Cohomology of group number 349 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 2.
  • It has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 3.


Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 3 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 2) · (t7  +  3/2·t6  +  t5  +  t3  +  t2  +  t  +  1/2)

    (t  +  1)2 · (t  −  1)3 · (t2  +  1)2 · (t4  +  1)
  • The a-invariants are -∞,-∞,-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 9:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_1, a nilpotent element of degree 1
  3. a_1_2, a nilpotent element of degree 1
  4. b_2_4, an element of degree 2
  5. a_3_5, a nilpotent element of degree 3
  6. a_3_6, a nilpotent element of degree 3
  7. c_4_7, a Duflot regular element of degree 4
  8. a_5_6, a nilpotent element of degree 5
  9. a_5_8, a nilpotent element of degree 5
  10. a_5_9, a nilpotent element of degree 5
  11. a_5_10, a nilpotent element of degree 5
  12. a_5_11, a nilpotent element of degree 5
  13. b_6_16, an element of degree 6
  14. a_7_19, a nilpotent element of degree 7
  15. a_7_20, a nilpotent element of degree 7
  16. c_8_21, a Duflot regular element of degree 8
  17. a_9_27, a nilpotent element of degree 9
  18. a_9_28, a nilpotent element of degree 9

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

Ring relations

There are 119 minimal relations of maximal degree 18:

  1. a_1_0·a_1_1
  2. a_1_0·a_1_2
  3. a_1_03
  4. a_1_13
  5. b_2_4·a_1_1 + a_1_23 + a_1_1·a_1_22 + a_1_12·a_1_2
  6. a_1_24
  7. a_1_1·a_3_5 + a_1_12·a_1_22
  8. a_1_2·a_3_5 + a_1_1·a_1_23 + a_1_12·a_1_22
  9. a_1_1·a_3_6 + a_1_12·a_1_22
  10. a_1_2·a_3_6 + b_2_4·a_1_22 + b_2_4·a_1_02
  11. b_2_4·a_1_23
  12. a_1_02·a_3_5
  13. a_1_02·a_3_6
  14. a_3_52 + b_2_42·a_1_02 + c_4_7·a_1_02
  15. a_1_1·a_5_6
  16. a_3_52 + a_1_0·a_5_6 + b_2_4·a_1_0·a_3_5 + b_2_42·a_1_02
  17. a_3_62 + a_1_0·a_5_8 + b_2_4·a_1_0·a_3_6
  18. a_1_2·a_5_8 + a_1_2·a_5_6 + a_1_1·a_5_9 + a_1_1·a_5_8 + b_2_42·a_1_22 + c_4_7·a_1_22
       + c_4_7·a_1_1·a_1_2 + c_4_7·a_1_12
  19. a_1_0·a_5_9 + b_2_42·a_1_02
  20. a_1_1·a_5_10 + c_4_7·a_1_12
  21. a_3_62 + a_1_0·a_5_10
  22. a_1_2·a_5_10 + b_2_42·a_1_22 + b_2_42·a_1_02 + c_4_7·a_1_1·a_1_2
  23. a_1_1·a_5_11 + c_4_7·a_1_12
  24. a_3_62 + a_3_5·a_3_6 + a_3_52 + a_1_0·a_5_11 + b_2_42·a_1_02
  25. a_1_2·a_5_11 + b_2_4·a_1_0·a_3_5 + b_2_42·a_1_22 + b_2_42·a_1_02
       + c_4_7·a_1_1·a_1_2
  26. a_1_22·a_5_6 + a_1_12·a_5_8 + c_4_7·a_1_12·a_1_2
  27. a_1_02·a_5_8
  28. b_2_4·a_5_10 + b_2_4·a_5_8 + b_2_4·a_5_6 + b_2_42·a_3_6 + b_2_42·a_3_5 + b_2_43·a_1_2
       + a_1_22·a_5_9 + a_1_22·a_5_6 + a_1_12·a_5_9 + b_2_4·c_4_7·a_1_2 + b_2_4·c_4_7·a_1_0
       + c_4_7·a_1_23 + c_4_7·a_1_12·a_1_2
  29. a_1_22·a_5_6 + a_1_02·a_5_11
  30. b_6_16·a_1_1 + a_1_1·a_1_2·a_5_9 + a_1_12·a_5_9 + c_4_7·a_1_23 + c_4_7·a_1_1·a_1_22
  31. b_6_16·a_1_0 + b_2_42·a_3_5 + b_2_4·c_4_7·a_1_0
  32. b_6_16·a_1_2 + b_2_4·a_5_6 + b_2_42·a_3_5 + b_2_43·a_1_2 + a_1_22·a_5_9
       + a_1_1·a_1_2·a_5_9 + a_1_12·a_5_9 + b_2_4·c_4_7·a_1_2 + b_2_4·c_4_7·a_1_0
       + c_4_7·a_1_1·a_1_22 + c_4_7·a_1_12·a_1_2
  33. a_3_5·a_5_6 + b_2_43·a_1_02 + c_4_7·a_1_0·a_3_5 + b_2_4·c_4_7·a_1_02
  34. a_1_23·a_5_9 + a_1_1·a_1_22·a_5_9 + a_1_12·a_1_2·a_5_9 + c_4_7·a_1_1·a_1_23
       + c_4_7·a_1_12·a_1_22
  35. a_3_5·a_5_9 + b_2_42·a_1_0·a_3_5 + a_1_1·a_1_22·a_5_9 + a_1_12·a_1_2·a_5_9
  36. a_3_6·a_5_9 + b_2_4·a_1_2·a_5_9 + b_2_4·a_1_0·a_5_8 + b_2_42·a_1_0·a_3_6
       + a_1_1·a_1_22·a_5_9 + a_1_12·a_1_2·a_5_9 + b_2_4·c_4_7·a_1_02
       + c_4_7·a_1_1·a_1_23 + c_4_7·a_1_12·a_1_22
  37. a_3_6·a_5_10 + a_3_6·a_5_8 + b_2_4·a_1_2·a_5_6 + b_2_4·a_1_0·a_5_8 + b_2_42·a_1_0·a_3_6
       + b_2_42·a_1_0·a_3_5 + b_2_43·a_1_22 + a_1_12·a_1_2·a_5_9 + b_2_4·c_4_7·a_1_22
       + b_2_4·c_4_7·a_1_02 + c_4_7·a_1_12·a_1_22
  38. a_3_6·a_5_6 + a_3_5·a_5_10 + a_3_5·a_5_8 + b_2_4·a_1_2·a_5_6 + b_2_42·a_1_0·a_3_5
       + b_2_43·a_1_02 + a_1_12·a_1_2·a_5_9 + c_4_7·a_1_0·a_3_6 + c_4_7·a_1_1·a_1_23
  39. a_3_6·a_5_11 + a_3_6·a_5_8 + a_3_6·a_5_6 + a_3_5·a_5_8 + b_2_4·a_1_2·a_5_6
       + b_2_4·a_1_0·a_5_8 + b_2_42·a_1_0·a_3_6 + b_2_42·a_1_0·a_3_5 + b_2_43·a_1_02
       + b_2_4·c_4_7·a_1_22 + b_2_4·c_4_7·a_1_02 + c_4_7·a_1_1·a_1_23
  40. a_3_6·a_5_6 + a_3_5·a_5_11 + a_3_5·a_5_8 + b_2_4·a_1_2·a_5_6 + b_2_42·a_1_0·a_3_6
       + b_2_42·a_1_0·a_3_5 + b_2_43·a_1_02 + a_1_12·a_1_2·a_5_9 + c_4_7·a_1_0·a_3_5
