Cohomology of group number 730 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
    ( − 1) · (t8  +  t7  +  3·t5  +  2·t3  +  t2  +  t  +  1)
    (t  +  1) · (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 17 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. a_2_3, a nilpotent element of degree 2
  5. b_2_4, an element of degree 2
  6. a_3_5, a nilpotent element of degree 3
  7. a_3_7, a nilpotent element of degree 3
  8. b_3_6, an element of degree 3
  9. c_4_10, a Duflot regular element of degree 4
  10. a_5_11, a nilpotent element of degree 5
  11. a_5_12, a nilpotent element of degree 5
  12. a_5_13, a nilpotent element of degree 5
  13. a_5_15, a nilpotent element of degree 5
  14. a_6_19, a nilpotent element of degree 6
  15. a_7_22, a nilpotent element of degree 7
  16. c_8_30, a Duflot regular element of degree 8
  17. a_9_35, 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 93 minimal relations of maximal degree 18:

  1. a_1_12 + a_1_02
  2. a_1_0·a_1_1 + a_1_02
  3. a_1_22 + a_1_0·a_1_2 + a_1_02
  4. a_1_03
  5. a_2_3·a_1_1 + a_2_3·a_1_0
  6. b_2_4·a_1_1 + b_2_4·a_1_0 + a_1_02·a_1_2
  7. a_2_32 + a_2_3·a_1_02
  8. a_1_1·a_3_5 + b_2_4·a_1_0·a_1_2 + b_2_4·a_1_02 + a_2_32
  9. a_1_0·a_3_5 + b_2_4·a_1_0·a_1_2 + b_2_4·a_1_02
  10. a_2_3·b_2_4 + a_1_1·a_3_7 + b_2_4·a_1_02 + a_2_32 + a_2_3·a_1_0·a_1_2
  11. a_2_3·b_2_4 + a_1_0·a_3_7 + b_2_4·a_1_02
  12. a_1_1·b_3_6 + a_1_0·b_3_6 + a_1_2·a_3_5 + b_2_4·a_1_02 + a_2_32
  13. b_2_4·a_1_02·a_1_2
  14. a_2_3·a_3_7
  15. a_2_3·a_3_5 + a_1_0·a_1_2·a_3_7 + a_1_02·a_3_7
  16. b_2_4·a_3_5 + b_2_42·a_1_2 + b_2_42·a_1_0 + a_1_02·b_3_6
  17. a_3_52 + b_2_42·a_1_0·a_1_2
  18. a_3_72 + b_2_4·a_1_0·a_3_7 + b_2_42·a_1_0·a_1_2 + b_2_42·a_1_02
       + a_1_02·a_1_2·a_3_7
  19. a_3_72 + a_3_5·a_3_7 + b_2_4·a_1_2·a_3_7 + b_2_42·a_1_0·a_1_2 + b_2_42·a_1_02
       + a_2_3·a_1_0·b_3_6 + a_1_02·a_1_2·a_3_7
  20. a_3_5·b_3_6 + b_2_4·a_1_2·b_3_6 + b_2_4·a_1_0·b_3_6 + b_2_42·a_1_02
       + c_4_10·a_1_1·a_1_2 + c_4_10·a_1_0·a_1_2
  21. b_3_62 + b_2_43 + a_3_5·b_3_6 + b_2_4·a_1_2·b_3_6 + a_1_1·a_5_11 + b_2_42·a_1_0·a_1_2
       + a_1_02·a_1_2·a_3_7 + c_4_10·a_1_1·a_1_2
  22. b_3_62 + b_2_43 + a_3_5·b_3_6 + b_2_4·a_1_2·b_3_6 + a_1_0·a_5_11 + b_2_42·a_1_0·a_1_2
       + a_1_02·a_1_2·b_3_6 + a_1_02·a_1_2·a_3_7 + c_4_10·a_1_1·a_1_2
  23. b_3_62 + b_2_43 + a_3_5·b_3_6 + b_2_4·a_1_2·b_3_6 + a_1_1·a_5_12 + b_2_42·a_1_0·a_1_2
       + a_1_02·a_1_2·b_3_6 + a_1_02·a_1_2·a_3_7 + c_4_10·a_1_1·a_1_2 + c_4_10·a_1_02
  24. b_3_62 + b_2_43 + a_3_5·b_3_6 + b_2_4·a_1_2·b_3_6 + a_1_0·a_5_12 + b_2_42·a_1_0·a_1_2
       + c_4_10·a_1_1·a_1_2 + c_4_10·a_1_02
  25. b_3_62 + b_2_43 + a_3_5·b_3_6 + b_2_4·a_1_2·b_3_6 + a_1_2·a_5_12 + a_1_1·a_5_13
       + b_2_42·a_1_0·a_1_2 + a_2_3·a_1_2·b_3_6 + c_4_10·a_1_1·a_1_2 + c_4_10·a_1_02
  26. b_3_62 + b_2_43 + b_2_4·a_1_0·b_3_6 + a_1_2·a_5_11 + a_1_0·a_5_13
       + b_2_42·a_1_0·a_1_2 + b_2_42·a_1_02 + a_2_3·a_1_2·b_3_6 + a_1_02·a_1_2·a_3_7
       + c_4_10·a_1_02
  27. b_3_62 + b_2_43 + a_3_5·b_3_6 + b_2_4·a_1_2·b_3_6 + a_3_72 + a_3_5·a_3_7
       + a_1_2·a_5_13 + b_2_4·a_1_2·a_3_7 + b_2_42·a_1_02 + a_2_3·a_1_2·b_3_6
       + a_1_02·a_1_2·b_3_6 + a_1_02·a_1_2·a_3_7 + c_4_10·a_1_1·a_1_2 + c_4_10·a_1_02
  28. b_3_62 + b_2_43 + a_3_5·b_3_6 + b_2_4·a_1_2·b_3_6 + a_3_72 + a_1_2·a_5_12
