Cohomology of group number 1378 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 4 minimal generators and exponent 4.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 3.
  • It has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 4.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 3.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t3  +  t  +  1) · (t4  −  3·t3  −  t  −  1)
    (t  +  1)2 · (t  −  1)4 · (t2  +  1)3
  • The a-invariants are -∞,-∞,-∞,-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 18 minimal generators of maximal degree 8:

  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_1_3, an element of degree 1
  5. a_3_5, a nilpotent element of degree 3
  6. a_3_7, a nilpotent element of degree 3
  7. a_3_8, a nilpotent element of degree 3
  8. a_3_6, a nilpotent element of degree 3
  9. a_3_11, a nilpotent element of degree 3
  10. b_3_9, an element of degree 3
  11. b_3_10, an element of degree 3
  12. c_4_19, a Duflot regular element of degree 4
  13. c_4_20, a Duflot regular element of degree 4
  14. c_4_21, a Duflot regular element of degree 4
  15. a_5_30, a nilpotent element of degree 5
  16. a_5_27, a nilpotent element of degree 5
  17. a_6_38, a nilpotent element of degree 6
  18. a_8_67, a nilpotent 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 93 minimal relations of maximal degree 16:

  1. a_1_1·a_1_2 + a_1_02
  2. a_1_22 + a_1_12 + a_1_0·a_1_2
  3. a_1_2·b_1_3 + a_1_0·a_1_1
  4. a_1_0·a_1_12
  5. a_1_02·a_1_2 + a_1_02·a_1_1
  6. a_1_0·a_1_1·b_1_3 + a_1_02·a_1_1 + a_1_03
  7. a_1_2·a_3_5 + a_1_1·a_3_7 + a_1_1·a_3_5 + a_1_0·a_3_7 + a_1_0·a_3_5
  8. a_1_2·a_3_7 + a_1_1·a_3_5 + a_1_0·a_3_5
  9. b_1_3·a_3_6 + a_1_1·a_3_8 + a_1_1·a_3_7 + a_1_1·a_3_5
  10. a_1_2·a_3_5 + a_1_1·a_3_6 + a_1_1·a_3_7 + a_1_1·a_3_5 + a_1_0·a_3_8
  11. a_1_2·a_3_8 + a_1_2·a_3_5 + a_1_1·a_3_5 + a_1_0·a_3_6 + a_1_0·a_3_5
  12. a_1_2·a_3_6 + a_1_2·a_3_8 + a_1_2·a_3_5 + a_1_1·a_3_11 + a_1_1·a_3_8 + a_1_1·a_3_7
       + a_1_0·a_3_5
  13. a_1_2·a_3_5 + a_1_1·a_3_8 + a_1_0·a_3_11 + a_1_0·a_3_8
  14. a_1_2·a_3_11 + a_1_2·a_3_8 + a_1_1·a_3_7 + a_1_0·a_3_8 + a_1_0·a_3_5
  15. b_1_3·a_3_7 + a_1_1·b_3_9 + a_1_0·b_3_9 + a_1_2·a_3_6 + a_1_2·a_3_8 + a_1_1·a_3_5
       + a_1_0·a_3_8
  16. a_1_2·b_3_9 + a_1_2·a_3_8 + a_1_1·a_3_5 + a_1_0·a_3_8
  17. b_1_3·a_3_7 + b_1_3·a_3_5 + a_1_1·b_3_10 + a_1_0·b_3_10 + a_1_2·a_3_6 + a_1_2·a_3_5
       + a_1_1·a_3_7 + a_1_0·a_3_5
  18. a_1_2·b_3_10 + a_1_2·a_3_6 + a_1_2·a_3_8 + a_1_2·a_3_5 + a_1_0·a_3_8
  19. a_1_0·a_1_1·a_3_5 + a_1_02·a_3_7 + a_1_02·a_3_5
  20. a_1_0·a_1_1·b_3_9 + a_1_0·a_1_1·a_3_7 + a_1_0·a_1_1·a_3_5 + a_1_02·a_3_11
       + a_1_02·a_3_8
  21. a_1_0·a_1_1·b_3_10 + a_1_02·a_3_6 + a_1_02·a_3_8 + a_1_02·a_3_5
  22. a_3_72 + a_3_5·a_3_7 + a_3_52
  23. a_3_7·a_3_11 + a_3_7·a_3_6 + a_3_5·a_3_6
  24. a_3_6·a_3_11 + a_3_8·a_3_6 + a_3_82 + a_3_7·a_3_6 + a_3_72 + a_3_5·a_3_6 + a_3_52
  25. a_3_7·a_3_6 + a_3_5·a_3_11
  26. a_3_112 + a_3_62 + a_3_8·a_3_6 + a_3_82 + a_3_7·a_3_6 + a_3_72 + a_3_5·a_3_6
       + a_3_52
  27. a_3_6·b_3_9 + a_3_8·a_3_6 + a_3_82 + a_3_7·a_3_6 + a_3_7·a_3_8 + a_3_72
  28. a_3_7·b_3_10 + a_3_7·b_3_9 + a_3_5·b_3_9
  29. a_3_6·b_3_10 + a_3_62 + a_3_8·a_3_6 + a_3_82 + a_3_7·a_3_8 + a_3_5·a_3_6 + a_3_5·a_3_8
  30. b_3_102 + a_3_7·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_8·a_3_6 + a_3_82 + a_3_72
       + a_3_5·a_3_6 + a_1_0·b_1_32·a_3_11 + c_4_19·b_1_32 + c_4_19·a_1_1·b_1_3
       + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_12 + c_4_19·a_1_0·a_1_2 + c_4_19·a_1_0·a_1_1
  31. b_3_102 + b_3_92 + b_1_33·b_3_10 + b_1_33·b_3_9 + a_3_7·b_3_9 + a_3_5·b_3_10
       + a_3_5·b_3_9 + b_1_33·a_3_8 + a_1_1·b_1_32·b_3_10 + a_1_0·b_1_32·b_3_9 + a_3_62
