + a_2_3·b_2_42·b_6_22·b_1_1 + a_2_3·b_2_45·b_1_1 + b_4_12·a_6_13·a_3_7
       + a_4_6·b_6_22·a_1_2·b_1_12 + b_2_53·a_6_13·a_1_2 + a_2_3·b_4_122·a_3_7
       + a_2_3·b_2_4·b_6_22·a_3_7 + a_2_3·b_2_44·a_3_7 + a_2_3·b_2_4·c_8_35·b_1_1
  100. b_6_22·b_7_28 + b_6_222·b_1_1 + b_4_12·b_6_22·b_1_13 + b_4_122·b_5_16
       + b_4_123·b_1_1 + b_2_5·b_4_12·b_7_27 + b_2_53·b_7_28 + b_2_46·b_1_1 + a_6_13·b_7_28
       + a_6_13·b_7_27 + b_4_12·b_6_22·a_1_2·b_1_12 + b_4_122·a_1_2·b_1_14
       + a_4_6·b_4_12·b_1_15 + a_4_6·b_4_122·b_1_1 + b_2_55·a_3_7 + b_2_4·b_4_122·a_3_7
       + b_2_42·b_6_22·a_3_7 + b_2_43·b_4_12·a_3_7 + b_2_45·a_3_7
       + a_2_3·b_2_5·b_4_12·b_5_15 + a_2_3·b_2_4·b_4_122·b_1_1 + a_2_3·b_2_42·b_6_22·b_1_1
       + a_2_3·b_2_43·b_4_12·b_1_1 + a_2_3·b_2_45·b_1_1 + b_4_12·a_6_13·a_3_7
       + a_4_6·b_6_22·a_1_2·b_1_12 + b_2_52·a_6_13·a_3_7 + a_2_3·b_4_122·a_3_7
       + a_2_3·b_2_54·a_3_7 + a_2_3·b_2_4·b_6_22·a_3_7 + a_2_3·b_2_42·b_4_12·a_3_7
       + a_2_3·b_2_44·a_3_7 + a_4_6·c_8_35·b_1_1 + b_2_4·c_8_35·a_3_7
       + a_2_3·b_2_5·c_8_35·a_1_2
  101. b_6_22·b_7_27 + b_4_122·b_5_15 + b_4_123·b_1_1 + b_2_52·b_4_12·b_5_15
       + b_2_42·b_4_122·b_1_1 + a_8_23·b_5_16 + b_6_222·a_1_2
       + b_4_12·b_6_22·a_1_2·b_1_12 + b_2_5·a_6_13·b_5_15 + a_2_3·b_4_12·b_7_27
       + a_2_3·b_4_12·b_6_22·b_1_1 + a_2_3·b_2_53·b_5_15 + a_2_3·b_2_4·b_4_122·b_1_1
       + a_2_3·b_2_43·b_4_12·b_1_1 + a_4_6·b_4_12·a_1_2·b_1_14 + b_2_52·a_6_13·a_3_7
       + b_2_53·a_6_13·a_1_2 + a_2_3·a_6_13·b_5_15 + a_2_3·b_4_122·a_3_7
       + a_2_3·b_2_4·b_6_22·a_3_7 + a_2_3·b_2_42·b_4_12·a_3_7 + a_2_3·b_2_44·a_3_7
       + b_2_42·c_8_35·b_1_1 + a_4_6·c_8_35·a_1_2 + a_2_3·b_2_5·c_8_35·a_1_2
  102. b_6_22·b_7_27 + b_4_122·b_5_15 + b_4_123·b_1_1 + b_2_5·b_4_12·b_7_28
       + b_2_5·b_4_12·b_7_27 + b_6_222·a_1_2 + b_4_12·b_6_22·a_3_7 + b_4_123·a_1_2
       + b_2_5·a_6_13·b_5_15 + b_2_43·b_4_12·a_3_7 + a_2_3·b_4_12·b_7_27