       + a_1_1·a_5_15 + b_2_42·a_1_0·a_1_2 + b_2_42·a_1_02 + a_1_02·a_1_2·b_3_6
       + a_1_02·a_1_2·a_3_7 + c_4_10·a_1_1·a_1_2
  29. b_3_62 + b_2_43 + b_2_4·a_1_0·b_3_6 + a_3_72 + a_1_2·a_5_11 + a_1_0·a_5_15
       + b_2_42·a_1_0·a_1_2 + a_1_02·a_1_2·b_3_6 + a_1_02·a_1_2·a_3_7
  30. b_3_62 + b_2_43 + a_3_5·b_3_6 + b_2_4·a_1_2·b_3_6 + a_1_2·a_5_15 + b_2_4·a_1_2·a_3_7
       + b_2_42·a_1_02 + a_1_02·a_1_2·b_3_6 + a_1_02·a_1_2·a_3_7 + c_4_10·a_1_02
  31. a_1_02·a_5_11
  32. a_2_3·a_5_12 + a_2_3·a_5_11 + a_2_3·a_1_0·a_1_2·b_3_6 + a_2_3·c_4_10·a_1_0
  33. b_2_4·a_5_12 + b_2_4·a_5_11 + b_2_4·a_1_02·b_3_6 + a_1_02·a_5_13
       + b_2_4·a_1_0·a_1_2·a_3_7 + a_2_3·a_1_0·a_1_2·b_3_6 + b_2_4·c_4_10·a_1_0
  34. a_2_3·a_5_15 + a_2_3·a_5_13 + b_2_4·a_1_0·a_1_2·a_3_7 + a_2_3·c_4_10·a_1_0
  35. b_2_4·a_5_15 + b_2_4·a_5_13 + b_2_42·a_3_7 + b_2_43·a_1_2 + a_1_2·a_3_7·b_3_6
       + b_2_4·a_1_02·b_3_6 + b_2_4·a_1_0·a_1_2·a_3_7 + a_2_3·a_1_0·a_1_2·b_3_6
       + b_2_4·c_4_10·a_1_0 + c_4_10·a_1_02·a_1_2
  36. b_2_4·a_5_12 + b_2_4·a_5_11 + a_1_0·a_3_7·b_3_6 + a_6_19·a_1_1 + b_2_4·a_1_0·a_1_2·b_3_6
       + a_2_3·a_5_11 + b_2_4·a_1_02·a_3_7 + a_2_3·a_1_0·a_1_2·b_3_6 + b_2_4·c_4_10·a_1_0
       + a_2_3·c_4_10·a_1_0 + c_4_10·a_1_02·a_1_2
  37. b_2_4·a_5_12 + b_2_4·a_5_11 + a_1_0·a_3_7·b_3_6 + a_6_19·a_1_0 + b_2_4·a_1_0·a_1_2·b_3_6
       + a_2_3·a_5_11 + b_2_4·a_1_02·a_3_7 + a_2_3·a_1_0·a_1_2·b_3_6 + b_2_4·c_4_10·a_1_0
       + a_2_3·c_4_10·a_1_0 + c_4_10·a_1_02·a_1_2
  38. a_1_2·a_3_7·b_3_6 + a_6_19·a_1_2 + b_2_4·a_1_02·b_3_6 + a_2_3·a_5_13 + a_2_3·a_5_11
       + b_2_4·a_1_02·a_3_7 + a_2_3·c_4_10·a_1_0
  39. a_3_5·a_5_12 + a_3_5·a_5_11 + a_2_3·a_1_0·a_5_11 + b_2_4·c_4_10·a_1_0·a_1_2
       + b_2_4·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_02
  40. b_3_6·a_5_12 + b_3_6·a_5_11 + a_3_7·a_5_12 + a_3_7·a_5_11 + a_3_5·a_5_13
       + b_2_4·a_1_0·a_5_13 + b_2_4·a_1_0·a_5_11 + b_2_43·a_1_02 + a_2_3·a_1_0·a_5_13
       + a_2_3·a_1_0·a_5_11 + c_4_10·a_1_0·b_3_6 + c_4_10·a_1_0·a_3_7 + b_2_4·c_4_10·a_1_02
       + a_2_3·c_4_10·a_1_02
  41. b_3_6·a_5_12 + b_3_6·a_5_11 + a_3_7·a_5_15 + a_3_7·a_5_13 + a_3_5·a_5_13 + a_3_5·a_5_11
       + b_2_4·a_1_0·a_5_11 + b_2_42·a_1_2·a_3_7 + b_2_42·a_1_0·a_3_7 + b_2_43·a_1_0·a_1_2
       + a_2_3·a_1_0·a_5_11 + c_4_10·a_1_0·b_3_6 + c_4_10·a_1_0·a_3_7
       + b_2_4·c_4_10·a_1_0·a_1_2 + a_2_3·c_4_10·a_1_0·a_1_2
  42. a_3_5·a_5_15 + a_3_5·a_5_13 + b_2_42·a_1_2·a_3_7 + b_2_42·a_1_0·a_3_7
       + b_2_43·a_1_02 + b_2_4·c_4_10·a_1_0·a_1_2 + b_2_4·c_4_10·a_1_02
       + a_2_3·c_4_10·a_1_02
  43. b_3_6·a_5_15 + b_3_6·a_5_13 + b_3_6·a_5_12 + b_3_6·a_5_11 + b_2_4·a_3_7·b_3_6
       + b_2_42·a_1_2·b_3_6 + a_3_7·a_5_12 + a_3_7·a_5_11 + a_3_5·a_5_13 + b_2_4·a_1_0·a_5_13
       + b_2_4·a_1_0·a_5_11 + b_2_42·a_1_2·a_3_7 + c_4_10·a_1_2·a_3_5 + c_4_10·a_1_0·a_3_7
  44. a_3_7·a_5_12 + a_3_7·a_5_11 + a_3_5·a_5_11 + b_2_4·a_1_0·a_5_13 + a_2_3·a_6_19
       + a_2_3·a_1_0·a_5_11 + c_4_10·a_1_0·a_3_7 + b_2_4·c_4_10·a_1_0·a_1_2
       + b_2_4·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_0·a_1_2
  45. b_3_6·a_5_12 + b_3_6·a_5_11 + a_3_5·a_5_13 + b_2_4·a_1_0·a_5_13 + b_2_4·a_1_0·a_5_11
       + b_2_43·a_1_02 + a_6_19·a_1_02 + c_4_10·a_1_0·b_3_6 + b_2_4·c_4_10·a_1_02