       + c_4_7·a_1_1·a_1_23
  41. a_3_6·a_5_6 + b_2_4·a_1_2·a_5_6 + b_2_4·a_1_0·a_5_11 + b_2_4·a_1_0·a_5_8
       + b_2_42·a_1_0·a_3_6 + b_2_42·a_1_0·a_3_5 + b_2_43·a_1_02 + c_4_7·a_1_0·a_3_6
       + b_2_4·c_4_7·a_1_02
  42. a_1_1·a_7_19 + a_1_1·a_1_22·a_5_9 + a_1_12·a_1_2·a_5_9 + c_4_7·a_1_12·a_1_22
  43. a_3_6·a_5_6 + a_3_5·a_5_8 + a_1_0·a_7_19 + b_2_4·a_1_2·a_5_6 + b_2_42·a_1_0·a_3_5
       + a_1_12·a_1_2·a_5_9 + c_4_7·a_1_0·a_3_6 + c_4_7·a_1_0·a_3_5 + c_4_7·a_1_1·a_1_23
       + c_4_7·a_1_12·a_1_22
  44. a_3_6·a_5_9 + a_1_2·a_7_19 + b_2_4·a_1_2·a_5_6 + b_2_4·a_1_0·a_5_8 + b_2_42·a_1_0·a_3_6
       + b_2_42·a_1_0·a_3_5 + a_1_1·a_1_22·a_5_9 + b_2_4·c_4_7·a_1_22
       + b_2_4·c_4_7·a_1_02 + c_4_7·a_1_1·a_1_23
  45. a_1_1·a_7_20 + a_1_12·a_1_2·a_5_9
  46. a_3_6·a_5_8 + a_3_6·a_5_6 + a_1_0·a_7_20 + b_2_42·a_1_0·a_3_6 + b_2_42·a_1_0·a_3_5
       + b_2_43·a_1_22 + b_2_43·a_1_02 + a_1_12·a_1_2·a_5_9 + b_2_4·c_4_7·a_1_22
  47. a_1_2·a_7_20 + b_2_4·a_1_2·a_5_6 + b_2_4·a_1_0·a_5_8 + b_2_42·a_1_0·a_3_5
       + b_2_43·a_1_02 + a_1_1·a_1_22·a_5_9 + a_1_12·a_1_2·a_5_9 + b_2_4·c_4_7·a_1_02
       + c_4_7·a_1_12·a_1_22
  48. b_6_16·a_3_6 + b_2_42·a_5_11 + b_2_42·a_5_8 + b_2_43·a_3_6 + a_1_12·a_1_22·a_5_9
       + b_2_4·c_4_7·a_3_6 + b_2_42·c_4_7·a_1_2 + b_2_42·c_4_7·a_1_0
  49. b_6_16·a_3_5 + b_2_44·a_1_0 + a_1_12·a_1_22·a_5_9 + b_2_4·c_4_7·a_3_5
       + b_2_42·c_4_7·a_1_0
  50. a_1_02·a_7_19
  51. a_1_02·a_7_20 + b_2_4·a_1_22·a_5_9 + a_1_12·a_1_22·a_5_9
  52. a_5_62 + b_2_44·a_1_02 + b_2_42·c_4_7·a_1_22 + b_2_42·c_4_7·a_1_02
       + c_4_72·a_1_02
  53. a_5_9·a_5_10 + b_2_42·a_1_2·a_5_9 + b_2_43·a_1_0·a_3_6 + c_4_7·a_1_1·a_5_9
       + b_2_42·c_4_7·a_1_02
  54. a_5_9·a_5_11 + a_5_6·a_5_10 + b_2_42·a_1_2·a_5_9 + b_2_42·a_1_2·a_5_6
       + b_2_43·a_1_0·a_3_6 + b_2_43·a_1_0·a_3_5 + b_2_44·a_1_02 + c_4_7·a_1_1·a_5_9
       + c_4_7·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_3_6 + b_2_4·c_4_7·a_1_0·a_3_5
  55. a_5_6·a_5_10 + a_5_6·a_5_8 + b_2_42·a_1_0·a_5_11 + b_2_42·a_1_0·a_5_8
       + b_2_43·a_1_0·a_3_6 + b_2_43·a_1_0·a_3_5 + b_2_44·a_1_02 + c_4_7·a_1_2·a_5_6
       + b_2_4·c_4_7·a_1_0·a_3_6 + b_2_42·c_4_7·a_1_22 + b_2_42·c_4_7·a_1_02
  56. a_5_112 + a_5_102 + b_2_42·a_1_0·a_5_8 + b_2_43·a_1_0·a_3_6 + b_2_44·a_1_22
       + c_4_7·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_3_6 + b_2_42·c_4_7·a_1_22
       + c_4_72·a_1_02
  57. a_5_10·a_5_11 + a_5_102 + a_5_8·a_5_11 + a_5_8·a_5_10 + a_5_6·a_5_10 + b_2_44·a_1_22
       + c_4_7·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_3_5 + b_2_42·c_4_7·a_1_02
  58. a_5_6·a_5_11 + a_5_6·a_5_10 + b_2_43·a_1_0·a_3_6 + b_2_43·a_1_0·a_3_5
       + b_2_44·a_1_02 + c_4_7·a_1_0·a_5_11 + c_4_7·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_3_5
       + b_2_42·c_4_7·a_1_02
  59. a_5_8·a_5_11 + a_5_8·a_5_10 + a_5_6·a_5_11 + a_3_6·a_7_19 + b_2_42·a_1_2·a_5_9
       + b_2_42·a_1_2·a_5_6 + b_2_42·a_1_0·a_5_8 + b_2_44·a_1_22 + b_2_42·c_4_7·a_1_22
       + c_4_72·a_1_02
  60. a_3_5·a_7_19 + b_2_42·a_1_0·a_5_8 + b_2_43·a_1_0·a_3_6 + b_2_43·a_1_0·a_3_5
       + c_4_7·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_3_6 + b_2_42·c_4_7·a_1_02
       + c_4_72·a_1_02
  61. a_5_6·a_5_10 + b_2_4·a_1_0·a_7_19 + b_2_42·a_1_2·a_5_6 + b_2_43·a_1_0·a_3_5
       + c_4_7·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_3_6 + b_2_4·c_4_7·a_1_0·a_3_5
  62. a_5_8·a_5_10 + a_5_6·a_5_8 + a_3_6·a_7_20 + b_2_42·a_1_2·a_5_9 + b_2_43·a_1_0·a_3_6
       + b_2_43·a_1_0·a_3_5 + b_2_44·a_1_22 + c_4_7·a_1_2·a_5_6 + c_4_7·a_1_1·a_5_8
  63. a_5_8·a_5_11 + a_5_8·a_5_10 + a_5_6·a_5_11 + a_5_6·a_5_8 + a_3_5·a_7_20
       + c_4_7·a_1_2·a_5_6 + c_4_7·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_3_6
       + b_2_4·c_4_7·a_1_0·a_3_5 + b_2_42·c_4_7·a_1_22 + b_2_42·c_4_7·a_1_02
       + c_4_72·a_1_02
  64. a_5_102 + a_5_8·a_5_10 + a_5_6·a_5_10 + a_5_6·a_5_8 + b_2_4·a_1_0·a_7_20
       + b_2_42·a_1_2·a_5_6 + b_2_42·a_1_0·a_5_8 + b_2_43·a_1_0·a_3_5 + b_2_44·a_1_22
       + b_2_44·a_1_02 + c_4_7·a_1_2·a_5_6 + c_4_7·a_1_1·a_5_8 + c_4_72·a_1_12
  65. a_5_102 + a_5_82 + b_2_42·a_1_0·a_5_8 + b_2_43·a_1_0·a_3_6 + b_2_44·a_1_22
       + c_8_21·a_1_12 + b_2_42·c_4_7·a_1_22 + c_4_72·a_1_22
  66. a_5_102 + b_2_42·a_1_0·a_5_8 + b_2_43·a_1_0·a_3_6 + b_2_44·a_1_02
       + c_8_21·a_1_02 + c_4_72·a_1_12
