Cohomology of group number 1367 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 4 conjugacy classes of maximal elementary abelian subgroups, which are all 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
    (t3  +  2·t  +  1) · (t3  +  t2  +  1)
    (t  +  1)2 · (t  −  1)4 · (t2  +  1)2
  • The a-invariants are -∞,-∞,-∞,-5,-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 15 minimal generators of maximal degree 5:

  1. b_1_0, an element of degree 1
  2. b_1_1, an element of degree 1
  3. b_1_2, an element of degree 1
  4. b_1_3, an element of degree 1
  5. c_2_7, a Duflot regular element of degree 2
  6. b_3_10, an element of degree 3
  7. b_3_11, an element of degree 3
  8. b_3_12, an element of degree 3
  9. b_3_13, an element of degree 3
  10. b_3_14, an element of degree 3
  11. b_3_15, an element of degree 3
  12. c_4_26, a Duflot regular element of degree 4
  13. c_4_27, a Duflot regular element of degree 4
  14. b_5_43, an element of degree 5
  15. b_5_44, an element of degree 5

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

Ring relations

There are 57 minimal relations of maximal degree 10:

  1. b_1_1·b_1_2
  2. b_1_2·b_1_3 + b_1_0·b_1_2 + b_1_0·b_1_1
  3. b_1_32 + b_1_0·b_1_2
  4. b_1_02·b_1_1
  5. b_1_0·b_1_1·b_1_3
  6. b_1_1·b_3_10 + c_2_7·b_1_0·b_1_1
  7. b_1_2·b_3_11 + b_1_2·b_3_10 + c_2_7·b_1_0·b_1_1
  8. b_1_3·b_3_10 + b_1_0·b_3_11
  9. b_1_2·b_3_13 + b_1_2·b_3_10 + c_2_7·b_1_0·b_1_2
  10. b_1_3·b_3_11 + b_1_1·b_3_12 + b_1_0·b_3_13 + c_2_7·b_1_0·b_1_2
  11. b_1_3·b_3_14 + b_1_2·b_3_12 + b_1_2·b_3_10 + b_1_1·b_3_12 + b_1_03·b_1_2
  12. b_1_2·b_3_12 + b_1_2·b_3_10 + b_1_0·b_3_14 + b_1_03·b_1_2 + c_2_7·b_1_0·b_1_3
       + c_2_7·b_1_0·b_1_2
  13. b_1_1·b_3_14 + b_1_1·b_3_11
  14. b_1_3·b_3_11 + b_1_2·b_3_15 + b_1_2·b_3_12 + b_1_1·b_3_12 + c_2_7·b_1_0·b_1_2
       + c_2_7·b_1_0·b_1_1
  15. b_1_3·b_3_15 + b_1_3·b_3_13 + b_1_3·b_3_11 + b_1_2·b_3_12 + b_1_2·b_3_10
       + c_2_7·b_1_0·b_1_3 + c_2_7·b_1_0·b_1_2
  16. b_1_3·b_3_12 + b_1_3·b_3_11 + b_1_1·b_3_12 + b_1_0·b_3_15 + c_2_7·b_1_0·b_1_3
       + c_2_7·b_1_0·b_1_2 + c_2_7·b_1_02
  17. b_1_3·b_3_13 + b_1_3·b_3_11 + b_1_1·b_3_15 + b_1_1·b_3_13 + b_1_1·b_3_11
       + c_2_7·b_1_0·b_1_2 + c_2_7·b_1_0·b_1_1
  18. b_1_0·b_1_1·b_3_12
  19. b_3_10·b_3_11 + b_3_102 + c_2_7·b_1_03·b_1_3 + c_2_7·b_1_04 + c_2_72·b_1_0·b_1_3