  46. b_3_6·a_5_12 + b_3_6·a_5_11 + b_2_4·a_3_7·b_3_6 + b_2_4·a_6_19 + b_2_42·a_1_2·b_3_6
       + b_2_42·a_1_0·b_3_6 + a_3_7·a_5_11 + a_3_5·a_5_13 + b_2_42·a_1_2·a_3_7
       + b_2_42·a_1_0·a_3_7 + b_2_43·a_1_02 + a_2_3·a_1_0·a_5_11 + c_4_10·a_1_0·b_3_6
       + c_4_10·a_1_0·a_3_7 + b_2_4·c_4_10·a_1_0·a_1_2 + b_2_4·c_4_10·a_1_02
       + a_2_3·c_4_10·a_1_02
  47. b_3_6·a_5_12 + b_3_6·a_5_11 + a_3_7·a_5_12 + a_3_7·a_5_11 + a_3_5·a_5_13 + a_3_5·a_5_11
       + b_2_4·a_1_0·a_5_11 + b_2_43·a_1_02 + a_6_19·a_1_0·a_1_2 + c_4_10·a_1_0·b_3_6
       + c_4_10·a_1_0·a_3_7 + b_2_4·c_4_10·a_1_0·a_1_2
  48. a_3_7·a_5_12 + a_3_7·a_5_11 + a_1_1·a_7_22 + b_2_42·a_1_0·a_3_7 + b_2_43·a_1_0·a_1_2
       + b_2_4·c_4_10·a_1_0·a_1_2
  49. a_3_7·a_5_12 + a_3_7·a_5_11 + a_1_0·a_7_22 + b_2_42·a_1_0·a_3_7 + b_2_43·a_1_0·a_1_2
       + a_2_3·a_1_0·a_5_11 + b_2_4·c_4_10·a_1_0·a_1_2 + a_2_3·c_4_10·a_1_0·a_1_2
       + a_2_3·c_4_10·a_1_02
  50. a_3_7·a_5_12 + a_3_7·a_5_11 + a_3_5·a_5_13 + a_1_2·a_7_22 + b_2_4·a_1_0·a_5_13
       + b_2_4·a_1_0·a_5_11 + b_2_42·a_1_2·a_3_7 + b_2_43·a_1_0·a_1_2 + b_2_43·a_1_02
       + c_4_10·a_1_2·a_3_7 + c_4_10·a_1_2·a_3_5 + c_4_10·a_1_0·a_3_7
       + b_2_4·c_4_10·a_1_0·a_1_2 + b_2_4·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_0·a_1_2
       + a_2_3·c_4_10·a_1_02
  51. a_6_19·a_3_7 + b_2_4·a_6_19·a_1_2 + b_2_42·a_1_0·a_1_2·b_3_6 + a_1_0·a_3_7·a_5_11
       + b_2_42·a_1_0·a_1_2·a_3_7 + a_2_3·a_1_02·a_5_13 + c_4_10·a_1_0·a_1_2·a_3_7
  52. a_6_19·a_3_7 + a_6_19·a_3_5 + b_2_4·a_6_19·a_1_0 + b_2_42·a_1_0·a_1_2·b_3_6
       + a_1_0·a_3_7·a_5_11 + b_2_42·a_1_0·a_1_2·a_3_7 + b_2_42·a_1_02·a_3_7
       + a_2_3·a_1_02·a_5_13 + c_4_10·a_1_0·a_1_2·a_3_7
  53. a_2_3·a_7_22 + b_2_42·a_1_0·a_1_2·a_3_7 + a_2_3·a_1_02·a_5_13
       + c_4_10·a_1_0·a_1_2·a_3_7
  54. b_2_4·a_7_22 + b_2_43·a_3_7 + b_2_44·a_1_2 + a_1_0·b_3_6·a_5_11 + b_2_4·a_6_19·a_1_0
       + b_2_42·a_1_0·a_1_2·b_3_6 + b_2_42·a_1_02·b_3_6 + a_1_0·a_3_7·a_5_13
       + b_2_4·c_4_10·a_3_7 + b_2_42·c_4_10·a_1_2 + c_4_10·a_1_0·a_1_2·a_3_7
  55. a_5_122 + a_5_112 + c_4_102·a_1_02
  56. a_5_11·a_5_12 + a_5_112 + a_1_02·a_3_7·a_5_13 + c_4_10·a_1_0·a_5_11
       + c_4_10·a_1_02·a_1_2·b_3_6 + c_4_10·a_1_02·a_1_2·a_3_7
  57. a_5_132 + a_5_11·a_5_13 + a_5_112 + a_2_3·b_3_6·a_5_13 + a_2_3·b_3_6·a_5_11
       + a_1_02·b_3_6·a_5_13 + c_4_10·a_1_0·a_5_13 + a_2_3·c_4_10·a_1_0·b_3_6
       + c_4_102·a_1_02
  58. a_5_13·a_5_15 + a_5_12·a_5_15 + a_5_12·a_5_13 + a_5_11·a_5_13 + a_5_112
       + b_2_4·a_3_7·a_5_13 + b_2_4·a_3_7·a_5_11 + b_2_42·a_1_0·a_5_13 + a_2_3·b_3_6·a_5_11
       + a_1_02·b_3_6·a_5_13 + c_4_10·a_1_1·a_5_13 + c_4_10·a_1_0·a_5_13
       + c_4_10·a_1_0·a_5_11 + b_2_4·c_4_10·a_1_0·a_3_7 + a_2_3·c_4_10·a_1_0·b_3_6
  59. a_5_152 + a_5_11·a_5_13 + a_5_112 + b_2_43·a_1_0·a_3_7 + a_2_3·b_3_6·a_5_13
       + a_2_3·b_3_6·a_5_11 + a_1_02·b_3_6·a_5_13 + c_4_10·a_1_0·a_5_13
       + a_2_3·c_4_10·a_1_0·b_3_6
  60. a_5_13·a_5_15 + a_5_11·a_5_15 + a_5_11·a_5_12 + b_2_4·a_3_7·a_5_13 + b_2_4·a_3_7·a_5_11
       + b_2_42·a_1_0·a_5_13 + a_2_3·b_3_6·a_5_11 + a_1_02·b_3_6·a_5_13
       + b_2_4·a_6_19·a_1_02 + c_4_10·a_1_1·a_5_13 + c_4_10·a_1_0·a_5_13
       + b_2_42·c_4_10·a_1_0·a_1_2 + a_2_3·c_4_10·a_1_2·b_3_6 + a_2_3·c_4_10·a_1_0·b_3_6
       + c_4_10·a_1_02·a_1_2·b_3_6 + c_4_102·a_1_02