  67. a_5_102 + a_5_8·a_5_9 + a_5_82 + a_5_6·a_5_9 + b_2_42·a_1_2·a_5_9
       + b_2_43·a_1_0·a_3_6 + b_2_43·a_1_0·a_3_5 + b_2_44·a_1_22 + c_8_21·a_1_1·a_1_2
       + c_4_7·a_1_2·a_5_9 + c_4_7·a_1_1·a_5_8 + b_2_42·c_4_7·a_1_22
       + b_2_42·c_4_7·a_1_02 + c_4_72·a_1_22 + c_4_72·a_1_12
  68. a_5_102 + a_5_92 + a_5_82 + b_2_42·a_1_0·a_5_8 + b_2_43·a_1_0·a_3_6
       + b_2_44·a_1_02 + c_8_21·a_1_22 + b_2_42·c_4_7·a_1_22
  69. a_5_102 + a_5_8·a_5_9 + a_5_82 + a_5_6·a_5_9 + a_1_1·a_9_27 + b_2_42·a_1_2·a_5_9
       + b_2_43·a_1_0·a_3_6 + b_2_43·a_1_0·a_3_5 + b_2_44·a_1_22 + c_4_7·a_1_2·a_5_9
       + c_4_7·a_1_1·a_5_9 + b_2_42·c_4_7·a_1_22 + b_2_42·c_4_7·a_1_02
       + c_4_72·a_1_22 + c_4_72·a_1_12
  70. a_5_8·a_5_10 + a_5_6·a_5_11 + a_5_6·a_5_10 + a_1_0·a_9_27 + b_2_42·a_1_2·a_5_6
       + b_2_43·a_1_0·a_3_6 + b_2_44·a_1_22 + b_2_44·a_1_02 + c_4_7·a_1_1·a_5_8
       + c_4_7·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_3_5 + b_2_42·c_4_7·a_1_22
  71. a_5_102 + a_5_92 + a_5_82 + a_5_6·a_5_9 + a_1_2·a_9_27 + b_2_42·a_1_2·a_5_9
       + b_2_43·a_1_0·a_3_6 + b_2_43·a_1_0·a_3_5 + b_2_44·a_1_22 + b_2_44·a_1_02
       + c_4_7·a_1_2·a_5_9 + c_4_7·a_1_2·a_5_6 + c_4_7·a_1_1·a_5_9 + c_4_7·a_1_1·a_5_8
       + b_2_4·c_4_7·a_1_0·a_3_5 + b_2_42·c_4_7·a_1_22 + c_4_72·a_1_22
       + c_4_72·a_1_1·a_1_2 + c_4_72·a_1_12
  72. a_5_102 + a_5_82 + a_1_1·a_9_28 + b_2_42·a_1_0·a_5_8 + b_2_43·a_1_0·a_3_6
       + b_2_44·a_1_22 + c_4_7·a_1_1·a_5_9 + c_4_7·a_1_1·a_5_8 + b_2_42·c_4_7·a_1_22
       + c_4_72·a_1_22
  73. a_5_102 + a_5_8·a_5_11 + a_5_8·a_5_10 + a_5_6·a_5_8 + a_1_0·a_9_28 + b_2_42·a_1_2·a_5_6
       + b_2_43·a_1_0·a_3_5 + c_4_7·a_1_2·a_5_6 + b_2_42·c_4_7·a_1_22
       + b_2_42·c_4_7·a_1_02 + c_4_72·a_1_12
  74. a_5_102 + a_5_8·a_5_9 + a_5_82 + a_5_6·a_5_8 + a_1_2·a_9_28 + b_2_42·a_1_2·a_5_9
       + b_2_42·a_1_2·a_5_6 + b_2_43·a_1_0·a_3_6 + b_2_44·a_1_22 + b_2_44·a_1_02
       + c_4_7·a_1_1·a_5_9 + c_4_7·a_1_0·a_5_8 + b_2_42·c_4_7·a_1_22 + c_4_72·a_1_1·a_1_2
  75. b_6_16·a_5_11 + b_6_16·a_5_10 + b_2_44·a_3_6 + b_2_45·a_1_2 + b_2_4·c_4_7·a_5_11
       + b_2_4·c_4_7·a_5_8 + b_2_4·c_4_7·a_5_6 + c_4_7·a_1_22·a_5_9 + c_4_7·a_1_12·a_5_9
       + c_4_7·a_1_02·a_5_11 + b_2_4·c_4_72·a_1_2 + b_2_4·c_4_72·a_1_0 + c_4_72·a_1_23
       + c_4_72·a_1_12·a_1_2
  76. b_6_16·a_5_11 + b_2_42·a_7_19 + b_2_43·a_5_9 + b_2_44·a_3_6 + b_2_4·c_4_7·a_5_11
       + b_2_42·c_4_7·a_3_6 + c_4_7·a_1_1·a_1_2·a_5_9 + c_4_7·a_1_12·a_5_9
       + c_4_72·a_1_12·a_1_2
  77. b_6_16·a_5_11 + b_6_16·a_5_8 + b_2_43·a_5_11 + b_2_43·a_5_8 + b_2_4·c_4_7·a_5_11
       + b_2_4·c_4_7·a_5_8 + b_2_4·c_4_7·a_5_6 + b_2_42·c_4_7·a_3_6 + b_2_43·c_4_7·a_1_0
       + c_8_21·a_1_1·a_1_22 + c_4_7·a_1_22·a_5_9 + b_2_4·c_4_72·a_1_0
  78. b_6_16·a_5_11 + b_6_16·a_5_9 + b_6_16·a_5_8 + b_2_4·a_9_27 + b_2_42·a_7_20
       + b_2_45·a_1_2 + b_2_45·a_1_0 + b_2_42·a_1_22·a_5_9 + b_2_4·c_8_21·a_1_2
       + b_2_4·c_8_21·a_1_0 + b_2_4·c_4_7·a_5_8 + b_2_42·c_4_7·a_3_5 + b_2_43·c_4_7·a_1_2
       + c_8_21·a_1_23 + c_4_7·a_1_1·a_1_2·a_5_9 + c_4_7·a_1_02·a_5_11
       + b_2_4·c_4_72·a_1_2 + c_4_72·a_1_1·a_1_22
  79. b_6_16·a_5_6 + b_2_43·a_5_6 + b_2_44·a_3_5 + b_2_45·a_1_0 + a_1_22·a_9_27
       + b_2_42·a_1_22·a_5_9 + b_2_4·c_4_7·a_5_6 + b_2_42·c_4_7·a_3_5 + b_2_43·c_4_7·a_1_2
       + c_8_21·a_1_23 + c_4_7·a_1_22·a_5_9 + c_4_7·a_1_1·a_1_2·a_5_9 + c_4_7·a_1_12·a_5_9
       + c_4_72·a_1_23 + c_4_72·a_1_12·a_1_2
  80. b_6_16·a_5_6 + b_2_43·a_5_6 + b_2_44·a_3_5 + b_2_45·a_1_0 + a_1_02·a_9_28
       + b_2_42·a_1_22·a_5_9 + b_2_4·c_4_7·a_5_6 + b_2_42·c_4_7·a_3_5 + b_2_43·c_4_7·a_1_2
       + c_4_7·a_1_02·a_5_11
  81. b_6_162 + b_2_46 + b_2_44·a_1_0·a_3_5 + b_2_45·a_1_02 + b_2_44·c_4_7
       + b_2_42·c_4_72
  82. a_5_11·a_7_20 + a_5_11·a_7_19 + a_5_10·a_7_19 + a_5_9·a_7_20 + a_5_8·a_7_20 + a_5_8·a_7_19
       + a_5_6·a_7_19 + b_2_42·a_1_0·a_7_20 + b_2_42·a_1_0·a_7_19 + b_2_43·a_1_2·a_5_9
       + b_2_43·a_1_2·a_5_6 + b_2_43·a_1_0·a_5_11 + b_2_44·a_1_0·a_3_5 + b_2_45·a_1_22
       + b_2_4·c_4_7·a_1_2·a_5_9 + b_2_4·c_4_7·a_1_0·a_5_11 + b_2_42·c_4_7·a_1_0·a_3_6
       + c_4_7·a_1_1·a_1_22·a_5_9 + b_2_4·c_4_72·a_1_22 + b_2_4·c_4_72·a_1_02
  83. a_5_11·a_7_19 + a_5_10·a_7_20 + a_5_9·a_7_20 + a_5_8·a_7_20 + a_5_8·a_7_19 + a_5_6·a_7_20
       + b_2_42·a_1_0·a_7_20 + b_2_43·a_1_2·a_5_9 + b_2_43·a_1_0·a_5_11
       + b_2_43·a_1_0·a_5_8 + b_2_44·a_1_0·a_3_6 + b_2_45·a_1_02 + c_4_7·a_1_0·a_7_19