       + c_2_72·b_1_02
  20. b_3_10·b_3_13 + b_3_102 + c_2_7·b_1_0·b_3_13 + c_2_7·b_1_03·b_1_2 + c_2_7·b_1_04
       + c_2_72·b_1_02
  21. b_3_11·b_3_14 + b_3_112 + b_3_10·b_3_14 + b_3_10·b_3_13 + c_2_7·b_1_0·b_3_11
  22. b_3_13·b_3_14 + b_3_11·b_3_13 + b_3_10·b_3_14 + b_3_102 + c_2_7·b_1_0·b_3_14
       + c_2_7·b_1_0·b_3_11 + c_2_7·b_1_03·b_1_2 + c_2_7·b_1_04 + c_2_72·b_1_0·b_1_3
       + c_2_72·b_1_02
  23. b_3_152 + b_3_14·b_3_15 + b_3_132 + b_3_12·b_3_13 + b_3_11·b_3_13 + b_3_11·b_3_12
       + b_3_10·b_3_15 + b_3_10·b_3_14 + b_1_03·b_3_14 + b_1_03·b_3_13 + b_1_05·b_1_2
       + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_03·b_1_3 + c_2_7·b_1_03·b_1_2 + c_2_72·b_1_0·b_1_3
       + c_2_72·b_1_02
  24. b_3_14·b_3_15 + b_3_13·b_3_14 + b_3_12·b_3_14 + b_3_12·b_3_13 + b_3_112 + b_3_10·b_3_14
       + b_1_03·b_3_13 + c_2_7·b_1_0·b_3_15 + c_2_7·b_1_0·b_3_11 + c_2_7·b_1_03·b_1_2
       + c_2_72·b_1_02
  25. b_3_142 + b_3_112 + b_1_23·b_3_14 + b_1_23·b_3_10 + b_1_03·b_3_13 + b_1_05·b_1_2
       + c_4_26·b_1_22 + c_2_7·b_1_03·b_1_2
  26. b_3_14·b_3_15 + b_3_12·b_3_13 + b_3_11·b_3_13 + b_3_11·b_3_12 + b_3_112 + b_3_10·b_3_15
       + b_3_10·b_3_14 + b_3_102 + b_1_03·b_3_13 + b_1_05·b_1_2 + c_4_26·b_1_0·b_1_2
       + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_03·b_1_2 + c_2_7·b_1_04 + c_2_72·b_1_0·b_1_3
       + c_2_72·b_1_02
  27. b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_132 + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_112
       + b_3_10·b_3_14 + b_3_10·b_3_13 + b_1_13·b_3_15 + b_1_13·b_3_13 + b_1_13·b_3_11
       + c_4_26·b_1_1·b_1_3 + c_2_7·b_1_03·b_1_2
  28. b_3_13·b_3_14 + b_3_12·b_3_13 + b_3_11·b_3_15 + b_3_11·b_3_12 + b_3_112 + b_3_10·b_3_15
       + b_3_10·b_3_14 + b_3_10·b_3_13 + c_4_26·b_1_0·b_1_1 + c_2_7·b_1_0·b_3_11
       + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_03·b_1_2
  29. b_3_132 + b_3_112 + b_1_13·b_3_13 + b_1_13·b_3_12 + b_1_13·b_3_11 + c_4_26·b_1_12
       + c_2_7·b_1_13·b_1_3 + c_2_72·b_1_0·b_1_2
  30. b_3_102 + b_1_23·b_3_10 + b_1_03·b_3_13 + c_4_27·b_1_22 + c_2_7·b_1_03·b_1_2
       + c_2_7·b_1_04 + c_2_72·b_1_02
  31. b_3_122 + b_3_102 + b_1_03·b_3_15 + b_1_03·b_3_14 + b_1_03·b_3_12 + b_1_03·b_3_10
       + c_4_27·b_1_0·b_1_2 + c_4_26·b_1_02 + c_2_72·b_1_02