  61. a_5_11·a_5_15 + a_5_11·a_5_13 + b_2_4·a_3_7·a_5_11 + b_2_42·a_1_0·a_5_13
       + b_2_42·a_1_0·a_5_11 + a_2_3·b_3_6·a_5_13 + a_2_3·b_3_6·a_5_11 + a_1_02·b_3_6·a_5_13
       + b_2_4·a_6_19·a_1_0·a_1_2 + c_4_10·a_1_0·a_5_11 + b_2_42·c_4_10·a_1_0·a_1_2
       + b_2_42·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_2·b_3_6 + a_2_3·c_4_10·a_1_0·b_3_6
       + c_4_10·a_1_02·a_1_2·a_3_7
  62. a_5_13·a_5_15 + a_5_11·a_5_15 + a_5_11·a_5_12 + a_3_7·a_7_22 + b_2_4·a_3_7·a_5_13
       + b_2_4·a_3_7·a_5_11 + b_2_42·a_1_0·a_5_13 + b_2_43·a_1_2·a_3_7 + b_2_43·a_1_0·a_3_7
       + b_2_44·a_1_0·a_1_2 + b_2_44·a_1_02 + a_1_02·b_3_6·a_5_13 + c_4_10·a_1_1·a_5_13
       + c_4_10·a_1_0·a_5_13 + b_2_4·c_4_10·a_1_2·a_3_7 + b_2_4·c_4_10·a_1_0·a_3_7
       + b_2_42·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_2·b_3_6 + a_2_3·c_4_10·a_1_0·b_3_6
       + c_4_10·a_1_02·a_1_2·b_3_6 + c_4_102·a_1_02
  63. a_5_11·a_5_15 + a_5_11·a_5_13 + a_5_11·a_5_12 + a_5_112 + a_3_5·a_7_22
       + b_2_4·a_3_7·a_5_11 + b_2_42·a_1_0·a_5_13 + b_2_42·a_1_0·a_5_11
       + b_2_43·a_1_2·a_3_7 + b_2_43·a_1_0·a_3_7 + b_2_44·a_1_02 + a_2_3·b_3_6·a_5_13
       + a_2_3·b_3_6·a_5_11 + b_2_4·c_4_10·a_1_2·a_3_7 + b_2_4·c_4_10·a_1_0·a_3_7
       + b_2_42·c_4_10·a_1_0·a_1_2 + a_2_3·c_4_10·a_1_2·b_3_6 + c_4_10·a_1_02·a_1_2·b_3_6
       + c_4_10·a_1_02·a_1_2·a_3_7
  64. b_3_6·a_7_22 + b_2_42·a_6_19 + b_2_43·a_1_0·b_3_6 + a_5_13·a_5_15 + a_5_11·a_5_13
       + a_5_112 + b_2_4·a_3_7·a_5_13 + b_2_4·a_3_7·a_5_11 + b_2_42·a_1_0·a_5_13
       + b_2_42·a_1_0·a_5_11 + b_2_43·a_1_2·a_3_7 + a_2_3·b_3_6·a_5_11 + c_4_10·a_3_7·b_3_6
       + b_2_4·c_4_10·a_1_2·b_3_6 + b_2_4·c_4_10·a_1_0·a_3_7 + b_2_42·c_4_10·a_1_0·a_1_2
       + b_2_42·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_2·b_3_6 + a_2_3·c_4_10·a_1_0·b_3_6
       + c_4_10·a_1_02·a_1_2·b_3_6 + c_4_102·a_1_1·a_1_2 + c_4_102·a_1_0·a_1_2
       + c_4_102·a_1_02
  65. a_5_13·a_5_15 + a_5_11·a_5_15 + a_5_11·a_5_12 + a_5_112 + b_2_4·a_3_7·a_5_13
       + b_2_4·a_3_7·a_5_11 + b_2_42·a_1_0·a_5_13 + b_2_44·a_1_0·a_1_2 + b_2_44·a_1_02
       + a_2_3·b_3_6·a_5_11 + c_8_30·a_1_02 + c_4_10·a_1_1·a_5_13 + c_4_10·a_1_0·a_5_13
       + b_2_42·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_2·b_3_6 + a_2_3·c_4_10·a_1_0·b_3_6
       + c_4_10·a_1_02·a_1_2·b_3_6
  66. a_5_12·a_5_13 + a_5_11·a_5_15 + a_5_11·a_5_13 + a_5_112 + b_2_4·a_3_7·a_5_11
       + b_2_42·a_1_0·a_5_13 + b_2_42·a_1_0·a_5_11 + b_2_44·a_1_02 + a_1_02·b_3_6·a_5_13
       + c_8_30·a_1_1·a_1_2 + c_4_10·a_1_0·a_5_11 + b_2_42·c_4_10·a_1_0·a_1_2
       + a_2_3·c_4_10·a_1_2·b_3_6 + c_4_10·a_1_02·a_1_2·b_3_6 + c_4_102·a_1_02
  67. a_5_11·a_5_15 + a_5_112 + b_2_4·a_3_7·a_5_11 + b_2_42·a_1_0·a_5_13
       + b_2_42·a_1_0·a_5_11 + b_2_44·a_1_02 + c_8_30·a_1_0·a_1_2 + c_4_10·a_1_0·a_5_13
       + c_4_10·a_1_0·a_5_11 + b_2_42·c_4_10·a_1_0·a_1_2 + a_2_3·c_4_10·a_1_2·b_3_6
       + c_4_10·a_1_02·a_1_2·b_3_6 + c_4_102·a_1_02
  68. a_5_12·a_5_13 + a_5_11·a_5_15 + a_5_11·a_5_13 + a_5_11·a_5_12 + a_5_112 + a_1_1·a_9_35
       + b_2_4·a_3_7·a_5_11 + b_2_42·a_1_0·a_5_13 + b_2_44·a_1_0·a_1_2 + a_2_3·b_3_6·a_5_13
       + a_1_02·b_3_6·a_5_13 + c_4_10·a_1_1·a_5_13 + b_2_4·c_4_10·a_1_0·a_3_7
       + b_2_42·c_4_10·a_1_0·a_1_2 + b_2_42·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_2·b_3_6