       + b_2_4·c_4_7·a_1_2·a_5_9 + b_2_4·c_4_7·a_1_2·a_5_6 + b_2_4·c_4_7·a_1_0·a_5_11
       + b_2_42·c_4_7·a_1_0·a_3_6 + b_2_42·c_4_7·a_1_0·a_3_5 + c_4_7·a_1_12·a_1_2·a_5_9
       + b_2_4·c_4_72·a_1_22 + c_4_72·a_1_12·a_1_22
  84. a_5_11·a_7_19 + a_5_10·a_7_19 + b_2_42·a_1_0·a_7_20 + b_2_42·a_1_0·a_7_19
       + b_2_43·a_1_0·a_5_11 + b_2_44·a_1_0·a_3_6 + b_2_45·a_1_22 + c_4_7·a_1_0·a_7_20
       + c_4_7·a_1_0·a_7_19 + b_2_4·c_4_7·a_1_0·a_5_11 + b_2_42·c_4_7·a_1_0·a_3_6
       + b_2_43·c_4_7·a_1_22 + b_2_43·c_4_7·a_1_02
  85. a_5_11·a_7_19 + a_5_8·a_7_19 + a_5_6·a_7_20 + a_5_6·a_7_19 + b_2_42·a_1_0·a_7_20
       + b_2_42·a_1_0·a_7_19 + b_2_43·a_1_2·a_5_6 + b_2_43·a_1_0·a_5_11
       + b_2_43·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_2·a_5_9 + b_2_4·c_4_7·a_1_2·a_5_6
       + b_2_4·c_4_7·a_1_0·a_5_11 + b_2_4·c_4_7·a_1_0·a_5_8 + b_2_42·c_4_7·a_1_0·a_3_6
       + b_2_42·c_4_7·a_1_0·a_3_5 + b_2_43·c_4_7·a_1_02 + c_8_21·a_1_1·a_1_23
       + c_4_7·a_1_1·a_1_22·a_5_9 + b_2_4·c_4_72·a_1_22 + b_2_4·c_4_72·a_1_02
       + c_4_72·a_1_1·a_1_23
  86. a_5_8·a_7_20 + a_5_6·a_7_20 + b_2_42·a_1_0·a_7_20 + b_2_42·a_1_0·a_7_19
       + b_2_43·a_1_2·a_5_6 + b_2_43·a_1_0·a_5_11 + b_2_45·a_1_02 + c_8_21·a_1_0·a_3_6
       + b_2_4·c_4_7·a_1_2·a_5_6 + b_2_42·c_4_7·a_1_0·a_3_6 + b_2_43·c_4_7·a_1_02
       + c_8_21·a_1_12·a_1_22 + c_4_7·a_1_1·a_1_22·a_5_9 + c_4_7·a_1_12·a_1_2·a_5_9
       + c_4_72·a_1_0·a_3_6
  87. a_5_10·a_7_19 + b_2_42·a_1_0·a_7_19 + b_2_43·a_1_2·a_5_9 + b_2_44·a_1_0·a_3_6
       + b_2_44·a_1_0·a_3_5 + b_2_45·a_1_22 + c_8_21·a_1_0·a_3_5 + c_4_7·a_1_0·a_7_19
       + b_2_42·c_4_7·a_1_0·a_3_5 + b_2_43·c_4_7·a_1_22 + b_2_43·c_4_7·a_1_02
       + c_4_7·a_1_1·a_1_22·a_5_9 + c_4_7·a_1_12·a_1_2·a_5_9 + c_4_72·a_1_0·a_3_5
       + c_4_72·a_1_12·a_1_22
  88. a_5_11·a_7_19 + a_5_9·a_7_20 + a_5_8·a_7_19 + a_5_6·a_7_20 + b_2_43·a_1_2·a_5_6
       + b_2_45·a_1_02 + c_4_7·a_1_0·a_7_19 + b_2_4·c_8_21·a_1_02
       + b_2_4·c_4_7·a_1_2·a_5_9 + b_2_4·c_4_7·a_1_0·a_5_11 + b_2_42·c_4_7·a_1_0·a_3_5
       + b_2_43·c_4_7·a_1_22 + b_2_43·c_4_7·a_1_02 + c_8_21·a_1_12·a_1_22
       + c_4_7·a_1_1·a_1_22·a_5_9 + c_4_7·a_1_12·a_1_2·a_5_9 + b_2_4·c_4_72·a_1_22
       + b_2_4·c_4_72·a_1_02 + c_4_72·a_1_12·a_1_22
  89. a_5_9·a_7_19 + a_5_6·a_7_19 + b_2_43·a_1_0·a_5_11 + b_2_45·a_1_22
       + c_4_7·a_1_0·a_7_19 + b_2_4·c_8_21·a_1_22 + b_2_4·c_4_7·a_1_2·a_5_9
       + b_2_4·c_4_7·a_1_2·a_5_6 + b_2_4·c_4_7·a_1_0·a_5_8 + b_2_42·c_4_7·a_1_0·a_3_6
       + b_2_43·c_4_7·a_1_22 + b_2_43·c_4_7·a_1_02 + c_4_7·a_1_1·a_1_22·a_5_9
       + b_2_4·c_4_72·a_1_22 + b_2_4·c_4_72·a_1_02 + c_4_72·a_1_1·a_1_23
  90. a_5_11·a_7_19 + a_5_10·a_7_19 + a_5_9·a_7_19 + a_5_8·a_7_20 + a_5_6·a_7_20 + a_3_6·a_9_27
       + b_2_42·a_1_0·a_7_20 + b_2_42·a_1_0·a_7_19 + b_2_43·a_1_2·a_5_6
       + b_2_43·a_1_0·a_5_11 + b_2_44·a_1_0·a_3_5 + b_2_45·a_1_22 + b_2_45·a_1_02
       + b_2_4·c_4_7·a_1_2·a_5_6 + b_2_4·c_4_7·a_1_0·a_5_8 + b_2_42·c_4_7·a_1_0·a_3_5
       + b_2_43·c_4_7·a_1_02 + c_8_21·a_1_12·a_1_22 + c_4_7·a_1_1·a_1_22·a_5_9
       + c_4_7·a_1_12·a_1_2·a_5_9 + c_4_72·a_1_0·a_3_6 + c_4_72·a_1_0·a_3_5
       + c_4_72·a_1_12·a_1_22
  91. a_5_8·a_7_19 + a_5_6·a_7_19 + a_3_5·a_9_27 + b_2_43·a_1_2·a_5_9 + b_2_43·a_1_2·a_5_6
       + b_2_44·a_1_0·a_3_6 + c_4_7·a_1_0·a_7_19 + b_2_4·c_4_7·a_1_2·a_5_9
       + b_2_4·c_4_7·a_1_2·a_5_6 + b_2_4·c_4_7·a_1_0·a_5_11 + b_2_42·c_4_7·a_1_0·a_3_6
       + b_2_42·c_4_7·a_1_0·a_3_5 + b_2_43·c_4_7·a_1_22 + b_2_43·c_4_7·a_1_02
       + c_8_21·a_1_12·a_1_22 + c_4_7·a_1_1·a_1_22·a_5_9 + c_4_7·a_1_12·a_1_2·a_5_9
       + c_4_72·a_1_0·a_3_6 + c_4_72·a_1_0·a_3_5 + b_2_4·c_4_72·a_1_22
  92. a_5_9·a_7_19 + b_2_4·a_1_2·a_9_27 + b_2_43·a_1_2·a_5_9 + b_2_43·a_1_0·a_5_11
       + b_2_44·a_1_0·a_3_6 + b_2_45·a_1_02 + b_2_4·c_4_7·a_1_2·a_5_6
       + b_2_42·c_4_7·a_1_0·a_3_5 + c_4_72·a_1_1·a_1_23 + c_4_72·a_1_12·a_1_22
  93. a_5_10·a_7_19 + a_5_8·a_7_20 + a_5_6·a_7_20 + a_3_6·a_9_28 + b_2_43·a_1_2·a_5_6
       + b_2_43·a_1_0·a_5_11 + b_2_44·a_1_0·a_3_6 + b_2_44·a_1_0·a_3_5 + c_4_7·a_1_0·a_7_19
       + b_2_4·c_4_7·a_1_2·a_5_9 + b_2_4·c_4_7·a_1_2·a_5_6 + b_2_4·c_4_7·a_1_0·a_5_11
       + b_2_42·c_4_7·a_1_0·a_3_6 + b_2_42·c_4_7·a_1_0·a_3_5 + b_2_43·c_4_7·a_1_22
       + c_4_7·a_1_1·a_1_22·a_5_9 + c_4_72·a_1_0·a_3_6 + c_4_72·a_1_0·a_3_5
       + b_2_4·c_4_72·a_1_22 + b_2_4·c_4_72·a_1_02 + c_4_72·a_1_1·a_1_23