       + a_3_7·a_3_6 + a_3_52 + a_1_0·b_1_32·a_3_11 + c_4_20·b_1_32 + c_4_19·b_1_32
       + c_4_19·a_1_1·b_1_3 + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_12 + c_4_19·a_1_0·a_1_1
  32. a_3_7·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_7·a_3_6 + a_3_72 + c_4_19·a_1_1·b_1_3
       + c_4_19·a_1_0·b_1_3 + c_4_20·a_1_12 + c_4_19·a_1_0·a_1_1 + c_4_19·a_1_02
  33. b_3_102 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_1_1·b_1_32·b_3_10 + a_1_1·b_1_32·b_3_9
       + a_1_0·b_1_32·b_3_10 + a_1_0·b_1_32·b_3_9 + a_3_8·a_3_6 + a_3_82 + a_3_7·a_3_6
       + a_3_72 + c_4_19·b_1_32 + c_4_20·a_1_1·b_1_3 + c_4_20·a_1_0·b_1_3
       + c_4_19·a_1_1·b_1_3 + c_4_19·a_1_0·b_1_3 + c_4_20·a_1_0·a_1_1 + c_4_19·a_1_0·a_1_1
       + c_4_19·a_1_02
  34. b_3_102 + a_3_8·a_3_6 + a_3_82 + a_3_7·a_3_6 + a_3_5·a_3_6 + a_3_52
       + a_1_0·b_1_32·a_3_11 + c_4_19·b_1_32 + c_4_20·a_1_02 + c_4_19·a_1_12
  35. a_3_7·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_7·a_3_6 + a_3_52 + c_4_19·a_1_1·b_1_3
       + c_4_19·a_1_0·b_1_3 + c_4_20·a_1_0·a_1_2 + c_4_19·a_1_12 + c_4_19·a_1_0·a_1_1
  36. a_3_7·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_62 + a_3_8·a_3_6 + a_3_72 + a_3_5·a_3_6
       + c_4_19·a_1_1·b_1_3 + c_4_19·a_1_0·b_1_3 + c_4_21·a_1_12 + c_4_19·a_1_12
       + c_4_19·a_1_0·a_1_1 + c_4_19·a_1_02
  37. b_3_102 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_1_1·b_1_32·b_3_10 + a_1_1·b_1_32·b_3_9
       + a_1_0·b_1_32·b_3_10 + a_1_0·b_1_32·b_3_9 + a_3_8·a_3_11 + a_3_8·a_3_6 + a_3_7·a_3_6
       + a_3_5·a_3_6 + a_3_52 + c_4_19·b_1_32 + c_4_20·a_1_1·b_1_3 + c_4_20·a_1_0·b_1_3
       + c_4_19·a_1_1·b_1_3 + c_4_19·a_1_0·b_1_3 + c_4_21·a_1_0·a_1_1 + c_4_19·a_1_02
  38. b_3_102 + a_3_8·a_3_6 + a_3_7·a_3_6 + a_3_72 + a_3_5·a_3_6 + a_1_0·b_1_32·a_3_11
       + c_4_19·b_1_32 + c_4_21·a_1_02 + c_4_19·a_1_12 + c_4_19·a_1_02
  39. b_3_102 + a_3_82 + a_3_72 + a_3_52 + a_1_0·b_1_32·a_3_11 + c_4_19·b_1_32
       + c_4_21·a_1_0·a_1_2
  40. b_3_102 + a_3_11·b_3_10 + a_3_11·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_9 + b_1_3·a_5_30
       + b_1_33·a_3_8 + a_1_1·b_1_32·b_3_9 + a_3_7·a_3_6 + a_3_72 + a_3_5·a_3_8 + a_3_52
       + c_4_19·b_1_32 + c_4_21·a_1_1·b_1_3 + c_4_21·a_1_0·b_1_3 + c_4_19·a_1_1·b_1_3
       + c_4_19·a_1_02
  41. b_3_102 + a_3_62 + a_3_8·a_3_11 + a_3_7·a_3_6 + a_3_5·a_3_6 + a_3_5·a_3_8 + a_1_1·a_5_30
       + c_4_19·b_1_32 + c_4_19·a_1_02
  42. b_3_102 + a_3_8·a_3_11 + a_3_8·a_3_6 + a_3_82 + a_3_7·a_3_6 + a_3_5·a_3_8 + a_3_52
       + a_1_0·a_5_30 + a_1_0·b_1_32·a_3_11 + c_4_19·b_1_32 + c_4_19·a_1_0·a_1_1
  43. b_3_102 + a_3_7·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_7·a_3_6 + a_3_72 + a_3_5·a_3_6
       + a_1_2·a_5_30 + a_1_0·b_1_32·a_3_11 + c_4_19·b_1_32 + c_4_19·a_1_1·b_1_3
       + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_12 + c_4_19·a_1_0·a_1_1
  44. b_3_102 + a_3_11·b_3_10 + a_3_5·b_3_10 + a_3_5·b_3_9 + b_1_3·a_5_27 + b_1_33·a_3_8
       + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_32·b_3_9 + a_3_62 + a_3_8·a_3_11 + a_3_8·a_3_6
       + a_3_7·a_3_8 + a_3_72 + a_3_5·a_3_6 + a_3_5·a_3_8 + a_1_0·b_1_32·a_3_11
       + c_4_19·b_1_32 + c_4_21·a_1_0·b_1_3 + c_4_20·a_1_1·b_1_3 + c_4_19·a_1_1·b_1_3
       + c_4_19·a_1_02
  45. b_3_102 + a_3_8·a_3_11 + a_3_8·a_3_6 + a_3_82 + a_3_7·a_3_6 + a_3_7·a_3_8 + a_3_72
       + a_3_5·a_3_6 + a_3_5·a_3_8 + a_1_1·a_5_27 + c_4_19·b_1_32 + c_4_19·a_1_12
       + c_4_19·a_1_02
  46. b_3_102 + a_3_7·a_3_8 + a_3_72 + a_3_5·a_3_8 + a_3_52 + a_1_0·a_5_27
       + a_1_0·b_1_32·a_3_11 + c_4_19·b_1_32
  47. b_3_102 + a_3_7·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_62 + a_3_82 + a_3_5·a_3_6
       + a_3_52 + a_1_2·a_5_27 + a_1_0·b_1_32·a_3_11 + c_4_19·b_1_32 + c_4_19·a_1_1·b_1_3
       + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_12 + c_4_19·a_1_0·a_1_1 + c_4_19·a_1_02
  48. a_1_0·a_3_5·b_3_9 + a_1_02·a_5_27 + a_1_02·a_5_30 + c_4_20·a_1_02·a_1_1
       + c_4_20·a_1_03
  49. b_1_32·a_5_27 + b_1_34·a_3_8 + a_1_1·b_3_9·b_3_10 + a_1_1·b_1_33·b_3_9
       + a_1_0·b_1_33·b_3_10 + a_1_0·b_1_33·b_3_9 + a_6_38·b_1_3 + a_1_0·a_3_5·b_3_9
       + c_4_21·a_1_1·b_1_32 + c_4_20·a_1_1·b_1_32 + c_4_21·a_1_02·a_1_1
       + c_4_21·a_1_03 + c_4_20·a_1_03
  50. a_1_0·b_1_3·a_5_27 + a_6_38·a_1_1 + a_1_02·a_5_30 + c_4_21·a_1_02·a_1_1
       + c_4_19·a_1_02·a_1_1
  51. a_1_0·b_1_3·a_5_27 + a_6_38·a_1_0 + a_1_0·a_1_1·a_5_27 + a_1_0·a_1_1·a_5_30
       + a_1_02·a_5_30 + c_4_20·a_1_02·a_1_1 + c_4_19·a_1_02·a_1_1
  52. a_1_0·a_3_5·b_3_9 + a_6_38·a_1_2 + a_1_0·a_1_1·a_5_27 + a_1_0·a_1_1·a_5_30
       + c_4_21·a_1_02·a_1_1 + c_4_21·a_1_03
  53. a_3_6·a_5_30 + a_3_8·a_5_30 + a_3_7·a_5_30 + a_1_0·b_1_32·a_5_30 + c_4_21·a_1_1·a_3_7
       + c_4_21·a_1_0·a_3_11 + c_4_21·a_1_0·a_3_6 + c_4_21·a_1_0·a_3_8 + c_4_20·a_1_1·a_3_5
       + c_4_20·a_1_0·a_3_11 + c_4_20·a_1_0·a_3_6 + c_4_19·a_1_1·a_3_11 + c_4_19·a_1_0·a_3_11
       + c_4_19·a_1_0·a_3_8 + c_4_19·a_1_0·a_3_7 + c_4_19·a_1_0·a_3_5
  54. a_3_5·a_5_30 + a_1_0·b_1_32·a_5_30 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_5
       + c_4_20·a_1_1·a_3_11 + c_4_20·a_1_1·a_3_7 + c_4_20·a_1_0·a_3_11 + c_4_20·a_1_0·a_3_7
       + c_4_19·a_1_1·a_3_7 + c_4_19·a_1_1·a_3_5 + c_4_19·a_1_0·a_3_6 + c_4_19·a_1_0·a_3_8
       + c_4_19·a_1_0·a_3_5
  55. b_3_10·a_5_30 + b_3_9·a_5_30 + b_1_32·a_3_8·b_3_10 + b_1_32·a_3_8·b_3_9
       + b_1_33·a_5_30 + b_1_35·a_3_8 + a_1_1·b_1_3·b_3_9·b_3_10 + a_1_1·b_1_34·b_3_10
       + a_3_8·a_5_30 + a_3_7·a_5_30 + c_4_21·a_1_1·b_3_10 + c_4_21·a_1_1·b_3_9
       + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_9
       + c_4_21·a_1_0·b_1_33 + c_4_20·b_1_3·a_3_11 + c_4_20·a_1_1·b_3_10
       + c_4_20·a_1_1·b_3_9 + c_4_20·a_1_1·b_1_33 + c_4_20·a_1_0·b_3_10 + c_4_20·a_1_0·b_3_9
       + c_4_19·b_1_3·a_3_11 + c_4_19·a_1_1·b_1_33 + c_4_19·a_1_0·b_3_10
       + c_4_19·a_1_0·b_3_9 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_0·a_3_11 + c_4_21·a_1_0·a_3_7
       + c_4_21·a_1_0·a_3_5 + c_4_20·a_1_1·a_3_11 + c_4_20·a_1_1·a_3_7 + c_4_20·a_1_1·a_3_5
       + c_4_20·a_1_0·a_3_11 + c_4_20·a_1_0·a_3_6 + c_4_20·a_1_0·a_3_7 + c_4_20·a_1_0·a_3_5
       + c_4_19·a_1_1·a_3_11 + c_4_19·a_1_1·a_3_7 + c_4_19·a_1_0·a_3_6 + c_4_19·a_1_0·a_3_7
       + c_4_19·a_1_0·a_3_5
  56. a_3_11·a_5_30 + a_3_7·a_5_30 + c_4_21·a_1_1·a_3_11 + c_4_21·a_1_1·a_3_7
       + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_11 + c_4_21·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_5
       + c_4_20·a_1_1·a_3_7 + c_4_20·a_1_0·a_3_7 + c_4_19·a_1_1·a_3_11 + c_4_19·a_1_0·a_3_6
       + c_4_19·a_1_0·a_3_8 + c_4_19·a_1_0·a_3_5
  57. a_3_8·a_5_27 + a_3_8·a_5_30 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_11
       + c_4_21·a_1_0·a_3_6 + c_4_21·a_1_0·a_3_8 + c_4_21·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_5
       + c_4_20·a_1_1·a_3_11 + c_4_20·a_1_1·a_3_5 + c_4_20·a_1_0·a_3_6 + c_4_20·a_1_0·a_3_8
       + c_4_20·a_1_0·a_3_7 + c_4_20·a_1_0·a_3_5 + c_4_19·a_1_1·a_3_7 + c_4_19·a_1_0·a_3_8
       + c_4_19·a_1_0·a_3_7 + c_4_19·a_1_0·a_3_5
  58. b_3_10·a_5_27 + b_1_32·a_3_8·b_3_10 + a_3_8·a_5_30 + c_4_21·a_1_0·b_3_10
       + c_4_20·a_1_0·b_3_10 + c_4_19·b_1_3·a_3_11 + c_4_19·a_1_1·b_1_33
       + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_1_33 + c_4_21·a_1_1·a_3_11
       + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_5 + c_4_20·a_1_1·a_3_11
       + c_4_20·a_1_0·a_3_6 + c_4_20·a_1_0·a_3_8 + c_4_20·a_1_0·a_3_7 + c_4_19·a_1_1·a_3_7
       + c_4_19·a_1_1·a_3_5 + c_4_19·a_1_0·a_3_11 + c_4_19·a_1_0·a_3_6 + c_4_19·a_1_0·a_3_8