       + c_4_10·a_1_02·a_1_2·b_3_6 + c_4_10·a_1_02·a_1_2·a_3_7 + c_4_102·a_1_1·a_1_2
       + c_4_102·a_1_02
  69. a_5_11·a_5_15 + a_5_11·a_5_12 + a_5_112 + a_1_0·a_9_35 + b_2_4·a_3_7·a_5_11
       + b_2_42·a_1_0·a_5_13 + b_2_44·a_1_0·a_1_2 + a_2_3·b_3_6·a_5_13
       + b_2_4·c_4_10·a_1_0·a_3_7 + b_2_42·c_4_10·a_1_0·a_1_2 + b_2_42·c_4_10·a_1_02
       + a_2_3·c_4_10·a_1_2·b_3_6 + c_4_10·a_1_02·a_1_2·b_3_6 + c_4_10·a_1_02·a_1_2·a_3_7
       + c_4_102·a_1_0·a_1_2 + c_4_102·a_1_02
  70. a_5_13·a_5_15 + a_5_12·a_5_13 + a_5_11·a_5_15 + a_5_11·a_5_13 + a_1_2·a_9_35
       + b_2_4·a_3_7·a_5_13 + b_2_4·a_3_7·a_5_11 + b_2_42·a_1_0·a_5_11 + b_2_44·a_1_0·a_1_2
       + b_2_44·a_1_02 + a_1_02·b_3_6·a_5_13 + c_4_10·a_1_0·a_5_13
       + b_2_4·c_4_10·a_1_2·a_3_7 + b_2_42·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_0·b_3_6
       + c_4_10·a_1_02·a_1_2·b_3_6 + c_4_10·a_1_02·a_1_2·a_3_7 + c_4_102·a_1_1·a_1_2
       + c_4_102·a_1_0·a_1_2
  71. a_6_19·a_5_12 + a_6_19·a_5_11 + b_2_43·a_1_02·a_3_7 + a_2_3·a_1_0·b_3_6·a_5_13
       + c_4_10·a_6_19·a_1_0
  72. a_6_19·a_5_15 + a_6_19·a_5_13 + b_2_43·a_1_0·a_1_2·b_3_6 + b_2_4·a_1_0·a_3_7·a_5_11
       + c_4_10·a_6_19·a_1_0 + b_2_4·c_4_10·a_1_0·a_1_2·a_3_7
  73. a_3_7·b_3_6·a_5_11 + a_6_19·a_5_11 + b_2_4·a_1_0·b_3_6·a_5_13
       + b_2_4·a_1_0·a_3_7·a_5_13 + b_2_43·a_1_02·a_3_7 + b_2_4·c_4_10·a_1_0·a_1_2·b_3_6
       + b_2_4·c_4_10·a_1_02·b_3_6 + a_2_3·c_8_30·a_1_0 + a_2_3·c_4_10·a_5_11
       + c_8_30·a_1_02·a_1_2 + a_2_3·c_4_10·a_1_0·a_1_2·b_3_6 + a_2_3·c_4_102·a_1_0
       + c_4_102·a_1_02·a_1_2
  74. a_3_7·b_3_6·a_5_13 + a_3_7·b_3_6·a_5_11 + a_6_19·a_5_13 + a_6_19·a_5_11
       + b_2_4·a_1_0·b_3_6·a_5_11 + b_2_4·a_1_0·a_3_7·a_5_11
       + b_2_4·c_4_10·a_1_0·a_1_2·b_3_6 + a_2_3·c_8_30·a_1_2 + a_2_3·c_4_10·a_5_11
       + c_4_10·a_1_02·a_5_13 + b_2_4·c_4_10·a_1_0·a_1_2·a_3_7 + b_2_4·c_4_10·a_1_02·a_3_7
       + a_2_3·c_4_10·a_1_0·a_1_2·b_3_6 + a_2_3·c_4_102·a_1_0 + c_4_102·a_1_02·a_1_2
  75. a_3_7·b_3_6·a_5_13 + a_6_19·a_5_13 + b_2_4·a_1_0·b_3_6·a_5_13
       + b_2_4·a_1_0·b_3_6·a_5_11 + a_2_3·a_9_35 + b_2_4·a_1_0·a_3_7·a_5_13
       + b_2_43·a_1_02·a_3_7 + b_2_4·c_4_10·a_1_02·b_3_6 + a_2_3·c_4_10·a_5_13
       + c_8_30·a_1_02·a_1_2 + c_4_10·a_1_02·a_5_13 + b_2_4·c_4_10·a_1_02·a_3_7
       + a_2_3·c_4_10·a_1_0·a_1_2·b_3_6 + a_2_3·c_4_102·a_1_2 + a_2_3·c_4_102·a_1_0
  76. b_2_4·a_9_35 + b_2_43·a_5_11 + a_3_7·b_3_6·a_5_13 + b_2_42·a_6_19·a_1_0
       + b_2_43·a_1_0·a_1_2·b_3_6 + b_2_4·a_1_0·a_3_7·a_5_13 + b_2_42·a_1_02·a_5_13
       + b_2_43·a_1_0·a_1_2·a_3_7 + a_2_3·a_1_0·b_3_6·a_5_13 + b_2_4·c_8_30·a_1_2
       + b_2_4·c_8_30·a_1_0 + b_2_4·c_4_10·a_5_13 + b_2_42·c_4_10·a_3_7
       + b_2_43·c_4_10·a_1_2 + c_8_30·a_1_02·a_1_2 + c_4_10·a_1_02·a_5_13
       + b_2_4·c_4_10·a_1_02·a_3_7 + a_2_3·c_4_10·a_1_0·a_1_2·b_3_6 + b_2_4·c_4_102·a_1_2
       + b_2_4·c_4_102·a_1_0 + c_4_102·a_1_02·a_1_2
  77. a_5_12·a_7_22 + a_5_11·a_7_22 + a_6_192 + b_2_44·a_1_0·a_3_7 + b_2_45·a_1_02
       + b_2_4·a_1_02·a_3_7·a_5_13 + b_2_42·c_4_10·a_1_0·a_3_7
       + b_2_43·c_4_10·a_1_0·a_1_2 + c_4_102·a_1_0·a_3_7 + b_2_4·c_4_102·a_1_0·a_1_2
       + a_2_3·c_4_102·a_1_0·a_1_2
  78. a_5_15·a_7_22 + a_5_13·a_7_22 + a_6_192 + b_2_45·a_1_02 + a_6_19·a_1_0·a_5_11
       + b_2_42·a_6_19·a_1_0·a_1_2 + b_2_43·c_4_10·a_1_0·a_1_2 + c_4_10·a_6_19·a_1_02