  94. a_5_11·a_7_19 + a_3_5·a_9_28 + b_2_42·a_1_0·a_7_19 + b_2_43·a_1_2·a_5_9
       + b_2_42·c_4_7·a_1_0·a_3_5 + c_8_21·a_1_12·a_1_22 + c_4_7·a_1_12·a_1_2·a_5_9
       + c_4_72·a_1_0·a_3_6 + c_4_72·a_1_0·a_3_5 + b_2_4·c_4_72·a_1_02
       + c_4_72·a_1_1·a_1_23
  95. a_5_10·a_7_19 + a_5_9·a_7_20 + a_5_8·a_7_19 + b_2_4·a_1_0·a_9_28 + b_2_42·a_1_0·a_7_20
       + b_2_42·a_1_0·a_7_19 + b_2_43·a_1_2·a_5_6 + b_2_43·a_1_0·a_5_8
       + b_2_44·a_1_0·a_3_5 + b_2_45·a_1_22 + b_2_4·c_4_7·a_1_2·a_5_9
       + b_2_4·c_4_7·a_1_0·a_5_11 + b_2_4·c_4_7·a_1_0·a_5_8 + b_2_42·c_4_7·a_1_0·a_3_6
       + b_2_43·c_4_7·a_1_22 + c_8_21·a_1_12·a_1_22 + c_4_7·a_1_1·a_1_22·a_5_9
       + c_4_7·a_1_12·a_1_2·a_5_9 + b_2_4·c_4_72·a_1_22 + c_4_72·a_1_12·a_1_22
  96. b_6_16·a_7_19 + b_2_42·a_9_27 + b_2_43·a_7_20 + b_2_44·a_5_11 + b_2_45·a_3_6
       + b_2_46·a_1_2 + b_2_46·a_1_0 + b_2_43·a_1_22·a_5_9 + b_2_4·c_4_7·a_7_19
       + b_2_42·c_8_21·a_1_2 + b_2_42·c_8_21·a_1_0 + b_2_42·c_4_7·a_5_11
       + b_2_42·c_4_7·a_5_9 + b_2_42·c_4_7·a_5_8 + b_2_42·c_4_7·a_5_6 + b_2_43·c_4_7·a_3_5
       + b_2_4·c_4_7·a_1_22·a_5_9 + c_4_7·a_1_12·a_1_22·a_5_9
  97. b_6_16·a_7_20 + b_6_16·a_7_19 + b_2_42·a_9_28 + b_2_43·a_7_19 + b_2_44·a_5_6
       + b_2_45·a_3_6 + b_2_45·a_3_5 + b_2_46·a_1_2 + b_2_4·c_4_7·a_7_20 + b_2_4·c_4_7·a_7_19
       + b_2_42·c_8_21·a_1_0 + b_2_42·c_4_7·a_5_11 + b_2_42·c_4_7·a_5_9
       + b_2_43·c_4_7·a_3_6 + b_2_43·c_4_7·a_3_5 + b_2_44·c_4_7·a_1_2
       + b_2_42·c_4_72·a_1_2
  98. a_7_202 + b_2_44·a_1_0·a_5_8 + b_2_45·a_1_0·a_3_6 + b_2_46·a_1_22
       + b_2_46·a_1_02 + c_8_21·a_1_0·a_5_8 + b_2_4·c_8_21·a_1_0·a_3_6
       + b_2_42·c_8_21·a_1_22 + b_2_42·c_4_7·a_1_0·a_5_8 + b_2_43·c_4_7·a_1_0·a_3_6
       + b_2_44·c_4_7·a_1_02 + c_4_72·a_1_0·a_5_8 + b_2_4·c_4_72·a_1_0·a_3_6
       + b_2_42·c_4_72·a_1_22 + b_2_42·c_4_72·a_1_02
  99. a_7_202 + a_7_19·a_7_20 + a_7_192 + b_2_43·a_1_0·a_7_19 + b_2_44·a_1_2·a_5_9
       + b_2_44·a_1_2·a_5_6 + b_2_45·a_1_0·a_3_6 + b_2_45·a_1_0·a_3_5 + b_2_46·a_1_22
       + c_8_21·a_1_0·a_5_11 + b_2_4·c_8_21·a_1_0·a_3_5 + b_2_4·c_4_7·a_1_0·a_7_20
       + b_2_42·c_4_7·a_1_2·a_5_6 + b_2_42·c_4_7·a_1_0·a_5_8 + b_2_43·c_4_7·a_1_0·a_3_6
       + b_2_43·c_4_7·a_1_0·a_3_5 + b_2_44·c_4_7·a_1_02 + c_4_72·a_1_0·a_5_11
       + b_2_4·c_4_72·a_1_0·a_3_5 + b_2_42·c_4_72·a_1_22
  100. a_7_202 + a_7_192 + b_2_46·a_1_22 + b_2_46·a_1_02 + c_8_21·a_1_0·a_5_8
       + b_2_4·c_8_21·a_1_0·a_3_6 + b_2_42·c_8_21·a_1_02 + c_4_7·c_8_21·a_1_02
       + c_4_72·a_1_0·a_5_8 + b_2_4·c_4_72·a_1_0·a_3_6 + b_2_42·c_4_72·a_1_22
       + c_4_73·a_1_02
  101. a_7_19·a_7_20 + a_7_192 + a_5_11·a_9_27 + a_5_9·a_9_27 + a_5_6·a_9_27
       + b_2_42·a_1_2·a_9_27 + b_2_43·a_1_0·a_7_19 + b_2_44·a_1_2·a_5_6
       + b_2_44·a_1_0·a_5_11 + b_2_44·a_1_0·a_5_8 + b_2_45·a_1_0·a_3_6 + b_2_46·a_1_22
       + b_2_46·a_1_02 + c_8_21·a_1_2·a_5_9 + c_8_21·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_7_20
       + b_2_4·c_4_7·a_1_0·a_7_19 + b_2_42·c_4_7·a_1_2·a_5_9 + b_2_42·c_4_7·a_1_0·a_5_11
       + b_2_43·c_4_7·a_1_0·a_3_6 + b_2_44·c_4_7·a_1_22 + c_4_7·c_8_21·a_1_22
       + c_4_72·a_1_2·a_5_9 + c_4_72·a_1_1·a_5_9 + b_2_4·c_4_72·a_1_0·a_3_6
       + b_2_42·c_4_72·a_1_22 + b_2_42·c_4_72·a_1_02 + c_4_73·a_1_22
       + c_4_73·a_1_12 + c_4_73·a_1_02
  102. a_7_202 + a_5_10·a_9_27 + a_5_8·a_9_27 + b_2_42·a_1_2·a_9_27 + b_2_43·a_1_0·a_7_20
       + b_2_44·a_1_2·a_5_6 + b_2_44·a_1_0·a_5_11 + b_2_45·a_1_0·a_3_5 + b_2_46·a_1_02
       + c_8_21·a_1_2·a_5_6 + c_8_21·a_1_1·a_5_9 + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_0·a_5_8
       + b_2_4·c_4_7·a_1_0·a_7_20 + b_2_4·c_4_7·a_1_0·a_7_19 + b_2_42·c_4_7·a_1_2·a_5_9
       + b_2_42·c_4_7·a_1_0·a_5_11 + b_2_42·c_4_7·a_1_0·a_5_8 + b_2_43·c_4_7·a_1_0·a_3_6
       + c_4_7·c_8_21·a_1_22 + c_4_7·c_8_21·a_1_1·a_1_2 + c_4_7·c_8_21·a_1_12
       + c_4_72·a_1_2·a_5_9 + c_4_72·a_1_1·a_5_9 + c_4_72·a_1_0·a_5_8
       + b_2_4·c_4_72·a_1_0·a_3_6 + b_2_42·c_4_72·a_1_22 + b_2_42·c_4_72·a_1_02
       + c_4_73·a_1_22
  103. a_7_202 + a_5_9·a_9_27 + b_2_43·a_1_0·a_7_20 + b_2_44·a_1_2·a_5_9
       + b_2_44·a_1_2·a_5_6 + b_2_44·a_1_0·a_5_11 + b_2_45·a_1_0·a_3_6
       + b_2_45·a_1_0·a_3_5 + b_2_46·a_1_02 + c_8_21·a_1_2·a_5_9 + c_8_21·a_1_2·a_5_6
       + c_8_21·a_1_0·a_5_8 + c_4_7·a_1_2·a_9_27 + b_2_4·c_8_21·a_1_0·a_3_6