  32. b_3_14·b_3_15 + b_3_13·b_3_14 + b_3_12·b_3_15 + b_3_12·b_3_14 + b_3_112 + b_3_10·b_3_14
       + b_3_10·b_3_13 + b_3_102 + b_1_13·b_3_15 + b_1_13·b_3_13 + b_1_13·b_3_12
       + b_1_13·b_3_11 + b_1_03·b_3_15 + b_1_03·b_3_11 + b_1_05·b_1_2 + c_4_27·b_1_1·b_1_3
       + c_4_26·b_1_0·b_1_3 + c_2_7·b_1_0·b_3_12 + c_2_7·b_1_0·b_3_11 + c_2_7·b_1_03·b_1_3
       + c_2_72·b_1_0·b_1_3 + c_2_72·b_1_02
  33. b_3_14·b_3_15 + b_3_13·b_3_14 + b_3_12·b_3_15 + b_3_12·b_3_14 + b_3_122 + b_3_11·b_3_12
       + b_3_112 + b_3_10·b_3_15 + b_3_10·b_3_14 + b_3_102 + b_1_03·b_3_14 + b_1_03·b_3_12
       + b_1_03·b_3_11 + b_1_03·b_3_10 + b_1_05·b_1_2 + c_4_27·b_1_0·b_1_1
       + c_4_26·b_1_0·b_1_3 + c_4_26·b_1_02 + c_2_7·b_1_0·b_3_12 + c_2_7·b_1_0·b_3_10
       + c_2_7·b_1_03·b_1_3 + c_2_7·b_1_04 + c_2_72·b_1_0·b_1_3 + c_2_72·b_1_02
  34. b_3_112 + b_3_102 + b_1_13·b_3_15 + b_1_13·b_3_11 + c_4_27·b_1_12
       + c_2_7·b_1_03·b_1_2 + c_2_7·b_1_04 + c_2_72·b_1_0·b_1_2 + c_2_72·b_1_02
  35. b_3_142 + b_3_13·b_3_14 + b_3_11·b_3_13 + b_3_112 + b_1_2·b_5_43 + b_1_23·b_3_10
       + b_1_03·b_3_14 + c_2_7·b_1_2·b_3_10 + c_2_7·b_1_03·b_1_3 + c_2_7·b_1_03·b_1_2
       + c_2_72·b_1_0·b_1_1
  36. b_3_12·b_3_14 + b_3_12·b_3_13 + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_112 + b_3_10·b_3_15
       + b_3_10·b_3_14 + b_3_102 + b_1_3·b_5_43 + b_1_03·b_3_15 + b_1_03·b_3_14
       + b_1_03·b_3_13 + b_1_03·b_3_11 + b_1_05·b_1_2 + c_2_7·b_1_1·b_3_15
       + c_2_7·b_1_1·b_3_13 + c_2_7·b_1_1·b_3_12 + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_0·b_3_11
       + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_03·b_1_3 + c_2_72·b_1_0·b_1_2 + c_2_72·b_1_0·b_1_1
       + c_2_72·b_1_02
  37. b_3_13·b_3_14 + b_3_12·b_3_15 + b_3_12·b_3_14 + b_3_12·b_3_13 + b_3_11·b_3_13
       + b_3_10·b_3_13 + b_3_10·b_3_12 + b_3_102 + b_1_0·b_5_43 + b_1_03·b_3_15
       + b_1_03·b_3_14 + b_1_03·b_3_12 + b_1_03·b_3_10 + c_4_26·b_1_0·b_1_3 + c_2_7·b_1_04
       + c_2_72·b_1_0·b_1_3 + c_2_72·b_1_02
  38. b_1_1·b_5_43 + c_2_7·b_1_1·b_3_13 + c_2_7·b_1_13·b_1_3 + c_2_72·b_1_1·b_1_3
  39. b_3_12·b_3_13 + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_11·b_3_12 + b_3_112 + b_3_10·b_3_15
       + b_3_102 + b_1_2·b_5_44 + b_1_23·b_3_10 + b_1_05·b_1_2 + c_2_7·b_1_2·b_3_14