       + c_4_19·a_1_0·a_3_7
  59. a_3_8·a_5_30 + a_3_7·a_5_27 + a_1_0·b_1_32·a_5_30 + c_4_21·a_1_1·a_3_7
       + c_4_21·a_1_0·a_3_11 + c_4_21·a_1_0·a_3_5 + c_4_20·a_1_1·a_3_11 + c_4_20·a_1_1·a_3_5
       + c_4_20·a_1_0·a_3_8 + c_4_20·a_1_0·a_3_5 + c_4_19·a_1_1·a_3_11 + c_4_19·a_1_1·a_3_7
       + c_4_19·a_1_0·a_3_11 + c_4_19·a_1_0·a_3_6 + c_4_19·a_1_0·a_3_8 + c_4_19·a_1_0·a_3_5
  60. a_3_6·a_5_27 + c_4_21·a_1_1·a_3_11 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_0·a_3_11
       + c_4_21·a_1_0·a_3_8 + c_4_21·a_1_0·a_3_5 + c_4_20·a_1_1·a_3_7 + c_4_20·a_1_0·a_3_6
       + c_4_20·a_1_0·a_3_7 + c_4_19·a_1_1·a_3_7 + c_4_19·a_1_0·a_3_6 + c_4_19·a_1_0·a_3_7
  61. a_3_5·a_5_27 + a_1_0·b_1_32·a_5_30 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_1·a_3_5
       + c_4_21·a_1_0·a_3_7 + c_4_20·a_1_0·a_3_6 + c_4_20·a_1_0·a_3_8 + c_4_20·a_1_0·a_3_7
       + c_4_19·a_1_1·a_3_11 + c_4_19·a_1_0·a_3_11 + c_4_19·a_1_0·a_3_6 + c_4_19·a_1_0·a_3_8
       + c_4_19·a_1_0·a_3_7
  62. b_3_10·a_5_30 + b_3_9·a_5_27 + b_1_32·a_3_8·b_3_10 + b_1_32·a_3_8·b_3_9
       + a_1_1·b_1_3·b_3_9·b_3_10 + a_3_8·a_5_30 + a_1_0·b_1_32·a_5_30 + c_4_21·a_1_1·b_3_10
       + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_9 + c_4_20·a_1_1·b_3_10 + c_4_20·a_1_0·b_3_10
       + c_4_20·a_1_0·b_3_9 + c_4_19·b_1_3·a_3_11 + c_4_19·a_1_1·b_1_33
       + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_9 + c_4_19·a_1_0·b_1_33 + c_4_21·a_1_1·a_3_5
       + c_4_21·a_1_0·a_3_11 + c_4_21·a_1_0·a_3_6 + c_4_21·a_1_0·a_3_8 + c_4_21·a_1_0·a_3_5
       + c_4_20·a_1_1·a_3_5 + c_4_20·a_1_0·a_3_11 + c_4_20·a_1_0·a_3_6 + c_4_20·a_1_0·a_3_8
       + c_4_19·a_1_1·a_3_11 + c_4_19·a_1_1·a_3_7 + c_4_19·a_1_0·a_3_6 + c_4_19·a_1_0·a_3_8
  63. a_3_11·a_5_27 + a_3_8·a_5_30 + a_3_7·a_5_30 + a_1_0·b_1_32·a_5_30 + c_4_21·a_1_1·a_3_7
       + c_4_21·a_1_0·a_3_6 + c_4_21·a_1_0·a_3_8 + c_4_20·a_1_1·a_3_11 + c_4_20·a_1_1·a_3_5
       + c_4_20·a_1_0·a_3_11 + c_4_20·a_1_0·a_3_6 + c_4_19·a_1_0·a_3_11
  64. a_3_8·a_5_30 + a_3_7·a_5_30 + a_1_0·b_1_32·a_5_30 + a_1_03·a_5_27 + c_4_21·a_1_1·a_3_5
       + c_4_21·a_1_0·a_3_11 + c_4_20·a_1_1·a_3_11 + c_4_20·a_1_1·a_3_7 + c_4_20·a_1_0·a_3_6
       + c_4_20·a_1_0·a_3_7 + c_4_20·a_1_0·a_3_5 + c_4_19·a_1_1·a_3_7 + c_4_19·a_1_1·a_3_5
       + c_4_19·a_1_0·a_3_7 + c_4_19·a_1_0·a_3_5
  65. a_3_7·a_5_30 + a_1_0·b_1_32·a_5_30 + a_6_38·a_1_0·b_1_3 + c_4_21·a_1_1·a_3_7
       + c_4_21·a_1_0·a_3_7 + c_4_20·a_1_1·a_3_11 + c_4_20·a_1_1·a_3_7 + c_4_20·a_1_1·a_3_5
       + c_4_20·a_1_0·a_3_11 + c_4_20·a_1_0·a_3_6 + c_4_20·a_1_0·a_3_8 + c_4_19·a_1_1·a_3_11
       + c_4_19·a_1_1·a_3_5 + c_4_19·a_1_0·a_3_11 + c_4_19·a_1_0·a_3_7 + c_4_19·a_1_0·a_3_5
  66. a_1_0·b_3_9·a_5_30 + a_6_38·a_3_8 + c_4_21·a_1_0·b_1_3·a_3_11
       + c_4_21·a_1_0·a_1_1·a_3_11 + c_4_21·a_1_0·a_1_1·a_3_7 + c_4_21·a_1_02·a_3_7
       + c_4_20·a_1_0·a_1_1·a_3_11 + c_4_20·a_1_02·a_3_6 + c_4_20·a_1_02·a_3_8
       + c_4_20·a_1_02·a_3_7 + c_4_20·a_1_02·a_3_5 + c_4_19·a_1_02·a_3_11
       + c_4_19·a_1_02·a_3_7 + c_4_19·a_1_02·a_3_5
  67. a_1_1·b_1_32·b_3_9·b_3_10 + a_1_0·b_1_32·b_3_9·b_3_10 + a_6_38·b_3_10
       + a_6_38·a_1_0·b_1_32 + c_4_21·a_1_1·b_1_3·b_3_10 + c_4_21·a_1_0·b_1_3·b_3_10
       + c_4_20·a_1_1·b_1_3·b_3_10 + c_4_20·a_1_0·b_1_3·b_3_10 + c_4_19·b_1_32·a_3_11
       + c_4_19·a_1_1·b_1_3·b_3_9 + c_4_19·a_1_1·b_1_34 + c_4_19·a_1_0·b_1_3·b_3_10
       + c_4_19·a_1_0·b_1_3·a_3_11 + c_4_21·a_1_0·a_1_1·a_3_11 + c_4_21·a_1_0·a_1_1·a_3_7
       + c_4_21·a_1_02·a_3_6 + c_4_21·a_1_02·a_3_7 + c_4_20·a_1_0·a_1_1·a_3_7
       + c_4_20·a_1_02·a_3_6 + c_4_20·a_1_02·a_3_8 + c_4_20·a_1_02·a_3_7
       + c_4_19·a_1_02·a_3_11
  68. a_6_38·a_3_7 + c_4_21·a_1_0·a_1_1·a_3_7 + c_4_21·a_1_02·a_3_7 + c_4_21·a_1_02·a_3_5