       + a_2_3·c_4_10·a_1_0·a_5_13 + c_4_102·a_1_0·a_3_7 + b_2_4·c_4_102·a_1_0·a_1_2
  79. a_5_13·a_7_22 + a_5_11·a_7_22 + a_6_192 + b_2_42·a_3_7·a_5_13 + b_2_42·a_3_7·a_5_11
       + b_2_43·a_1_0·a_5_13 + b_2_44·a_1_0·a_3_7 + b_2_45·a_1_02 + a_6_19·a_1_0·a_5_13
       + a_6_19·a_1_0·a_5_11 + b_2_4·a_1_02·a_3_7·a_5_13 + c_8_30·a_1_2·a_3_5
       + c_4_10·a_3_7·a_5_13 + c_4_10·a_3_7·a_5_11 + c_4_10·a_1_2·a_7_22
       + b_2_4·c_8_30·a_1_02 + b_2_4·c_4_10·a_1_0·a_5_13 + b_2_42·c_4_10·a_1_2·a_3_7
       + b_2_43·c_4_10·a_1_02 + c_4_10·a_6_19·a_1_0·a_1_2 + c_4_10·a_6_19·a_1_02
       + c_4_102·a_1_2·a_3_7 + c_4_102·a_1_2·a_3_5 + a_2_3·c_4_102·a_1_02
  80. a_6_192 + b_2_44·a_1_0·a_3_7 + b_2_45·a_1_02 + b_2_42·a_6_19·a_1_02
       + a_2_3·c_8_30·a_1_02
  81. a_5_11·a_7_22 + a_6_192 + b_2_42·a_3_7·a_5_11 + b_2_43·a_1_0·a_5_13
       + b_2_43·a_1_0·a_5_11 + b_2_44·a_1_0·a_3_7 + b_2_45·a_1_02 + a_6_19·a_1_0·a_5_11
       + b_2_4·a_1_02·b_3_6·a_5_13 + b_2_42·a_6_19·a_1_0·a_1_2 + b_2_42·a_6_19·a_1_02
       + b_2_4·a_1_02·a_3_7·a_5_13 + c_4_10·a_3_7·a_5_11 + b_2_4·c_4_10·a_1_0·a_5_13
       + b_2_4·c_4_10·a_1_0·a_5_11 + b_2_43·c_4_10·a_1_0·a_1_2 + b_2_43·c_4_10·a_1_02
       + c_4_10·a_6_19·a_1_0·a_1_2 + a_2_3·c_8_30·a_1_0·a_1_2 + a_2_3·c_4_10·a_1_0·a_5_13
       + b_2_4·c_4_102·a_1_0·a_1_2 + b_2_4·c_4_102·a_1_02 + a_2_3·c_4_102·a_1_0·a_1_2
  82. a_3_7·a_9_35 + b_2_42·a_3_7·a_5_11 + a_6_19·a_1_0·a_5_13 + c_8_30·a_1_2·a_3_7
       + c_8_30·a_1_0·a_3_7 + c_4_10·a_3_7·a_5_13 + b_2_42·c_4_10·a_1_2·a_3_7
       + b_2_42·c_4_10·a_1_0·a_3_7 + b_2_43·c_4_10·a_1_0·a_1_2 + b_2_43·c_4_10·a_1_02
       + a_2_3·c_4_10·a_1_0·a_5_13 + c_4_102·a_1_2·a_3_7 + c_4_102·a_1_0·a_3_7
       + a_2_3·c_4_102·a_1_0·a_1_2 + a_2_3·c_4_102·a_1_02
  83. a_5_13·a_7_22 + a_3_5·a_9_35 + a_6_192 + b_2_42·a_3_7·a_5_13 + b_2_43·a_1_0·a_5_13
       + b_2_43·a_1_0·a_5_11 + b_2_44·a_1_0·a_3_7 + b_2_45·a_1_02 + a_6_19·a_1_0·a_5_11
       + b_2_4·a_1_02·b_3_6·a_5_13 + b_2_42·a_6_19·a_1_0·a_1_2 + b_2_42·a_6_19·a_1_02
       + b_2_4·a_1_02·a_3_7·a_5_13 + c_4_10·a_3_7·a_5_13 + b_2_4·c_8_30·a_1_0·a_1_2
       + b_2_4·c_4_10·a_1_0·a_5_13 + b_2_42·c_4_10·a_1_2·a_3_7 + b_2_42·c_4_10·a_1_0·a_3_7
       + b_2_43·c_4_10·a_1_0·a_1_2 + b_2_43·c_4_10·a_1_02 + a_2_3·c_4_10·a_1_0·a_5_11
       + c_4_102·a_1_2·a_3_5 + b_2_4·c_4_102·a_1_0·a_1_2 + b_2_4·c_4_102·a_1_02
  84. b_3_6·a_9_35 + b_2_42·b_3_6·a_5_11 + a_5_13·a_7_22 + a_6_192 + b_2_43·a_1_0·a_5_11
       + a_6_19·a_1_0·a_5_13 + a_6_19·a_1_0·a_5_11 + b_2_42·a_6_19·a_1_0·a_1_2
       + b_2_4·a_1_02·a_3_7·a_5_13 + c_8_30·a_1_2·b_3_6 + c_8_30·a_1_0·b_3_6
       + c_4_10·b_3_6·a_5_13 + b_2_4·c_4_10·a_6_19 + b_2_42·c_4_10·a_1_0·b_3_6
       + c_4_10·a_3_7·a_5_13 + c_4_10·a_3_7·a_5_11 + b_2_4·c_4_10·a_1_0·a_5_13
       + b_2_42·c_4_10·a_1_2·a_3_7 + b_2_42·c_4_10·a_1_0·a_3_7 + b_2_43·c_4_10·a_1_02
       + c_4_10·a_6_19·a_1_0·a_1_2 + a_2_3·c_4_10·a_1_0·a_5_11 + c_4_102·a_1_2·b_3_6
       + c_4_102·a_1_0·b_3_6 + c_4_102·a_1_2·a_3_5 + c_4_102·a_1_0·a_3_7
       + b_2_4·c_4_102·a_1_0·a_1_2
  85. a_6_19·a_7_22 + b_2_44·a_1_0·a_1_2·b_3_6 + b_2_43·a_1_02·a_5_13
       + b_2_42·c_4_10·a_1_0·a_1_2·b_3_6 + c_4_10·a_1_0·a_3_7·a_5_11
       + c_4_102·a_1_0·a_1_2·a_3_7
  86. a_7_222 + b_2_45·a_1_0·a_3_7 + b_2_4·c_4_102·a_1_0·a_3_7