       + b_2_4·c_4_7·a_1_0·a_7_19 + b_2_42·c_4_7·a_1_2·a_5_9 + b_2_42·c_4_7·a_1_0·a_5_8
       + b_2_43·c_4_7·a_1_0·a_3_6 + c_4_7·c_8_21·a_1_1·a_1_2 + c_4_72·a_1_1·a_5_9
       + c_4_72·a_1_0·a_5_8 + b_2_4·c_4_72·a_1_0·a_3_6 + b_2_4·c_4_72·a_1_0·a_3_5
       + c_4_73·a_1_1·a_1_2
  104. a_5_9·a_9_27 + a_5_8·a_9_27 + a_5_6·a_9_28 + b_2_43·a_1_0·a_7_19 + b_2_44·a_1_0·a_5_8
       + b_2_45·a_1_0·a_3_6 + b_2_45·a_1_0·a_3_5 + b_2_46·a_1_02 + c_8_21·a_1_2·a_5_9
       + c_8_21·a_1_1·a_5_9 + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_0·a_5_8
       + b_2_4·c_8_21·a_1_0·a_3_6 + b_2_4·c_8_21·a_1_0·a_3_5 + b_2_42·c_4_7·a_1_0·a_5_11
       + b_2_43·c_4_7·a_1_0·a_3_6 + b_2_43·c_4_7·a_1_0·a_3_5 + c_4_7·c_8_21·a_1_1·a_1_2
       + c_4_7·c_8_21·a_1_12 + c_4_72·a_1_0·a_5_8 + b_2_4·c_4_72·a_1_0·a_3_5
       + c_4_73·a_1_12
  105. a_7_192 + a_5_9·a_9_28 + a_5_6·a_9_27 + b_2_42·a_1_2·a_9_27 + b_2_44·a_1_2·a_5_9
       + b_2_44·a_1_0·a_5_8 + b_2_45·a_1_0·a_3_5 + b_2_46·a_1_22 + c_8_21·a_1_1·a_5_9
       + b_2_4·c_4_7·a_1_0·a_7_20 + b_2_42·c_4_7·a_1_2·a_5_9 + b_2_42·c_4_7·a_1_2·a_5_6
       + b_2_42·c_4_7·a_1_0·a_5_8 + b_2_43·c_4_7·a_1_0·a_3_6 + b_2_43·c_4_7·a_1_0·a_3_5
       + b_2_44·c_4_7·a_1_22 + c_4_7·c_8_21·a_1_22 + c_4_7·c_8_21·a_1_1·a_1_2
       + c_4_72·a_1_2·a_5_9 + c_4_72·a_1_1·a_5_8 + c_4_72·a_1_0·a_5_11
       + b_2_4·c_4_72·a_1_0·a_3_5 + b_2_42·c_4_72·a_1_02 + c_4_73·a_1_22
       + c_4_73·a_1_12 + c_4_73·a_1_02
  106. a_7_202 + a_7_19·a_7_20 + a_5_8·a_9_28 + b_2_42·a_1_2·a_9_27 + b_2_43·a_1_0·a_7_20
       + b_2_44·a_1_2·a_5_6 + b_2_44·a_1_0·a_5_11 + c_8_21·a_1_1·a_5_8
       + b_2_4·c_8_21·a_1_0·a_3_6 + b_2_4·c_4_7·a_1_0·a_7_20 + b_2_42·c_4_7·a_1_2·a_5_9
       + b_2_42·c_4_7·a_1_0·a_5_8 + b_2_43·c_4_7·a_1_0·a_3_6 + b_2_43·c_4_7·a_1_0·a_3_5
       + b_2_44·c_4_7·a_1_22 + c_4_7·c_8_21·a_1_1·a_1_2 + c_4_72·a_1_2·a_5_9
       + c_4_72·a_1_1·a_5_8 + c_4_72·a_1_0·a_5_11 + b_2_4·c_4_72·a_1_0·a_3_5
       + b_2_42·c_4_72·a_1_22 + b_2_42·c_4_72·a_1_02 + c_4_73·a_1_22
       + c_4_73·a_1_02
  107. a_7_202 + a_7_192 + a_5_9·a_9_27 + a_5_6·a_9_27 + b_2_42·a_1_2·a_9_27
       + b_2_42·a_1_0·a_9_28 + b_2_43·a_1_0·a_7_20 + b_2_44·a_1_0·a_5_11
       + b_2_45·a_1_0·a_3_6 + b_2_45·a_1_0·a_3_5 + b_2_46·a_1_22 + b_2_46·a_1_02
       + c_8_21·a_1_2·a_5_9 + c_8_21·a_1_0·a_5_8 + b_2_4·c_8_21·a_1_0·a_3_6
       + b_2_4·c_8_21·a_1_0·a_3_5 + b_2_4·c_4_7·a_1_0·a_7_20 + b_2_42·c_4_7·a_1_2·a_5_6
       + b_2_42·c_4_7·a_1_0·a_5_11 + b_2_43·c_4_7·a_1_0·a_3_6 + b_2_43·c_4_7·a_1_0·a_3_5
       + b_2_44·c_4_7·a_1_22 + c_4_7·c_8_21·a_1_22 + c_4_7·c_8_21·a_1_1·a_1_2
       + c_4_72·a_1_2·a_5_9 + c_4_72·a_1_1·a_5_8 + c_4_72·a_1_0·a_5_11
       + c_4_72·a_1_0·a_5_8 + b_2_4·c_4_72·a_1_0·a_3_6 + b_2_42·c_4_72·a_1_02
       + c_4_73·a_1_22 + c_4_73·a_1_12 + c_4_73·a_1_02
  108. a_7_202 + a_5_11·a_9_28 + a_5_9·a_9_27 + a_5_8·a_9_27 + a_5_6·a_9_27
       + b_2_42·a_1_2·a_9_27 + b_2_43·a_1_0·a_7_20 + b_2_43·a_1_0·a_7_19
       + b_2_44·a_1_2·a_5_9 + b_2_44·a_1_0·a_5_11 + b_2_46·a_1_02 + c_8_21·a_1_2·a_5_9
       + c_8_21·a_1_2·a_5_6 + c_8_21·a_1_1·a_5_9 + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_0·a_5_8
       + b_2_4·c_8_21·a_1_0·a_3_6 + b_2_4·c_8_21·a_1_0·a_3_5 + b_2_4·c_4_7·a_1_0·a_7_19
       + b_2_42·c_4_7·a_1_2·a_5_9 + b_2_43·c_4_7·a_1_0·a_3_6 + b_2_43·c_4_7·a_1_0·a_3_5
       + b_2_44·c_4_7·a_1_22 + c_4_7·c_8_21·a_1_1·a_1_2 + c_4_72·a_1_1·a_5_9
       + c_4_72·a_1_1·a_5_8 + c_4_72·a_1_0·a_5_11 + b_2_4·c_4_72·a_1_0·a_3_6
       + b_2_4·c_4_72·a_1_0·a_3_5 + c_4_73·a_1_12
  109. a_7_19·a_7_20 + a_5_10·a_9_28 + b_2_44·a_1_2·a_5_6 + b_2_44·a_1_0·a_5_11
       + b_2_44·a_1_0·a_5_8 + b_2_45·a_1_0·a_3_6 + b_2_45·a_1_0·a_3_5 + b_2_46·a_1_22
       + c_8_21·a_1_0·a_5_8 + b_2_4·c_8_21·a_1_0·a_3_6 + b_2_4·c_8_21·a_1_0·a_3_5
       + b_2_4·c_4_7·a_1_0·a_7_20 + b_2_4·c_4_7·a_1_0·a_7_19 + b_2_42·c_4_7·a_1_2·a_5_9
       + b_2_42·c_4_7·a_1_2·a_5_6 + b_2_43·c_4_7·a_1_0·a_3_6 + c_4_7·c_8_21·a_1_12
       + c_4_72·a_1_1·a_5_9 + c_4_72·a_1_1·a_5_8 + c_4_72·a_1_0·a_5_11
       + c_4_72·a_1_0·a_5_8 + b_2_4·c_4_72·a_1_0·a_3_6 + b_2_42·c_4_72·a_1_22
       + c_4_73·a_1_02
  110. a_7_202 + a_5_8·a_9_27 + b_2_43·a_1_0·a_7_19 + b_2_44·a_1_2·a_5_9
       + b_2_44·a_1_2·a_5_6 + b_2_44·a_1_0·a_5_11 + b_2_44·a_1_0·a_5_8
       + b_2_45·a_1_0·a_3_6 + c_8_21·a_1_2·a_5_6 + c_8_21·a_1_1·a_5_9 + c_8_21·a_1_1·a_5_8