       + c_4_20·a_1_02·a_3_11 + c_4_20·a_1_02·a_3_6 + c_4_20·a_1_02·a_3_7
       + c_4_19·a_1_0·a_1_1·a_3_11 + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_02·a_3_11
       + c_4_19·a_1_02·a_3_6 + c_4_19·a_1_02·a_3_7
  69. a_6_38·a_3_6 + c_4_21·a_1_0·a_1_1·a_3_7 + c_4_21·a_1_02·a_3_11 + c_4_21·a_1_02·a_3_8
       + c_4_21·a_1_02·a_3_5 + c_4_20·a_1_0·a_1_1·a_3_11 + c_4_20·a_1_0·a_1_1·a_3_7
       + c_4_20·a_1_02·a_3_11 + c_4_20·a_1_02·a_3_6 + c_4_20·a_1_02·a_3_8
       + c_4_20·a_1_02·a_3_5 + c_4_19·a_1_0·a_1_1·a_3_11 + c_4_19·a_1_0·a_1_1·a_3_7
       + c_4_19·a_1_02·a_3_11 + c_4_19·a_1_02·a_3_6 + c_4_19·a_1_02·a_3_7
  70. a_6_38·a_3_5 + c_4_21·a_1_02·a_3_5 + c_4_20·a_1_0·a_1_1·a_3_11
       + c_4_20·a_1_0·a_1_1·a_3_7 + c_4_20·a_1_02·a_3_8 + c_4_20·a_1_02·a_3_7
       + c_4_20·a_1_02·a_3_5 + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_02·a_3_11
       + c_4_19·a_1_02·a_3_8
  71. b_1_3·b_3_9·a_5_30 + b_1_33·a_3_8·b_3_9 + b_1_34·a_5_30 + b_1_36·a_3_8
       + a_1_1·b_1_32·b_3_9·b_3_10 + a_1_1·b_1_35·b_3_9 + a_1_0·b_1_32·b_3_9·b_3_10
       + a_1_0·b_1_35·b_3_10 + a_1_0·b_1_35·b_3_9 + a_6_38·b_3_9 + a_1_0·b_1_35·a_3_11
       + c_4_21·a_1_1·b_1_34 + c_4_21·a_1_0·b_1_34 + c_4_20·b_1_32·a_3_11
       + c_4_20·a_1_1·b_1_3·b_3_10 + c_4_20·a_1_0·b_1_34 + c_4_19·a_1_1·b_1_34
       + c_4_19·a_1_0·b_1_34 + c_4_20·a_1_0·b_1_3·a_3_11 + c_4_21·a_1_02·a_3_11
       + c_4_21·a_1_02·a_3_6 + c_4_21·a_1_02·a_3_8 + c_4_20·a_1_0·a_1_1·a_3_11
       + c_4_20·a_1_0·a_1_1·a_3_7 + c_4_20·a_1_02·a_3_11 + c_4_20·a_1_02·a_3_6
       + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_02·a_3_11 + c_4_19·a_1_02·a_3_8
  72. a_1_0·b_3_9·a_5_30 + a_1_0·b_1_33·a_5_30 + a_6_38·a_3_11 + a_6_38·a_1_0·b_1_32
       + c_4_20·a_1_0·b_1_3·a_3_11 + c_4_19·a_1_0·b_1_3·a_3_11 + c_4_21·a_1_0·a_1_1·a_3_11
       + c_4_21·a_1_0·a_1_1·a_3_7 + c_4_21·a_1_02·a_3_11 + c_4_21·a_1_02·a_3_6
       + c_4_21·a_1_02·a_3_8 + c_4_20·a_1_02·a_3_8 + c_4_20·a_1_02·a_3_7
       + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_02·a_3_11 + c_4_19·a_1_02·a_3_6
       + c_4_19·a_1_02·a_3_8 + c_4_19·a_1_02·a_3_7
  73. a_3_8·b_3_9·b_3_10 + b_1_33·a_3_8·b_3_10 + a_1_1·b_1_35·b_3_9
       + a_1_0·b_1_32·b_3_9·b_3_10 + a_1_0·b_1_35·b_3_9 + a_8_67·b_1_3 + a_6_38·b_1_33
       + a_1_0·b_3_9·a_5_30 + a_1_0·b_1_33·a_5_30 + c_4_21·b_1_32·a_3_11
       + c_4_21·a_1_0·b_1_3·b_3_10 + c_4_21·a_1_0·b_1_3·b_3_9 + c_4_20·a_1_1·b_1_3·b_3_10
       + c_4_20·a_1_1·b_1_34 + c_4_20·a_1_0·b_1_3·b_3_9 + c_4_20·a_1_0·b_1_34
       + c_4_19·b_1_32·a_3_11 + c_4_19·b_1_32·a_3_8 + c_4_19·a_1_1·b_1_3·b_3_10
       + c_4_19·a_1_1·b_1_3·b_3_9 + c_4_19·a_1_1·b_1_34 + c_4_19·a_1_0·b_1_3·b_3_9
       + c_4_21·a_1_0·b_1_3·a_3_11 + c_4_20·a_1_0·b_1_3·a_3_11 + c_4_21·a_1_0·a_1_1·a_3_11
       + c_4_21·a_1_0·a_1_1·a_3_7 + c_4_21·a_1_02·a_3_8 + c_4_20·a_1_0·a_1_1·a_3_7
       + c_4_20·a_1_02·a_3_8 + c_4_20·a_1_02·a_3_7 + c_4_19·a_1_0·a_1_1·a_3_11
       + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_02·a_3_11 + c_4_19·a_1_02·a_3_8
       + c_4_19·a_1_02·a_3_7 + c_4_19·a_1_02·a_3_5
  74. a_1_0·b_3_9·a_5_30 + a_1_0·b_1_33·a_5_30 + a_8_67·a_1_1 + c_4_21·a_1_0·b_1_3·a_3_11
       + c_4_20·a_1_0·b_1_3·a_3_11 + c_4_21·a_1_0·a_1_1·a_3_7 + c_4_21·a_1_02·a_3_11
       + c_4_21·a_1_02·a_3_6 + c_4_21·a_1_02·a_3_7 + c_4_21·a_1_02·a_3_5
       + c_4_20·a_1_0·a_1_1·a_3_7 + c_4_20·a_1_02·a_3_6 + c_4_20·a_1_02·a_3_7
       + c_4_19·a_1_0·a_1_1·a_3_11 + c_4_19·a_1_02·a_3_11
  75. a_8_67·a_1_0 + a_6_38·a_1_0·b_1_32 + c_4_21·a_1_0·b_1_3·a_3_11
       + c_4_19·a_1_0·b_1_3·a_3_11 + c_4_21·a_1_02·a_3_11 + c_4_21·a_1_02·a_3_6
       + c_4_21·a_1_02·a_3_7 + c_4_20·a_1_0·a_1_1·a_3_11 + c_4_20·a_1_0·a_1_1·a_3_7
       + c_4_20·a_1_02·a_3_11 + c_4_20·a_1_02·a_3_6 + c_4_20·a_1_02·a_3_8