       + c_2_7·b_1_2·b_3_10 + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_04 + c_2_72·b_1_0·b_1_1
       + c_2_72·b_1_02
  40. b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_132 + b_3_12·b_3_14 + b_3_10·b_3_15 + b_3_10·b_3_13
       + b_1_3·b_5_44 + b_1_13·b_3_15 + b_1_13·b_3_13 + b_1_13·b_3_12 + b_1_13·b_3_11
       + b_1_03·b_3_15 + b_1_03·b_3_14 + b_1_03·b_3_13 + b_1_05·b_1_2 + c_4_26·b_1_0·b_1_3
       + c_2_7·b_1_1·b_3_15 + c_2_7·b_1_1·b_3_13 + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_0·b_3_10
       + c_2_7·b_1_03·b_1_3 + c_2_7·b_1_03·b_1_2 + c_2_7·b_1_04 + c_2_72·b_1_0·b_1_3
       + c_2_72·b_1_0·b_1_1
  41. b_3_12·b_3_13 + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_11·b_3_12 + b_3_112 + b_3_10·b_3_13
       + b_3_10·b_3_12 + b_3_102 + b_1_0·b_5_44 + b_1_03·b_3_15 + b_1_03·b_3_12
       + b_1_05·b_1_2 + c_4_26·b_1_0·b_1_3 + c_4_26·b_1_02 + c_2_7·b_1_0·b_3_12
       + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_04 + c_2_72·b_1_0·b_1_3
  42. b_3_13·b_3_15 + b_3_12·b_3_13 + b_3_11·b_3_12 + b_3_112 + b_3_10·b_3_15 + b_3_10·b_3_13
       + b_1_1·b_5_44 + b_1_13·b_3_13 + b_1_13·b_3_12 + c_2_7·b_1_1·b_3_13
       + c_2_7·b_1_1·b_3_12 + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_13·b_1_3 + c_2_7·b_1_0·b_3_11
       + c_2_7·b_1_0·b_3_10 + c_2_72·b_1_1·b_1_3 + c_2_72·b_1_0·b_1_2
  43. b_3_13·b_5_43 + b_1_25·b_3_10 + c_4_27·b_1_2·b_3_14 + c_4_27·b_1_2·b_3_10
       + c_4_27·b_1_24 + c_4_26·b_1_2·b_3_10 + c_2_7·b_1_23·b_3_10 + c_2_7·b_1_13·b_3_11
       + c_2_7·b_1_03·b_3_14 + c_2_7·b_1_03·b_3_13 + c_2_7·c_4_27·b_1_22
       + c_2_7·c_4_27·b_1_12 + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_12
       + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_72·b_1_1·b_3_15 + c_2_72·b_1_1·b_3_13
       + c_2_72·b_1_1·b_3_12 + c_2_72·b_1_1·b_3_11 + c_2_72·b_1_13·b_1_3
       + c_2_72·b_1_0·b_3_13 + c_2_72·b_1_03·b_1_3 + c_2_73·b_1_0·b_1_1
  44. b_3_15·b_5_43 + b_3_14·b_5_43 + b_3_12·b_5_43 + b_3_10·b_5_43 + b_1_25·b_3_14
       + b_1_25·b_3_10 + b_1_02·b_1_2·b_5_43 + b_1_03·b_5_43 + c_4_27·b_1_0·b_3_14
       + c_4_27·b_1_0·b_3_13 + c_4_26·b_1_2·b_3_14 + c_4_26·b_1_24 + c_4_26·b_1_0·b_3_13
       + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_10 + c_4_26·b_1_03·b_1_3
       + c_4_26·b_1_03·b_1_2 + c_4_26·b_1_04 + c_2_7·b_1_2·b_5_43 + c_2_7·b_1_23·b_3_14