       + a_2_3·b_2_52·b_7_27 + a_2_3·b_2_4·b_4_122·b_1_1 + a_2_3·b_2_42·b_6_22·b_1_1
       + a_2_3·b_2_43·b_4_12·b_1_1 + a_2_3·b_2_45·b_1_1 + b_4_12·a_8_23·a_1_2
       + a_4_6·b_6_22·a_1_2·b_1_12 + a_4_6·b_4_122·a_1_2 + b_2_53·a_6_13·a_1_2
       + a_2_3·a_6_13·b_5_15 + a_2_3·b_2_54·a_3_7 + a_2_3·b_2_4·b_6_22·a_3_7
       + b_2_42·c_8_35·b_1_1
  103. b_2_5·b_4_12·b_7_28 + b_2_5·b_4_12·b_7_27 + b_2_52·b_4_12·b_5_15
       + b_2_42·b_4_122·b_1_1 + a_8_23·b_5_15 + b_4_12·b_6_22·a_3_7
       + b_4_12·b_6_22·a_1_2·b_1_12 + b_4_123·a_1_2 + b_2_4·b_4_122·a_3_7
       + b_2_43·b_4_12·a_3_7 + a_2_3·b_4_12·b_6_22·b_1_1 + a_2_3·b_2_52·b_7_27
       + a_2_3·b_2_53·b_5_15 + a_2_3·b_2_4·b_4_122·b_1_1 + a_2_3·b_2_42·b_6_22·b_1_1
       + a_2_3·b_2_45·b_1_1 + a_4_6·b_4_12·a_1_2·b_1_14 + b_2_53·a_6_13·a_1_2
       + a_2_3·a_6_13·b_5_15 + a_2_3·b_2_4·b_6_22·a_3_7 + a_2_3·b_2_42·b_4_12·a_3_7
  104. b_7_282 + b_6_222·b_1_12 + b_4_122·b_1_16 + b_2_5·b_4_123
       + b_2_52·b_4_12·b_6_22 + b_2_54·b_6_22 + b_2_55·b_4_11 + b_2_4·b_4_123
       + b_2_42·b_4_12·b_6_22 + b_2_43·b_4_122 + b_2_44·b_6_22 + b_4_122·a_1_2·b_5_16
       + b_4_123·a_1_2·b_1_1 + b_2_52·b_4_12·a_6_13 + b_2_54·a_6_13 + b_2_42·b_4_12·a_6_13
       + b_2_44·a_6_13 + b_2_45·b_1_1·a_3_7 + a_2_3·b_4_123 + a_2_3·b_2_5·b_4_12·b_6_22
       + a_2_3·b_2_52·b_4_122 + a_2_3·b_2_53·b_6_22 + a_2_3·b_2_4·b_4_12·b_6_22
       + a_2_3·b_2_42·b_4_122 + a_2_3·b_2_43·b_6_22 + a_2_3·b_2_4·b_4_12·a_6_13
       + a_2_3·b_2_44·b_1_1·a_3_7
  105. b_7_272 + b_2_5·b_4_123 + b_2_52·b_4_12·b_6_22 + b_2_53·b_4_122 + b_2_54·b_6_22
       + b_2_55·b_4_11 + b_2_44·b_6_22 + b_2_45·b_4_12 + b_2_47 + b_2_52·b_4_12·a_6_13
       + b_2_54·a_6_13 + b_2_44·a_6_13 + b_2_45·b_1_1·a_3_7 + a_2_3·b_2_5·b_4_12·b_6_22
       + a_2_3·b_2_52·b_4_122 + a_2_3·b_2_53·b_6_22 + a_2_3·b_2_42·b_4_122
       + b_2_43·c_8_35 + a_2_3·b_2_42·c_8_35 + a_2_3·c_8_35·b_1_1·a_3_7
  106. b_7_27·b_7_28 + b_7_272 + b_2_52·b_4_12·b_6_22 + b_2_53·b_4_122 + b_2_54·b_6_22