       + c_4_20·a_1_02·a_3_5 + c_4_19·a_1_0·a_1_1·a_3_11 + c_4_19·a_1_0·a_1_1·a_3_7
       + c_4_19·a_1_02·a_3_11 + c_4_19·a_1_02·a_3_8 + c_4_19·a_1_02·a_3_7
       + c_4_19·a_1_02·a_3_5
  76. a_8_67·a_1_2 + c_4_21·a_1_02·a_3_11 + c_4_21·a_1_02·a_3_7 + c_4_20·a_1_02·a_3_8
       + c_4_20·a_1_02·a_3_7 + c_4_20·a_1_02·a_3_5 + c_4_19·a_1_0·a_1_1·a_3_11
       + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_02·a_3_11 + c_4_19·a_1_02·a_3_8
       + c_4_19·a_1_02·a_3_7
  77. a_5_302 + c_4_212·a_1_12 + c_4_212·a_1_02 + c_4_20·c_4_21·a_1_12
       + c_4_20·c_4_21·a_1_02 + c_4_202·a_1_12 + c_4_202·a_1_0·a_1_2
       + c_4_19·c_4_21·a_1_0·a_1_2 + c_4_19·c_4_21·a_1_02 + c_4_19·c_4_20·a_1_12
       + c_4_19·c_4_20·a_1_0·a_1_2 + c_4_192·a_1_12
  78. a_5_272 + c_4_212·a_1_12 + c_4_212·a_1_0·a_1_2 + c_4_212·a_1_02
       + c_4_20·c_4_21·a_1_12 + c_4_20·c_4_21·a_1_0·a_1_2 + c_4_202·a_1_12
       + c_4_202·a_1_0·a_1_2 + c_4_202·a_1_02 + c_4_19·c_4_21·a_1_12
       + c_4_19·c_4_21·a_1_02 + c_4_19·c_4_20·a_1_0·a_1_2 + c_4_19·c_4_20·a_1_02
       + c_4_192·a_1_12
  79. a_5_30·a_5_27 + a_6_38·a_1_0·b_3_9 + c_4_21·a_1_0·a_5_30 + c_4_21·a_1_0·b_1_32·a_3_11
       + c_4_20·a_1_1·a_5_30 + c_4_19·a_1_1·a_5_27 + c_4_19·a_1_1·a_5_30
       + c_4_212·a_1_0·a_1_2 + c_4_212·a_1_02 + c_4_20·c_4_21·a_1_0·a_1_2
       + c_4_20·c_4_21·a_1_02 + c_4_202·a_1_12 + c_4_202·a_1_02
       + c_4_19·c_4_21·a_1_12 + c_4_19·c_4_21·a_1_0·a_1_2 + c_4_19·c_4_21·a_1_0·a_1_1
       + c_4_19·c_4_20·a_1_02 + c_4_192·a_1_12
  80. a_6_38·a_5_30 + a_6_38·b_1_32·a_3_8 + a_6_38·a_1_0·b_1_3·b_3_9 + c_4_20·a_6_38·a_1_0
       + c_4_21·a_1_0·a_1_1·a_5_27 + c_4_21·a_1_02·a_5_27 + c_4_21·a_1_02·a_5_30
       + c_4_20·a_1_0·a_1_1·a_5_27 + c_4_20·a_1_0·a_1_1·a_5_30 + c_4_20·a_1_02·a_5_30
       + c_4_19·a_1_0·a_1_1·a_5_30 + c_4_19·a_1_02·a_5_30 + c_4_20·c_4_21·a_1_03
       + c_4_19·c_4_20·a_1_02·a_1_1 + c_4_19·c_4_20·a_1_03 + c_4_192·a_1_03
  81. a_6_38·a_5_27 + a_6_38·b_1_32·a_3_8 + c_4_21·a_6_38·a_1_0 + c_4_20·a_6_38·a_1_0
       + c_4_19·a_1_0·b_1_3·a_5_30 + c_4_19·a_1_0·b_1_33·a_3_11 + c_4_19·a_6_38·a_1_0
       + c_4_21·a_1_0·a_1_1·a_5_30 + c_4_21·a_1_02·a_5_27 + c_4_20·a_1_0·a_1_1·a_5_27
       + c_4_20·a_1_0·a_1_1·a_5_30 + c_4_20·a_1_02·a_5_27 + c_4_20·a_1_02·a_5_30
       + c_4_212·a_1_02·a_1_1 + c_4_212·a_1_03 + c_4_20·c_4_21·a_1_02·a_1_1
       + c_4_20·c_4_21·a_1_03 + c_4_202·a_1_02·a_1_1 + c_4_202·a_1_03
       + c_4_19·c_4_21·a_1_02·a_1_1 + c_4_19·c_4_21·a_1_03 + c_4_19·c_4_20·a_1_03
       + c_4_192·a_1_02·a_1_1 + c_4_192·a_1_03
  82. a_8_67·a_3_8 + a_6_38·a_5_30 + a_6_38·b_1_32·a_3_8 + a_6_38·a_1_0·b_1_34
       + c_4_21·a_1_0·b_1_33·a_3_11 + c_4_19·a_1_0·b_1_3·a_5_30
       + c_4_19·a_1_0·b_1_33·a_3_11 + c_4_21·a_1_0·a_1_1·a_5_27 + c_4_21·a_1_0·a_1_1·a_5_30
       + c_4_21·a_1_02·a_5_27 + c_4_21·a_1_02·a_5_30 + c_4_20·a_1_0·a_1_1·a_5_27
       + c_4_19·a_1_0·a_1_1·a_5_30 + c_4_19·a_1_02·a_5_30 + c_4_20·c_4_21·a_1_02·a_1_1
       + c_4_202·a_1_02·a_1_1 + c_4_19·c_4_21·a_1_02·a_1_1 + c_4_19·c_4_20·a_1_02·a_1_1
       + c_4_19·c_4_20·a_1_03
  83. a_8_67·b_3_10 + a_6_38·a_1_0·b_1_34 + c_4_21·a_1_1·b_3_9·b_3_10
       + c_4_21·a_1_1·b_1_33·b_3_9 + c_4_21·a_1_0·b_3_9·b_3_10
       + c_4_21·a_1_0·b_1_33·b_3_10 + c_4_21·a_1_0·b_1_33·b_3_9 + c_4_21·a_6_38·b_1_3
       + c_4_20·a_1_0·b_3_9·b_3_10 + c_4_19·b_1_3·a_3_8·b_3_10 + c_4_19·b_1_3·a_3_8·b_3_9
       + c_4_19·b_1_34·a_3_11 + c_4_19·b_1_34·a_3_8 + c_4_19·a_1_1·b_1_36
       + c_4_19·a_1_0·b_3_9·b_3_10 + c_4_19·a_1_0·b_1_33·b_3_10 + c_4_19·a_6_38·b_1_3
       + c_4_21·a_1_0·b_1_33·a_3_11 + c_4_19·a_1_0·b_1_3·a_5_30 + c_4_21·a_1_02·a_5_27
       + c_4_21·a_1_02·a_5_30 + c_4_20·a_1_0·a_1_1·a_5_27 + c_4_19·a_1_0·a_1_1·a_5_27
       + c_4_212·a_1_1·b_1_32 + c_4_212·a_1_0·b_1_32 + c_4_20·c_4_21·a_1_1·b_1_32