       + c_2_7·b_1_13·b_3_12 + c_2_7·b_1_13·b_3_11 + c_2_7·b_1_03·b_3_15
       + c_2_7·b_1_03·b_3_14 + c_2_7·b_1_03·b_3_13 + c_2_7·b_1_03·b_3_12
       + c_2_7·b_1_03·b_3_10 + c_2_7·b_1_06 + c_2_7·c_4_27·b_1_1·b_1_3
       + c_2_7·c_4_27·b_1_12 + c_2_7·c_4_27·b_1_0·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2
       + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_22 + c_2_7·c_4_26·b_1_1·b_1_3
       + c_2_7·c_4_26·b_1_12 + c_2_7·c_4_26·b_1_0·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_2
       + c_2_7·c_4_26·b_1_02 + c_2_72·b_1_2·b_3_10 + c_2_72·b_1_1·b_3_15
       + c_2_72·b_1_1·b_3_13 + c_2_72·b_1_1·b_3_12 + c_2_72·b_1_1·b_3_11
       + c_2_72·b_1_13·b_1_3 + c_2_72·b_1_0·b_3_15 + c_2_72·b_1_0·b_3_13
       + c_2_72·b_1_0·b_3_11 + c_2_72·b_1_03·b_1_3 + c_2_72·b_1_03·b_1_2
       + c_2_73·b_1_02
  45. b_3_10·b_5_43 + b_1_25·b_3_10 + b_1_02·b_1_2·b_5_43 + b_1_03·b_5_43 + b_1_05·b_3_14
       + b_1_05·b_3_13 + b_1_05·b_3_12 + b_1_05·b_3_11 + b_1_05·b_3_10 + b_1_07·b_1_2
       + c_4_27·b_1_2·b_3_14 + c_4_27·b_1_2·b_3_10 + c_4_27·b_1_24 + c_4_26·b_1_2·b_3_10
       + c_2_7·b_1_23·b_3_10 + c_2_7·b_1_0·b_5_43 + c_2_7·b_1_03·b_3_13
       + c_2_7·b_1_03·b_3_12 + c_2_7·b_1_03·b_3_11 + c_2_7·c_4_27·b_1_22
       + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_72·b_1_0·b_3_11
       + c_2_72·b_1_03·b_1_2 + c_2_73·b_1_0·b_1_3
  46. b_3_15·b_5_43 + b_3_12·b_5_43 + b_3_11·b_5_43 + b_3_10·b_5_43 + b_1_03·b_5_44
       + b_1_05·b_3_15 + b_1_05·b_3_14 + b_1_05·b_3_11 + b_1_05·b_3_10 + c_4_27·b_1_0·b_3_14
       + c_4_27·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_10
       + c_2_7·b_1_13·b_3_12 + c_2_7·b_1_13·b_3_11 + c_2_7·b_1_03·b_3_15
       + c_2_7·b_1_03·b_3_14 + c_2_7·b_1_03·b_3_12 + c_2_7·b_1_03·b_3_11
       + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_12 + c_2_7·c_4_27·b_1_0·b_1_3
       + c_2_7·c_4_27·b_1_0·b_1_2 + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_1·b_1_3
       + c_2_7·c_4_26·b_1_12 + c_2_7·c_4_26·b_1_0·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_1
       + c_2_7·c_4_26·b_1_02 + c_2_72·b_1_1·b_3_15 + c_2_72·b_1_1·b_3_13
       + c_2_72·b_1_1·b_3_12 + c_2_72·b_1_1·b_3_11 + c_2_72·b_1_13·b_1_3
       + c_2_72·b_1_0·b_3_15 + c_2_72·b_1_0·b_3_14 + c_2_72·b_1_0·b_3_11