       + b_2_55·b_4_11 + b_2_45·b_4_12 + b_2_47 + b_6_222·a_1_2·b_1_1
       + b_4_12·b_6_22·a_1_2·b_1_13 + b_4_122·a_1_2·b_5_16 + b_4_122·a_6_13
       + a_4_6·b_4_12·b_6_22 + b_2_52·b_4_12·a_6_13 + b_2_54·a_6_13 + b_2_4·a_6_13·b_6_22
       + b_2_45·b_1_1·a_3_7 + a_2_3·b_2_5·b_4_12·b_6_22 + a_2_3·b_2_54·b_4_11
       + a_2_3·b_2_42·b_4_122 + a_2_3·b_2_43·b_6_22 + a_2_3·b_2_44·b_4_12
       + a_4_6·b_4_12·a_1_2·b_1_15 + a_4_6·b_4_122·a_1_2·b_1_1 + a_2_3·a_6_13·b_6_22
       + a_2_3·b_4_12·a_8_23 + a_2_3·b_2_53·a_6_13 + b_2_4·c_8_35·b_1_1·a_3_7
       + a_4_6·c_8_35·a_1_2·b_1_1
  107. b_7_27·b_7_28 + b_7_272 + b_2_52·b_4_12·b_6_22 + b_2_53·b_4_122 + b_2_54·b_6_22
       + b_2_55·b_4_11 + b_2_45·b_4_12 + b_2_47 + b_6_222·a_1_2·b_1_1
       + b_4_12·b_6_22·a_1_2·b_1_13 + b_4_122·a_1_2·b_5_16 + b_4_122·a_6_13
       + a_4_6·b_4_12·b_6_22 + b_2_52·b_4_12·a_6_13 + b_2_54·a_6_13 + b_2_4·a_6_13·b_6_22
       + b_2_45·b_1_1·a_3_7 + a_2_3·b_2_5·b_4_12·b_6_22 + a_2_3·b_2_54·b_4_11
       + a_2_3·b_2_42·b_4_122 + a_2_3·b_2_43·b_6_22 + a_2_3·b_2_44·b_4_12 + a_6_13·a_8_23
       + b_4_12·b_6_22·a_1_2·a_3_7 + a_4_6·b_6_22·a_1_2·b_1_13
       + a_4_6·b_4_12·a_1_2·b_1_15 + a_2_3·a_6_13·b_6_22 + a_2_3·b_2_43·a_6_13
       + b_2_4·c_8_35·b_1_1·a_3_7 + a_4_6·c_8_35·a_1_2·b_1_1
  108. b_7_27·b_7_28 + b_4_122·b_1_1·b_5_16 + b_4_123·b_1_12 + b_2_5·b_4_123
       + b_2_43·b_4_122 + b_2_44·b_6_22 + b_6_22·a_8_23 + b_4_12·b_6_22·a_1_2·b_1_13
       + a_4_6·b_6_22·b_1_14 + b_2_5·b_4_12·a_8_23 + b_2_5·b_4_11·a_8_23
       + b_2_42·b_4_12·a_6_13 + a_2_3·b_2_54·b_4_12 + a_2_3·b_2_4·b_4_12·b_6_22
       + a_2_3·b_2_42·b_4_122 + a_2_3·b_2_44·b_4_12 + a_2_3·b_2_46
       + b_4_12·b_6_22·a_1_2·a_3_7 + a_4_6·b_6_22·a_1_2·b_1_13
       + a_4_6·b_4_12·a_1_2·b_1_15 + a_2_3·b_2_52·a_8_23 + b_2_43·c_8_35
       + a_4_6·c_8_35·b_1_12 + b_2_4·c_8_35·b_1_1·a_3_7 + a_4_6·c_8_35·a_1_2·b_1_1