       + c_4_20·c_4_21·a_1_0·b_1_32 + c_4_19·c_4_21·a_1_1·b_1_32
       + c_4_19·c_4_21·a_1_0·b_1_32 + c_4_19·c_4_20·a_1_0·b_1_32
       + c_4_192·a_1_1·b_1_32 + c_4_192·a_1_0·b_1_32 + c_4_20·c_4_21·a_1_02·a_1_1
       + c_4_20·c_4_21·a_1_03 + c_4_19·c_4_21·a_1_02·a_1_1 + c_4_19·c_4_21·a_1_03
       + c_4_19·c_4_20·a_1_02·a_1_1 + c_4_19·c_4_20·a_1_03
  84. a_8_67·a_3_7 + c_4_20·a_6_38·a_1_0 + c_4_19·a_1_0·b_1_3·a_5_30
       + c_4_19·a_1_0·b_1_33·a_3_11 + c_4_19·a_6_38·a_1_0 + c_4_21·a_1_0·a_1_1·a_5_30
       + c_4_20·a_1_0·a_1_1·a_5_27 + c_4_20·a_1_0·a_1_1·a_5_30 + c_4_20·a_1_02·a_5_27
       + c_4_19·a_1_02·a_5_27 + c_4_19·a_1_02·a_5_30 + c_4_212·a_1_02·a_1_1
       + c_4_20·c_4_21·a_1_02·a_1_1 + c_4_202·a_1_02·a_1_1 + c_4_19·c_4_21·a_1_02·a_1_1
       + c_4_19·c_4_20·a_1_02·a_1_1 + c_4_19·c_4_20·a_1_03
  85. a_8_67·a_3_6 + c_4_21·a_1_0·a_1_1·a_5_30 + c_4_21·a_1_02·a_5_30
       + c_4_20·a_1_0·a_1_1·a_5_30 + c_4_20·a_1_02·a_5_27 + c_4_19·a_1_0·a_1_1·a_5_27
       + c_4_19·a_1_0·a_1_1·a_5_30 + c_4_19·a_1_02·a_5_30 + c_4_212·a_1_02·a_1_1
       + c_4_20·c_4_21·a_1_03 + c_4_202·a_1_02·a_1_1 + c_4_202·a_1_03
       + c_4_19·c_4_21·a_1_03 + c_4_19·c_4_20·a_1_02·a_1_1 + c_4_19·c_4_20·a_1_03
       + c_4_192·a_1_02·a_1_1
  86. a_8_67·a_3_5 + c_4_20·a_6_38·a_1_0 + c_4_19·a_6_38·a_1_0 + c_4_21·a_1_02·a_5_27
       + c_4_21·a_1_02·a_5_30 + c_4_19·a_1_0·a_1_1·a_5_27 + c_4_19·a_1_02·a_5_30
       + c_4_20·c_4_21·a_1_02·a_1_1 + c_4_202·a_1_02·a_1_1 + c_4_19·c_4_21·a_1_02·a_1_1
       + c_4_19·c_4_21·a_1_03 + c_4_19·c_4_20·a_1_03 + c_4_192·a_1_03
  87. a_1_1·b_1_37·b_3_10 + a_1_1·b_1_37·b_3_9 + a_1_0·b_1_34·b_3_9·b_3_10
       + a_1_0·b_1_37·b_3_10 + a_1_0·b_1_37·b_3_9 + a_8_67·b_3_9 + a_6_38·b_1_32·b_3_9
       + a_1_0·b_1_37·a_3_11 + a_6_38·a_5_30 + a_6_38·b_1_32·a_3_8 + c_4_21·b_1_32·a_5_30
       + c_4_21·b_1_34·a_3_8 + c_4_21·a_1_1·b_3_9·b_3_10 + c_4_21·a_1_1·b_1_33·b_3_9
       + c_4_21·a_1_0·b_3_9·b_3_10 + c_4_21·a_1_0·b_1_33·b_3_9 + c_4_21·a_6_38·b_1_3
       + c_4_20·b_1_3·a_3_8·b_3_10 + c_4_20·a_1_1·b_3_9·b_3_10 + c_4_20·a_1_1·b_1_33·b_3_9
       + c_4_20·a_1_1·b_1_36 + c_4_20·a_1_0·b_1_36 + c_4_19·b_1_3·a_3_8·b_3_9
       + c_4_19·b_1_32·a_5_30 + c_4_19·a_1_1·b_1_33·b_3_10 + c_4_19·a_1_1·b_1_33·b_3_9
       + c_4_19·a_1_0·b_1_33·b_3_9 + c_4_19·a_1_0·b_1_36 + c_4_19·a_6_38·b_1_3
       + c_4_21·a_1_0·b_1_33·a_3_11 + c_4_19·a_1_0·b_1_3·a_5_30 + c_4_19·a_6_38·a_1_0
       + c_4_21·a_1_0·a_1_1·a_5_30 + c_4_21·a_1_02·a_5_30 + c_4_20·a_1_02·a_5_30
       + c_4_19·a_1_0·a_1_1·a_5_30 + c_4_19·a_1_02·a_5_27 + c_4_20·c_4_21·a_1_0·b_1_32
       + c_4_202·a_1_0·b_1_32 + c_4_19·c_4_20·a_1_1·b_1_32
       + c_4_19·c_4_20·a_1_0·b_1_32 + c_4_212·a_1_03 + c_4_202·a_1_02·a_1_1
       + c_4_19·c_4_20·a_1_03
  88. a_8_67·a_3_11 + a_6_38·a_1_0·b_1_34 + c_4_21·a_1_0·b_1_3·a_5_30
       + c_4_20·a_1_0·b_1_3·a_5_30 + c_4_19·a_6_38·a_1_0 + c_4_21·a_1_0·a_1_1·a_5_27
       + c_4_21·a_1_0·a_1_1·a_5_30 + c_4_21·a_1_02·a_5_27 + c_4_20·a_1_0·a_1_1·a_5_27
       + c_4_20·a_1_0·a_1_1·a_5_30 + c_4_19·a_1_0·a_1_1·a_5_27 + c_4_19·a_1_02·a_5_30
       + c_4_202·a_1_02·a_1_1 + c_4_19·c_4_21·a_1_02·a_1_1 + c_4_19·c_4_21·a_1_03
       + c_4_192·a_1_03
  89. a_6_382
  90. a_8_67·a_5_30 + a_6_38·a_1_0·b_1_33·b_3_9 + a_6_38·a_1_0·b_1_36
       + c_4_21·a_1_0·b_1_35·a_3_11 + c_4_21·a_6_38·a_3_11 + c_4_21·a_6_38·a_1_0·b_1_32
       + c_4_20·a_6_38·a_3_8 + c_4_19·a_1_0·b_1_35·a_3_11 + c_4_19·a_6_38·a_3_8
       + c_4_19·c_4_21·a_1_0·b_1_3·a_3_11 + c_4_19·c_4_20·a_1_0·b_1_3·a_3_11
       + c_4_212·a_1_0·a_1_1·a_3_11 + c_4_212·a_1_02·a_3_11 + c_4_212·a_1_02·a_3_6
       + c_4_212·a_1_02·a_3_8 + c_4_212·a_1_02·a_3_7 + c_4_212·a_1_02·a_3_5
       + c_4_20·c_4_21·a_1_0·a_1_1·a_3_11 + c_4_20·c_4_21·a_1_02·a_3_6