       + c_4_7·a_1_0·a_9_28 + b_2_4·c_4_7·a_1_0·a_7_20 + b_2_4·c_4_7·a_1_0·a_7_19
       + b_2_42·c_4_7·a_1_2·a_5_9 + b_2_42·c_4_7·a_1_2·a_5_6 + b_2_42·c_4_7·a_1_0·a_5_8
       + b_2_43·c_4_7·a_1_0·a_3_6 + b_2_44·c_4_7·a_1_22 + b_2_44·c_4_7·a_1_02
       + c_4_7·c_8_21·a_1_22 + c_4_7·c_8_21·a_1_12 + c_4_72·a_1_2·a_5_9
       + c_4_72·a_1_1·a_5_8 + b_2_4·c_4_72·a_1_0·a_3_5 + b_2_42·c_4_72·a_1_22
       + c_4_73·a_1_22
  111. b_6_16·a_9_27 + b_2_43·a_9_28 + b_2_43·a_9_27 + b_2_44·a_7_20 + b_2_44·a_7_19
       + b_2_45·a_5_9 + b_2_45·a_5_8 + b_2_46·a_3_5 + b_2_47·a_1_2 + b_2_47·a_1_0
       + b_2_42·a_1_02·a_9_28 + b_2_4·c_8_21·a_5_6 + b_2_42·c_4_7·a_7_20
       + b_2_42·c_4_7·a_7_19 + b_2_43·c_4_7·a_5_8 + b_2_44·c_4_7·a_3_5
       + b_2_45·c_4_7·a_1_2 + b_2_45·c_4_7·a_1_0 + c_8_21·a_1_22·a_5_9
       + c_8_21·a_1_1·a_1_2·a_5_9 + c_8_21·a_1_12·a_5_9 + c_8_21·a_1_02·a_5_11
       + b_2_42·c_4_7·a_1_22·a_5_9 + b_2_4·c_4_7·c_8_21·a_1_2 + b_2_4·c_4_72·a_5_11
       + b_2_4·c_4_72·a_5_9 + b_2_43·c_4_72·a_1_2 + b_2_43·c_4_72·a_1_0
       + c_4_7·c_8_21·a_1_23 + c_4_7·c_8_21·a_1_1·a_1_22 + c_4_7·c_8_21·a_1_12·a_1_2
       + c_4_72·a_1_12·a_5_9 + b_2_4·c_4_73·a_1_2 + c_4_73·a_1_1·a_1_22
       + c_4_73·a_1_12·a_1_2
  112. b_6_16·a_9_28 + b_2_43·a_9_27 + b_2_44·a_7_19 + b_2_45·a_5_8 + b_2_47·a_1_0
       + b_2_4·c_4_7·a_9_28 + b_2_4·c_4_7·a_9_27 + b_2_42·c_8_21·a_3_5 + b_2_43·c_8_21·a_1_2
       + b_2_43·c_8_21·a_1_0 + b_2_43·c_4_7·a_5_11 + b_2_43·c_4_7·a_5_8
       + b_2_44·c_4_7·a_3_5 + b_2_45·c_4_7·a_1_0 + c_8_21·a_1_1·a_1_2·a_5_9
       + c_8_21·a_1_12·a_5_9 + c_8_21·a_1_02·a_5_11 + b_2_42·c_4_7·a_1_22·a_5_9
       + b_2_4·c_4_7·c_8_21·a_1_2 + b_2_4·c_4_7·c_8_21·a_1_0 + b_2_4·c_4_72·a_5_11
       + b_2_4·c_4_72·a_5_9 + b_2_43·c_4_72·a_1_2 + c_4_7·c_8_21·a_1_23
       + c_4_7·c_8_21·a_1_12·a_1_2 + c_4_72·a_1_12·a_5_9 + b_2_4·c_4_73·a_1_2
       + c_4_73·a_1_1·a_1_22 + c_4_73·a_1_12·a_1_2
  113. a_7_20·a_9_27 + b_2_45·a_1_2·a_5_6 + b_2_45·a_1_0·a_5_11 + b_2_45·a_1_0·a_5_8
       + b_2_46·a_1_0·a_3_6 + b_2_47·a_1_22 + c_8_21·a_1_0·a_7_20
       + b_2_4·c_8_21·a_1_2·a_5_6 + b_2_42·c_8_21·a_1_0·a_3_6 + b_2_42·c_8_21·a_1_0·a_3_5
       + b_2_42·c_4_7·a_1_0·a_7_19 + b_2_43·c_8_21·a_1_22 + b_2_43·c_4_7·a_1_2·a_5_6
       + b_2_43·c_4_7·a_1_0·a_5_8 + b_2_44·c_4_7·a_1_0·a_3_6 + c_8_21·a_1_1·a_1_22·a_5_9
       + c_8_21·a_1_12·a_1_2·a_5_9 + c_4_7·c_8_21·a_1_0·a_3_6 + c_4_7·c_8_21·a_1_0·a_3_5
       + c_4_72·a_1_0·a_7_19 + b_2_4·c_4_72·a_1_2·a_5_6 + b_2_42·c_4_72·a_1_0·a_3_6
       + b_2_43·c_4_72·a_1_22 + b_2_43·c_4_72·a_1_02 + c_4_7·c_8_21·a_1_1·a_1_23
       + c_4_7·c_8_21·a_1_12·a_1_22 + c_4_72·a_1_1·a_1_22·a_5_9 + c_4_73·a_1_0·a_3_6
       + c_4_73·a_1_0·a_3_5 + b_2_4·c_4_73·a_1_02 + c_4_73·a_1_1·a_1_23
       + c_4_73·a_1_12·a_1_22
  114. a_7_20·a_9_28 + b_2_43·a_1_2·a_9_27 + b_2_44·a_1_0·a_7_20 + b_2_47·a_1_02
       + c_8_21·a_1_0·a_7_20 + c_8_21·a_1_0·a_7_19 + b_2_4·c_8_21·a_1_2·a_5_6
       + b_2_4·c_8_21·a_1_0·a_5_11 + b_2_4·c_8_21·a_1_0·a_5_8 + b_2_42·c_4_7·a_1_0·a_7_19
       + b_2_43·c_4_7·a_1_2·a_5_6 + b_2_43·c_4_7·a_1_0·a_5_11 + b_2_43·c_4_7·a_1_0·a_5_8
       + c_8_21·a_1_12·a_1_2·a_5_9 + b_2_4·c_4_7·c_8_21·a_1_02
       + b_2_4·c_4_72·a_1_0·a_5_11 + b_2_43·c_4_72·a_1_02 + c_4_7·c_8_21·a_1_1·a_1_23
       + c_4_72·a_1_1·a_1_22·a_5_9 + b_2_4·c_4_73·a_1_02 + c_4_73·a_1_1·a_1_23
       + c_4_73·a_1_12·a_1_22
  115. a_7_19·a_9_28 + b_2_43·a_1_0·a_9_28 + b_2_44·a_1_0·a_7_19 + b_2_45·a_1_2·a_5_9
       + b_2_46·a_1_0·a_3_5 + b_2_47·a_1_22 + c_8_21·a_1_0·a_7_19
       + b_2_4·c_8_21·a_1_2·a_5_6 + b_2_4·c_4_7·a_1_2·a_9_27 + b_2_42·c_8_21·a_1_0·a_3_6
       + b_2_42·c_4_7·a_1_0·a_7_20 + b_2_43·c_8_21·a_1_02 + b_2_43·c_4_7·a_1_2·a_5_6
       + b_2_44·c_4_7·a_1_0·a_3_5 + b_2_45·c_4_7·a_1_22 + b_2_45·c_4_7·a_1_02
       + c_8_21·a_1_1·a_1_22·a_5_9 + c_8_21·a_1_12·a_1_2·a_5_9 + c_4_7·c_8_21·a_1_0·a_3_6
       + c_4_72·a_1_0·a_7_20 + b_2_4·c_4_72·a_1_2·a_5_9 + b_2_4·c_4_72·a_1_0·a_5_11
       + b_2_4·c_4_72·a_1_0·a_5_8 + b_2_43·c_4_72·a_1_22 + c_4_7·c_8_21·a_1_1·a_1_23
       + c_4_7·c_8_21·a_1_12·a_1_22 + c_4_72·a_1_12·a_1_2·a_5_9 + c_4_73·a_1_0·a_3_6
       + b_2_4·c_4_73·a_1_22 + b_2_4·c_4_73·a_1_02
  116. a_7_19·a_9_28 + a_7_19·a_9_27 + b_2_44·a_1_0·a_7_20 + b_2_45·a_1_2·a_5_9
       + b_2_45·a_1_0·a_5_8 + b_2_46·a_1_0·a_3_5 + b_2_47·a_1_02
       + b_2_4·c_8_21·a_1_2·a_5_9 + b_2_4·c_8_21·a_1_2·a_5_6 + b_2_4·c_8_21·a_1_0·a_5_11