  109. a_8_23·b_7_28 + a_8_23·b_7_27 + b_6_222·a_1_2·b_1_12 + b_4_12·b_6_22·a_1_2·b_1_14
       + b_4_122·b_6_22·a_1_2 + b_4_122·a_6_13·b_1_1 + b_4_123·a_3_7
       + a_4_6·b_6_22·b_1_15 + b_2_5·a_6_13·b_7_27 + b_2_52·a_6_13·b_5_15
       + b_2_4·b_4_12·b_6_22·a_3_7 + a_2_3·b_2_54·b_5_15 + a_2_3·b_2_42·b_4_122·b_1_1
       + a_2_3·b_2_44·b_4_12·b_1_1 + a_2_3·b_2_46·b_1_1 + b_4_122·a_6_13·a_1_2
       + a_4_6·b_6_22·a_1_2·b_1_14 + a_4_6·b_4_12·a_1_2·b_1_16
       + a_4_6·b_4_12·b_6_22·a_1_2 + a_2_3·b_2_5·a_6_13·b_5_15 + a_2_3·b_2_55·a_3_7
       + a_2_3·b_2_4·b_4_122·a_3_7 + a_2_3·b_2_43·b_4_12·a_3_7 + a_4_6·c_8_35·b_1_13
       + a_2_3·b_2_42·c_8_35·b_1_1 + a_2_3·b_2_5·c_8_35·a_3_7 + a_2_3·b_2_4·c_8_35·a_3_7
  110. a_8_23·b_7_27 + b_4_12·a_6_13·b_5_15 + b_4_123·a_1_2·b_1_12
       + a_4_6·b_4_122·b_1_13 + b_2_4·b_4_12·b_6_22·a_3_7 + a_2_3·b_4_122·b_5_15
       + a_2_3·b_4_123·b_1_1 + a_2_3·b_2_53·b_7_27 + a_2_3·b_2_42·b_4_122·b_1_1
       + a_2_3·b_2_43·b_6_22·b_1_1 + a_2_3·b_2_44·b_4_12·b_1_1 + b_4_12·a_8_23·a_3_7
       + b_4_122·a_6_13·a_1_2 + a_4_6·b_6_22·a_1_2·b_1_14 + a_4_6·b_4_12·b_6_22·a_1_2
       + a_4_6·b_4_122·a_1_2·b_1_12 + b_2_54·a_6_13·a_1_2 + a_2_3·a_6_13·b_7_27
       + a_2_3·b_2_5·a_6_13·b_5_15 + a_2_3·b_2_55·a_3_7 + a_2_3·b_2_56·a_1_2
       + a_2_3·b_2_4·b_4_122·a_3_7 + a_2_3·b_2_45·a_3_7 + a_4_6·c_8_35·a_1_2·b_1_12
       + a_2_3·b_2_4·c_8_35·a_3_7
  111. a_8_232

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 16.
  • The completion test was perfect: It applied in the last degree in which a generator or relation was found.
  • The following is a filter regular homogeneous system of parameters:
    1. c_8_35, a Duflot regular element of degree 8
    2. b_1_14 + b_4_12 + b_2_52, an element of degree 4
    3. b_1_1·b_5_16 + b_2_5·b_4_12 + b_2_4·b_4_12 + b_2_4·b_4_11 + b_2_43, an element of degree 6
  • The Raw Filter Degree Type of that HSOP is [-1, 4, 9, 15].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].