       + c_4_102·a_1_02·a_1_2·a_3_7
  87. a_5_11·a_9_35 + b_2_46·a_1_0·a_1_2 + b_2_46·a_1_02 + b_2_4·a_6_19·a_1_0·a_5_11
       + b_2_43·a_6_19·a_1_0·a_1_2 + b_2_43·a_6_19·a_1_02 + c_8_30·a_1_0·a_5_13
       + b_2_4·c_4_10·a_3_7·a_5_11 + b_2_42·c_8_30·a_1_02 + b_2_42·c_4_10·a_1_0·a_5_13
       + b_2_42·c_4_10·a_1_0·a_5_11 + b_2_44·c_4_10·a_1_02 + a_2_3·c_8_30·a_1_0·b_3_6
       + a_2_3·c_4_10·b_3_6·a_5_11 + c_8_30·a_1_02·a_1_2·b_3_6
       + c_4_10·a_1_02·b_3_6·a_5_13 + b_2_4·c_4_10·a_6_19·a_1_0·a_1_2
       + b_2_4·c_4_10·a_6_19·a_1_02 + c_8_30·a_1_02·a_1_2·a_3_7
       + c_4_10·a_1_02·a_3_7·a_5_13 + a_2_3·c_4_102·a_1_2·b_3_6
       + a_2_3·c_4_102·a_1_0·b_3_6 + c_4_102·a_1_02·a_1_2·a_3_7 + c_4_103·a_1_0·a_1_2
       + c_4_103·a_1_02
  88. a_5_13·a_9_35 + b_2_46·a_1_0·a_1_2 + b_2_4·a_6_19·a_1_0·a_5_11
       + b_2_42·a_1_02·b_3_6·a_5_13 + b_2_43·a_6_19·a_1_0·a_1_2 + c_8_30·a_1_1·a_5_13
       + c_8_30·a_1_0·a_5_11 + b_2_4·c_4_10·a_3_7·a_5_13 + b_2_42·c_8_30·a_1_0·a_1_2
       + b_2_42·c_8_30·a_1_02 + b_2_42·c_4_10·a_1_0·a_5_13 + b_2_42·c_4_10·a_1_0·a_5_11
       + b_2_44·c_4_10·a_1_0·a_1_2 + b_2_44·c_4_10·a_1_02 + a_2_3·c_8_30·a_1_0·b_3_6
       + c_8_30·a_1_02·a_1_2·b_3_6 + b_2_4·c_4_10·a_6_19·a_1_02
       + c_8_30·a_1_02·a_1_2·a_3_7 + c_4_10·c_8_30·a_1_1·a_1_2 + c_4_10·c_8_30·a_1_02
       + c_4_102·a_1_1·a_5_13 + c_4_102·a_1_0·a_5_11 + a_2_3·c_4_102·a_1_2·b_3_6
       + a_2_3·c_4_102·a_1_0·b_3_6 + c_4_102·a_1_02·a_1_2·b_3_6 + c_4_103·a_1_02
  89. a_5_12·a_9_35 + b_2_46·a_1_0·a_1_2 + b_2_46·a_1_02 + b_2_4·a_6_19·a_1_0·a_5_11
       + b_2_43·a_6_19·a_1_0·a_1_2 + b_2_43·a_6_19·a_1_02 + c_8_30·a_1_1·a_5_13
       + b_2_4·c_4_10·a_3_7·a_5_11 + b_2_42·c_8_30·a_1_02 + b_2_42·c_4_10·a_1_0·a_5_13
       + b_2_44·c_4_10·a_1_02 + a_2_3·c_8_30·a_1_0·b_3_6 + a_2_3·c_4_10·b_3_6·a_5_13
       + a_2_3·c_4_10·b_3_6·a_5_11 + c_4_10·a_1_02·b_3_6·a_5_13
       + b_2_4·c_4_10·a_6_19·a_1_0·a_1_2 + b_2_4·c_4_10·a_6_19·a_1_02
       + c_4_10·a_1_02·a_3_7·a_5_13 + c_4_10·c_8_30·a_1_1·a_1_2 + c_4_10·c_8_30·a_1_02
       + c_4_102·a_1_1·a_5_13 + b_2_4·c_4_102·a_1_0·a_3_7 + b_2_42·c_4_102·a_1_0·a_1_2
       + a_2_3·c_4_102·a_1_2·b_3_6 + a_2_3·c_4_102·a_1_0·b_3_6
  90. a_5_15·a_9_35 + b_2_43·a_3_7·a_5_11 + b_2_44·a_1_0·a_5_13 + b_2_44·a_1_0·a_5_11
       + b_2_46·a_1_0·a_1_2 + b_2_4·a_6_19·a_1_0·a_5_11 + b_2_43·a_6_19·a_1_0·a_1_2
       + c_8_30·a_1_1·a_5_13 + c_8_30·a_1_0·a_5_11 + b_2_4·c_8_30·a_1_2·a_3_7
       + b_2_4·c_8_30·a_1_0·a_3_7 + b_2_42·c_8_30·a_1_0·a_1_2 + b_2_42·c_4_10·a_1_0·a_5_13
       + b_2_42·c_4_10·a_1_0·a_5_11 + b_2_43·c_4_10·a_1_0·a_3_7
       + a_2_3·c_4_10·b_3_6·a_5_13 + a_2_3·c_4_10·b_3_6·a_5_11
       + b_2_4·c_4_10·a_6_19·a_1_02 + c_4_102·a_1_0·a_5_11 + b_2_4·c_4_102·a_1_2·a_3_7
       + b_2_42·c_4_102·a_1_0·a_1_2 + a_2_3·c_4_102·a_1_2·b_3_6
       + a_2_3·c_4_102·a_1_0·b_3_6 + c_4_102·a_1_02·a_1_2·b_3_6
       + c_4_102·a_1_02·a_1_2·a_3_7 + c_4_103·a_1_1·a_1_2
  91. a_6_19·a_9_35 + b_2_42·a_6_19·a_5_11 + b_2_43·a_1_0·a_3_7·a_5_11
       + b_2_44·a_1_02·a_5_13 + b_2_45·a_1_0·a_1_2·a_3_7 + b_2_45·a_1_02·a_3_7
       + b_2_4·a_6_19·a_1_02·a_5_13 + a_6_19·c_8_30·a_1_2 + a_6_19·c_8_30·a_1_0
       + c_4_10·a_6_19·a_5_13 + b_2_43·c_4_10·a_1_0·a_1_2·b_3_6
       + b_2_4·c_4_10·a_1_0·a_3_7·a_5_11 + b_2_43·c_4_10·a_1_0·a_1_2·a_3_7