       + c_2_72·b_1_03·b_1_3 + c_2_72·b_1_04 + c_2_73·b_1_0·b_1_3 + c_2_73·b_1_0·b_1_1
       + c_2_73·b_1_02
  47. b_3_15·b_5_43 + b_3_13·b_5_44 + b_3_12·b_5_44 + b_3_12·b_5_43 + b_1_13·b_5_44
       + b_1_15·b_3_15 + b_1_15·b_3_12 + b_1_03·b_5_43 + b_1_05·b_3_12 + b_1_05·b_3_11
       + b_1_05·b_3_10 + b_1_07·b_1_2 + c_4_27·b_1_1·b_3_15 + c_4_27·b_1_1·b_3_13
       + c_4_27·b_1_1·b_3_12 + c_4_27·b_1_13·b_1_3 + c_4_27·b_1_14 + c_4_27·b_1_0·b_3_13
       + c_4_27·b_1_03·b_1_2 + c_4_26·b_1_1·b_3_15 + c_4_26·b_1_13·b_1_3 + c_4_26·b_1_14
       + c_4_26·b_1_0·b_3_15 + c_4_26·b_1_0·b_3_12 + c_4_26·b_1_03·b_1_2
       + c_2_7·b_1_13·b_3_13 + c_2_7·b_1_13·b_3_11 + c_2_7·b_1_03·b_3_14
       + c_2_7·b_1_03·b_3_13 + c_2_7·b_1_03·b_3_11 + c_2_7·b_1_03·b_3_10 + c_2_7·b_1_06
       + c_2_7·c_4_27·b_1_0·b_1_2 + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_2
       + c_2_7·c_4_26·b_1_02 + c_2_72·b_1_1·b_3_12 + c_2_72·b_1_13·b_1_3
       + c_2_72·b_1_0·b_3_15 + c_2_72·b_1_0·b_3_14 + c_2_72·b_1_0·b_3_13
       + c_2_72·b_1_03·b_1_3 + c_2_72·b_1_04 + c_2_73·b_1_0·b_1_3 + c_2_73·b_1_0·b_1_2
       + c_2_73·b_1_02
  48. b_3_14·b_5_43 + b_3_11·b_5_43 + b_3_10·b_5_44 + b_3_10·b_5_43 + b_1_25·b_3_14
       + c_4_27·b_1_2·b_3_14 + c_4_27·b_1_24 + c_4_26·b_1_2·b_3_14 + c_4_26·b_1_2·b_3_10
       + c_4_26·b_1_24 + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_10 + c_4_26·b_1_03·b_1_2
       + c_2_7·b_1_23·b_3_10 + c_2_7·b_1_03·b_3_15 + c_2_7·b_1_03·b_3_14
       + c_2_7·b_1_03·b_3_11 + c_2_7·b_1_06 + c_2_7·c_4_27·b_1_22
       + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_72·b_1_0·b_3_15 + c_2_72·b_1_0·b_3_10
       + c_2_72·b_1_03·b_1_2 + c_2_72·b_1_04
  49. b_3_15·b_5_43 + b_3_14·b_5_43 + b_3_12·b_5_43 + b_3_11·b_5_44 + b_3_11·b_5_43
       + b_3_10·b_5_43 + b_1_25·b_3_14 + b_1_15·b_3_15 + b_1_15·b_3_12 + b_1_02·b_1_2·b_5_43
       + b_1_03·b_5_43 + b_1_05·b_3_13 + c_4_27·b_1_2·b_3_14 + c_4_27·b_1_24
       + c_4_27·b_1_1·b_3_13 + c_4_27·b_1_0·b_3_14 + c_4_27·b_1_0·b_3_13
       + c_4_27·b_1_03·b_1_2 + c_4_26·b_1_2·b_3_14 + c_4_26·b_1_2·b_3_10 + c_4_26·b_1_24
       + c_4_26·b_1_1·b_3_12 + c_4_26·b_1_1·b_3_11 + c_4_26·b_1_13·b_1_3 + c_4_26·b_1_14
       + c_4_26·b_1_0·b_3_10 + c_4_26·b_1_03·b_1_3 + c_4_26·b_1_03·b_1_2 + c_4_26·b_1_04
       + c_2_7·b_1_23·b_3_10 + c_2_7·b_1_13·b_3_13 + c_2_7·b_1_13·b_3_12