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. a_1_0 → 0, an element of degree 1
  2. a_1_2 → 0, an element of degree 1
  3. b_1_1 → 0, an element of degree 1
  4. a_2_3 → 0, an element of degree 2
  5. b_2_4 → 0, an element of degree 2
  6. b_2_5 → 0, an element of degree 2
  7. a_3_7 → 0, an element of degree 3
  8. a_4_6 → 0, an element of degree 4
  9. b_4_11 → 0, an element of degree 4
  10. b_4_12 → 0, an element of degree 4
  11. b_5_15 → 0, an element of degree 5
  12. b_5_16 → 0, an element of degree 5
  13. a_6_13 → 0, an element of degree 6
  14. b_6_22 → 0, an element of degree 6
  15. b_7_27 → 0, an element of degree 7
  16. b_7_28 → 0, an element of degree 7
  17. a_8_23 → 0, an element of degree 8
  18. c_8_35 → c_1_08, an element of degree 8

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

  1. a_1_0 → 0, an element of degree 1
  2. a_1_2 → 0, an element of degree 1
  3. b_1_1 → c_1_1, an element of degree 1
  4. a_2_3 → 0, an element of degree 2
  5. b_2_4 → 0, an element of degree 2
  6. b_2_5 → 0, an element of degree 2
  7. a_3_7 → 0, an element of degree 3
  8. a_4_6 → 0, an element of degree 4
  9. b_4_11 → 0, an element of degree 4
  10. b_4_12 → c_1_24 + c_1_12·c_1_22, an element of degree 4
  11. b_5_15 → c_1_1·c_1_24 + c_1_13·c_1_22, an element of degree 5
  12. b_5_16 → c_1_1·c_1_24 + c_1_13·c_1_22, an element of degree 5
  13. a_6_13 → 0, an element of degree 6
  14. b_6_22 → c_1_26 + c_1_14·c_1_22 + c_1_02·c_1_14 + c_1_04·c_1_12, an element of degree 6
  15. b_7_27 → 0, an element of degree 7
  16. b_7_28 → c_1_1·c_1_26 + c_1_13·c_1_24 + c_1_02·c_1_15 + c_1_04·c_1_13, an element of degree 7
  17. a_8_23 → 0, an element of degree 8
  18. c_8_35 → c_1_28 + c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_16·c_1_22
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22 + c_1_02·c_1_16
       + c_1_04·c_1_24 + c_1_04·c_1_12·c_1_22 + c_1_08, an element of degree 8

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

  1. a_1_0 → 0, an element of degree 1
  2. a_1_2 → 0, an element of degree 1
  3. b_1_1 → 0, an element of degree 1
  4. a_2_3 → 0, an element of degree 2
  5. b_2_4 → 0, an element of degree 2
  6. b_2_5 → c_1_22, an element of degree 2
  7. a_3_7 → 0, an element of degree 3
  8. a_4_6 → 0, an element of degree 4
  9. b_4_11 → c_1_12·c_1_22, an element of degree 4
  10. b_4_12 → c_1_12·c_1_22 + c_1_14, an element of degree 4
  11. b_5_15 → c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  12. b_5_16 → c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  13. a_6_13 → 0, an element of degree 6
  14. b_6_22 → c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_16, an element of degree 6
  15. b_7_27 → c_1_12·c_1_25 + c_1_16·c_1_2, an element of degree 7
  16. b_7_28 → c_1_14·c_1_23 + c_1_16·c_1_2, an element of degree 7
  17. a_8_23 → 0, an element of degree 8
  18. c_8_35 → 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. a_1_0 → 0, an element of degree 1
  2. a_1_2 → 0, an element of degree 1
  3. b_1_1 → c_1_2, an element of degree 1
  4. a_2_3 → 0, an element of degree 2
  5. b_2_4 → c_1_22, an element of degree 2
  6. b_2_5 → c_1_22, an element of degree 2
  7. a_3_7 → 0, an element of degree 3
  8. a_4_6 → 0, an element of degree 4
  9. b_4_11 → c_1_24, an element of degree 4
  10. b_4_12 → c_1_24 + c_1_12·c_1_22 + c_1_14, an element of degree 4
  11. b_5_15 → c_1_25, an element of degree 5
  12. b_5_16 → c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  13. a_6_13 → 0, an element of degree 6
  14. b_6_22 → c_1_26 + c_1_14·c_1_22 + c_1_16 + c_1_02·c_1_24 + c_1_04·c_1_22, an element of degree 6
  15. b_7_27 → c_1_12·c_1_25 + c_1_16·c_1_2 + c_1_02·c_1_25 + c_1_04·c_1_23, an element of degree 7
  16. b_7_28 → c_1_14·c_1_23 + c_1_16·c_1_2 + c_1_02·c_1_25 + c_1_04·c_1_23, an element of degree 7
  17. a_8_23 → 0, an element of degree 8
  18. c_8_35 → c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_16·c_1_22 + c_1_18 + 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_12·c_1_22
       + c_1_04·c_1_14 + 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