       + b_2_43·c_4_10·a_1_02·a_3_7 + a_2_3·c_8_30·a_1_0·a_1_2·b_3_6
       + c_4_102·a_6_19·a_1_2 + c_4_102·a_6_19·a_1_0 + b_2_4·c_4_102·a_1_0·a_1_2·a_3_7
  92. a_7_22·a_9_35 + b_2_44·a_3_7·a_5_11 + b_2_45·a_1_0·a_5_13 + b_2_45·a_1_0·a_5_11
       + b_2_42·a_6_19·a_1_0·a_5_13 + b_2_43·a_1_02·a_3_7·a_5_13 + c_8_30·a_1_2·a_7_22
       + b_2_42·c_8_30·a_1_0·a_3_7 + b_2_42·c_4_10·a_3_7·a_5_13
       + b_2_42·c_4_10·a_3_7·a_5_11 + b_2_43·c_8_30·a_1_0·a_1_2
       + b_2_43·c_4_10·a_1_0·a_5_13 + b_2_44·c_4_10·a_1_0·a_3_7
       + b_2_45·c_4_10·a_1_0·a_1_2 + b_2_45·c_4_10·a_1_02 + a_6_19·c_8_30·a_1_02
       + b_2_42·c_4_10·a_6_19·a_1_02 + a_2_3·c_8_30·a_1_0·a_5_13
       + a_2_3·c_8_30·a_1_0·a_5_11 + b_2_4·c_4_10·a_1_02·a_3_7·a_5_13
       + c_4_10·c_8_30·a_1_2·a_3_5 + c_4_10·c_8_30·a_1_0·a_3_7 + c_4_102·a_3_7·a_5_13
       + b_2_4·c_4_10·c_8_30·a_1_0·a_1_2 + b_2_4·c_4_10·c_8_30·a_1_02
       + b_2_4·c_4_102·a_1_0·a_5_11 + b_2_42·c_4_102·a_1_2·a_3_7
       + b_2_43·c_4_102·a_1_0·a_1_2 + b_2_43·c_4_102·a_1_02 + c_4_102·a_6_19·a_1_02
       + a_2_3·c_4_10·c_8_30·a_1_02 + a_2_3·c_4_102·a_1_0·a_5_13
       + a_2_3·c_4_102·a_1_0·a_5_11 + c_4_103·a_1_2·a_3_7 + c_4_103·a_1_2·a_3_5
       + c_4_103·a_1_0·a_3_7 + b_2_4·c_4_103·a_1_02 + a_2_3·c_4_103·a_1_0·a_1_2
  93. a_9_352 + b_2_48·a_1_0·a_1_2 + b_2_48·a_1_02 + b_2_44·a_1_02·b_3_6·a_5_13
       + b_2_45·a_6_19·a_1_02 + b_2_44·c_8_30·a_1_02 + b_2_46·c_4_10·a_1_0·a_1_2
       + b_2_46·c_4_10·a_1_02 + c_8_302·a_1_0·a_1_2 + b_2_43·c_4_102·a_1_0·a_3_7
       + b_2_4·c_4_102·a_6_19·a_1_0·a_1_2 + c_4_102·c_8_30·a_1_0·a_1_2
       + b_2_42·c_4_103·a_1_02 + c_4_103·a_1_02·a_1_2·b_3_6
       + c_4_103·a_1_02·a_1_2·a_3_7 + c_4_104·a_1_0·a_1_2

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_10, a Duflot regular element of degree 4
    2. c_8_30, 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_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. a_2_3 → 0, an element of degree 2
  5. b_2_4 → 0, an element of degree 2
  6. a_3_5 → 0, an element of degree 3
  7. a_3_7 → 0, an element of degree 3
  8. b_3_6 → 0, an element of degree 3
  9. c_4_10 → c_1_04, an element of degree 4
  10. a_5_11 → 0, an element of degree 5
  11. a_5_12 → 0, an element of degree 5
  12. a_5_13 → 0, an element of degree 5
  13. a_5_15 → 0, an element of degree 5
  14. a_6_19 → 0, an element of degree 6
  15. a_7_22 → 0, an element of degree 7
  16. c_8_30 → c_1_18 + c_1_08, an element of degree 8
  17. a_9_35 → 0, an element of degree 9

Restriction map to a maximal el. ab. subgp. 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. a_2_3 → 0, an element of degree 2
  5. b_2_4 → c_1_22, an element of degree 2
  6. a_3_5 → 0, an element of degree 3
  7. a_3_7 → 0, an element of degree 3
  8. b_3_6 → c_1_23, an element of degree 3
  9. c_4_10 → c_1_24 + c_1_04, an element of degree 4
  10. a_5_11 → 0, an element of degree 5
  11. a_5_12 → 0, an element of degree 5
  12. a_5_13 → 0, an element of degree 5
  13. a_5_15 → 0, an element of degree 5
  14. a_6_19 → 0, an element of degree 6
  15. a_7_22 → 0, an element of degree 7
  16. c_8_30 → c_1_14·c_1_24 + c_1_18 + c_1_04·c_1_24 + c_1_08, an element of degree 8
  17. a_9_35 → 0, 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