       + c_2_7·b_1_13·b_3_11 + c_2_7·b_1_15·b_1_3 + c_2_7·b_1_03·b_3_15
       + c_2_7·b_1_03·b_3_14 + c_2_7·b_1_03·b_3_13 + c_2_7·b_1_03·b_3_12
       + c_2_7·b_1_03·b_3_10 + c_2_7·b_1_05·b_1_3 + c_2_7·b_1_05·b_1_2 + c_2_7·b_1_06
       + c_2_7·c_4_27·b_1_22 + c_2_7·c_4_27·b_1_0·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2
       + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_12
       + c_2_7·c_4_26·b_1_0·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_02
       + c_2_72·b_1_1·b_3_15 + c_2_72·b_1_1·b_3_13 + c_2_72·b_1_1·b_3_12
       + c_2_72·b_1_1·b_3_11 + c_2_72·b_1_13·b_1_3 + c_2_72·b_1_0·b_3_15
       + c_2_72·b_1_03·b_1_3 + c_2_73·b_1_0·b_1_3 + c_2_73·b_1_0·b_1_2
       + c_2_73·b_1_0·b_1_1 + c_2_73·b_1_02
  50. b_3_14·b_5_44 + b_3_14·b_5_43 + b_1_25·b_3_14 + b_1_15·b_3_15 + b_1_15·b_3_12
       + b_1_02·b_1_2·b_5_43 + b_1_05·b_3_14 + b_1_07·b_1_2 + c_4_27·b_1_2·b_3_10
       + c_4_27·b_1_24 + c_4_27·b_1_1·b_3_13 + c_4_26·b_1_2·b_3_14 + c_4_26·b_1_2·b_3_10
       + c_4_26·b_1_24 + c_4_26·b_1_1·b_3_12 + c_4_26·b_1_1·b_3_11 + c_4_26·b_1_13·b_1_3
       + c_4_26·b_1_14 + c_2_7·b_1_23·b_3_14 + c_2_7·b_1_13·b_3_13 + c_2_7·b_1_15·b_1_3
       + c_2_7·b_1_03·b_3_14 + c_2_7·b_1_03·b_3_11 + c_2_7·b_1_05·b_1_3
       + c_2_7·b_1_05·b_1_2 + c_2_7·c_4_27·b_1_22 + c_2_7·c_4_27·b_1_1·b_1_3
       + c_2_7·c_4_27·b_1_12 + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_22
       + c_2_7·c_4_26·b_1_0·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_7·c_4_26·b_1_0·b_1_1
       + c_2_72·b_1_0·b_3_14 + c_2_72·b_1_0·b_3_11 + c_2_72·b_1_03·b_1_3
       + c_2_72·b_1_03·b_1_2 + c_2_73·b_1_0·b_1_2
  51. b_3_15·b_5_44 + b_3_15·b_5_43 + b_3_12·b_5_44 + b_3_12·b_5_43 + b_3_11·b_5_43
       + b_3_10·b_5_43 + b_1_12·b_1_3·b_5_44 + b_1_13·b_5_44 + b_1_05·b_3_15 + b_1_05·b_3_14
       + b_1_05·b_3_13 + b_1_05·b_3_11 + b_1_07·b_1_2 + c_4_27·b_1_1·b_3_13
       + c_4_27·b_1_1·b_3_12 + c_4_27·b_1_1·b_3_11 + c_4_27·b_1_14 + c_4_27·b_1_0·b_3_14
       + c_4_26·b_1_1·b_3_13 + c_4_26·b_1_0·b_3_14 + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_12
       + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_03·b_1_3 + c_2_7·b_1_13·b_3_11
       + c_2_7·b_1_15·b_1_3 + c_2_7·b_1_03·b_3_15 + c_2_7·b_1_03·b_3_14