       + c_4_20·c_4_21·a_1_02·a_3_8 + c_4_20·c_4_21·a_1_02·a_3_7
       + c_4_202·a_1_0·a_1_1·a_3_11 + c_4_202·a_1_02·a_3_11 + c_4_202·a_1_02·a_3_6
       + c_4_202·a_1_02·a_3_7 + c_4_202·a_1_02·a_3_5 + c_4_19·c_4_21·a_1_02·a_3_11
       + c_4_19·c_4_21·a_1_02·a_3_8 + c_4_19·c_4_20·a_1_0·a_1_1·a_3_11
       + c_4_19·c_4_20·a_1_0·a_1_1·a_3_7 + c_4_19·c_4_20·a_1_02·a_3_11
       + c_4_19·c_4_20·a_1_02·a_3_7 + c_4_19·c_4_20·a_1_02·a_3_5
       + c_4_192·a_1_0·a_1_1·a_3_11 + c_4_192·a_1_0·a_1_1·a_3_7 + c_4_192·a_1_02·a_3_11
       + c_4_192·a_1_02·a_3_6 + c_4_192·a_1_02·a_3_8 + c_4_192·a_1_02·a_3_5
  91. a_8_67·a_5_27 + a_6_38·a_1_0·b_1_33·b_3_9 + a_6_38·a_1_0·b_1_36
       + c_4_21·a_1_0·b_1_35·a_3_11 + c_4_21·a_6_38·a_3_11 + c_4_20·a_6_38·a_3_11
       + c_4_20·a_6_38·a_1_0·b_1_32 + c_4_19·a_1_0·b_1_35·a_3_11
       + c_4_19·a_6_38·a_1_0·b_1_32 + c_4_212·a_1_0·b_1_3·a_3_11
       + c_4_20·c_4_21·a_1_0·b_1_3·a_3_11 + c_4_19·c_4_20·a_1_0·b_1_3·a_3_11
       + c_4_212·a_1_0·a_1_1·a_3_11 + c_4_212·a_1_0·a_1_1·a_3_7 + c_4_212·a_1_02·a_3_11
       + c_4_212·a_1_02·a_3_5 + c_4_20·c_4_21·a_1_0·a_1_1·a_3_11
       + c_4_20·c_4_21·a_1_02·a_3_8 + c_4_20·c_4_21·a_1_02·a_3_5
       + c_4_202·a_1_0·a_1_1·a_3_7 + c_4_202·a_1_02·a_3_11 + c_4_202·a_1_02·a_3_6
       + c_4_202·a_1_02·a_3_5 + c_4_19·c_4_21·a_1_0·a_1_1·a_3_11
       + c_4_19·c_4_21·a_1_02·a_3_8 + c_4_19·c_4_20·a_1_0·a_1_1·a_3_7
       + c_4_19·c_4_20·a_1_02·a_3_11 + c_4_192·a_1_0·a_1_1·a_3_11
       + c_4_192·a_1_02·a_3_11 + c_4_192·a_1_02·a_3_6 + c_4_192·a_1_02·a_3_5
  92. a_6_38·a_8_67 + c_4_21·a_6_38·a_1_0·b_3_9 + c_4_19·a_6_38·b_1_3·a_3_8
       + c_4_19·a_6_38·a_1_0·b_3_9 + c_4_19·a_6_38·a_1_0·b_1_33
  93. a_8_672

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_4_19, a Duflot regular element of degree 4
    2. c_4_20, a Duflot regular element of degree 4
    3. c_4_21, a Duflot regular element of degree 4
    4. b_1_32, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 8, 10].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

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

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 3

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. a_1_2 → 0, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. a_3_5 → 0, an element of degree 3
  6. a_3_7 → 0, an element of degree 3
  7. a_3_8 → 0, an element of degree 3
  8. a_3_6 → 0, an element of degree 3
  9. a_3_11 → 0, an element of degree 3
  10. b_3_9 → 0, an element of degree 3
  11. b_3_10 → 0, an element of degree 3
  12. c_4_19 → c_1_24 + c_1_14, an element of degree 4
  13. c_4_20 → c_1_14, an element of degree 4
  14. c_4_21 → c_1_14 + c_1_04, an element of degree 4
  15. a_5_30 → 0, an element of degree 5
  16. a_5_27 → 0, an element of degree 5
  17. a_6_38 → 0, an element of degree 6
  18. a_8_67 → 0, an element of degree 8

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

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. a_1_2 → 0, an element of degree 1
  4. b_1_3 → c_1_3, an element of degree 1
  5. a_3_5 → 0, an element of degree 3
  6. a_3_7 → 0, an element of degree 3
  7. a_3_8 → 0, an element of degree 3
  8. a_3_6 → 0, an element of degree 3
  9. a_3_11 → 0, an element of degree 3
  10. b_3_9 → c_1_12·c_1_3, an element of degree 3
  11. b_3_10 → c_1_22·c_1_3 + c_1_12·c_1_3, an element of degree 3
  12. c_4_19 → c_1_24 + c_1_14, an element of degree 4
  13. c_4_20 → c_1_22·c_1_32 + c_1_14, an element of degree 4
  14. c_4_21 → c_1_14 + c_1_02·c_1_32 + c_1_04, an element of degree 4
  15. a_5_30 → 0, an element of degree 5
  16. a_5_27 → 0, an element of degree 5
  17. a_6_38 → 0, an element of degree 6
  18. a_8_67 → 0, 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