       + b_2_4·c_8_21·a_1_0·a_5_8 + b_2_4·c_4_7·a_1_0·a_9_28 + b_2_43·c_8_21·a_1_22
       + b_2_43·c_8_21·a_1_02 + b_2_43·c_4_7·a_1_2·a_5_9 + b_2_43·c_4_7·a_1_2·a_5_6
       + b_2_43·c_4_7·a_1_0·a_5_11 + b_2_43·c_4_7·a_1_0·a_5_8 + b_2_45·c_4_7·a_1_22
       + c_8_21·a_1_1·a_1_22·a_5_9 + c_4_7·c_8_21·a_1_0·a_3_6 + c_4_7·c_8_21·a_1_0·a_3_5
       + b_2_4·c_4_7·c_8_21·a_1_22 + b_2_4·c_4_72·a_1_0·a_5_8
       + b_2_42·c_4_72·a_1_0·a_3_6 + b_2_42·c_4_72·a_1_0·a_3_5
       + b_2_43·c_4_72·a_1_02 + c_4_73·a_1_0·a_3_6 + c_4_73·a_1_0·a_3_5
       + b_2_4·c_4_73·a_1_02
  117. a_9_272 + b_2_46·a_1_0·a_5_8 + b_2_47·a_1_0·a_3_6 + b_2_48·a_1_22
       + b_2_48·a_1_02 + b_2_42·c_8_21·a_1_0·a_5_8 + b_2_43·c_8_21·a_1_0·a_3_6
       + b_2_46·c_4_7·a_1_22 + c_8_212·a_1_22 + c_8_212·a_1_02
       + b_2_42·c_4_7·c_8_21·a_1_22 + b_2_44·c_4_72·a_1_02 + c_4_72·c_8_21·a_1_22
       + c_4_72·c_8_21·a_1_02 + c_4_73·a_1_0·a_5_8 + b_2_4·c_4_73·a_1_0·a_3_6
       + b_2_42·c_4_73·a_1_22 + c_4_74·a_1_12 + c_4_74·a_1_02
  118. a_9_282 + b_2_48·a_1_02 + b_2_42·c_8_21·a_1_0·a_5_8 + b_2_43·c_8_21·a_1_0·a_3_6
       + b_2_44·c_8_21·a_1_22 + b_2_44·c_4_7·a_1_0·a_5_8 + b_2_45·c_4_7·a_1_0·a_3_6
       + c_8_212·a_1_12 + c_8_212·a_1_02 + c_4_7·c_8_21·a_1_0·a_5_8
       + b_2_4·c_4_7·c_8_21·a_1_0·a_3_6 + b_2_42·c_4_7·c_8_21·a_1_02
       + b_2_44·c_4_72·a_1_02 + c_4_72·c_8_21·a_1_22 + b_2_42·c_4_73·a_1_02
       + c_4_74·a_1_12
  119. a_9_27·a_9_28 + b_2_44·a_1_2·a_9_27 + b_2_45·a_1_0·a_7_20 + b_2_46·a_1_0·a_5_11
       + b_2_46·a_1_0·a_5_8 + b_2_47·a_1_0·a_3_5 + c_8_21·a_1_2·a_9_27 + c_8_21·a_1_0·a_9_28
       + b_2_4·c_8_21·a_1_0·a_7_20 + b_2_42·c_8_21·a_1_2·a_5_9
       + b_2_42·c_8_21·a_1_0·a_5_11 + b_2_42·c_4_7·a_1_2·a_9_27
       + b_2_43·c_8_21·a_1_0·a_3_6 + b_2_43·c_4_7·a_1_0·a_7_19 + b_2_44·c_8_21·a_1_22
       + b_2_44·c_8_21·a_1_02 + b_2_44·c_4_7·a_1_2·a_5_6 + b_2_45·c_4_7·a_1_0·a_3_6
       + b_2_45·c_4_7·a_1_0·a_3_5 + b_2_46·c_4_7·a_1_22 + b_2_46·c_4_7·a_1_02
       + c_8_212·a_1_22 + c_8_212·a_1_1·a_1_2 + c_4_7·c_8_21·a_1_1·a_5_9
       + c_4_7·c_8_21·a_1_1·a_5_8 + c_4_7·c_8_21·a_1_0·a_5_8 + c_4_72·a_1_0·a_9_28
       + b_2_42·c_4_7·c_8_21·a_1_02 + b_2_42·c_4_72·a_1_0·a_5_11
       + b_2_42·c_4_72·a_1_0·a_5_8 + b_2_43·c_4_72·a_1_0·a_3_6
       + b_2_43·c_4_72·a_1_0·a_3_5 + b_2_44·c_4_72·a_1_22 + b_2_44·c_4_72·a_1_02
       + c_4_72·c_8_21·a_1_22 + c_4_72·c_8_21·a_1_02 + b_2_4·c_4_73·a_1_0·a_3_6
       + b_2_42·c_4_73·a_1_02 + c_4_74·a_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 18.
  • 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_4_7, a Duflot regular element of degree 4
    2. c_8_21, a Duflot regular element of degree 8
    3. b_2_4, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 9, 11].
  • 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 2

  1. a_1_00, an element of degree 1
  2. a_1_10, an element of degree 1
  3. a_1_20, an element of degree 1
  4. b_2_40, an element of degree 2
  5. a_3_50, an element of degree 3
  6. a_3_60, an element of degree 3
  7. c_4_7c_1_04, an element of degree 4
  8. a_5_60, an element of degree 5
  9. a_5_80, an element of degree 5
  10. a_5_90, an element of degree 5
  11. a_5_100, an element of degree 5
  12. a_5_110, an element of degree 5
  13. b_6_160, an element of degree 6
  14. a_7_190, an element of degree 7
  15. a_7_200, an element of degree 7
  16. c_8_21c_1_18, an element of degree 8
  17. a_9_270, an element of degree 9
  18. a_9_280, an element of degree 9

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

  1. a_1_00, an element of degree 1
  2. a_1_10, an element of degree 1
  3. a_1_20, an element of degree 1
  4. b_2_4c_1_22, an element of degree 2
  5. a_3_50, an element of degree 3
  6. a_3_60, an element of degree 3
  7. c_4_7c_1_04, an element of degree 4
  8. a_5_60, an element of degree 5
  9. a_5_80, an element of degree 5
  10. a_5_90, an element of degree 5
  11. a_5_100, an element of degree 5
  12. a_5_110, an element of degree 5
  13. b_6_16c_1_26 + c_1_02·c_1_24 + c_1_04·c_1_22, an element of degree 6
  14. a_7_190, an element of degree 7
  15. a_7_200, an element of degree 7
  16. c_8_21c_1_14·c_1_24 + c_1_18, an element of degree 8
  17. a_9_270, an element of degree 9
  18. a_9_280, an element of degree 9


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