       + c_2_7·b_1_03·b_3_12 + c_2_7·b_1_03·b_3_11 + c_2_7·b_1_05·b_1_3
       + c_2_7·b_1_05·b_1_2 + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_12
       + c_2_7·c_4_27·b_1_0·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2 + c_2_7·c_4_27·b_1_0·b_1_1
       + c_2_7·c_4_26·b_1_0·b_1_3 + c_2_7·c_4_26·b_1_02 + c_2_72·b_1_1·b_3_12
       + c_2_72·b_1_13·b_1_3 + c_2_72·b_1_0·b_3_13 + c_2_72·b_1_0·b_3_11
       + c_2_72·b_1_0·b_3_10 + c_2_72·b_1_03·b_1_2 + c_2_73·b_1_0·b_1_3 + c_2_73·b_1_02
  52. b_3_15·b_5_43 + b_3_14·b_5_43 + b_3_12·b_5_44 + b_3_12·b_5_43 + b_1_25·b_3_14
       + b_1_15·b_3_15 + b_1_15·b_3_13 + b_1_15·b_3_11 + b_1_03·b_5_43 + b_1_05·b_3_12
       + b_1_05·b_3_11 + b_1_05·b_3_10 + b_1_07·b_1_2 + c_4_27·b_1_2·b_3_14 + c_4_27·b_1_24
       + c_4_27·b_1_1·b_3_15 + c_4_27·b_1_1·b_3_13 + c_4_27·b_1_1·b_3_12 + c_4_27·b_1_1·b_3_11
       + c_4_27·b_1_0·b_3_13 + c_4_27·b_1_03·b_1_2 + c_4_26·b_1_2·b_3_14
       + c_4_26·b_1_2·b_3_10 + c_4_26·b_1_24 + c_4_26·b_1_1·b_3_12 + c_4_26·b_1_13·b_1_3
       + c_4_26·b_1_0·b_3_15 + c_4_26·b_1_0·b_3_12 + c_2_7·b_1_3·b_5_44 + c_2_7·b_1_23·b_3_10
       + c_2_7·b_1_13·b_3_15 + c_2_7·b_1_13·b_3_13 + c_2_7·b_1_13·b_3_12
       + c_2_7·b_1_03·b_3_14 + c_2_7·b_1_03·b_3_13 + c_2_7·b_1_03·b_3_10 + c_2_7·b_1_06
       + c_2_7·c_4_27·b_1_22 + c_2_7·c_4_27·b_1_12 + c_2_7·c_4_27·b_1_0·b_1_2
       + c_2_7·c_4_26·b_1_12 + c_2_7·c_4_26·b_1_0·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_2
       + c_2_7·c_4_26·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_02 + c_2_72·b_1_1·b_3_12
       + c_2_72·b_1_13·b_1_3 + c_2_72·b_1_0·b_3_15 + c_2_72·b_1_0·b_3_13
       + c_2_72·b_1_0·b_3_11 + c_2_72·b_1_03·b_1_3 + c_2_72·b_1_04 + c_2_73·b_1_0·b_1_3
       + c_2_73·b_1_02
  53. b_3_15·b_5_43 + b_3_14·b_5_43 + b_3_12·b_5_44 + b_3_10·b_5_43 + b_1_25·b_3_14
       + b_1_15·b_3_15 + b_1_15·b_3_13 + b_1_15·b_3_11 + b_1_05·b_3_15 + b_1_05·b_3_12
       + b_1_05·b_3_10 + c_4_27·b_1_2·b_3_14 + c_4_27·b_1_24 + c_4_27·b_1_1·b_3_15
       + c_4_27·b_1_1·b_3_13 + c_4_27·b_1_1·b_3_12 + c_4_27·b_1_1·b_3_11 + c_4_27·b_1_0·b_3_14
       + c_4_27·b_1_03·b_1_2 + c_4_26·b_1_2·b_3_14 + c_4_26·b_1_2·b_3_10 + c_4_26·b_1_24
       + c_4_26·b_1_1·b_3_12 + c_4_26·b_1_13·b_1_3 + c_4_26·b_1_0·b_3_15
       + c_4_26·b_1_0·b_3_14 + c_4_26·b_1_0·b_3_12 + c_4_26·b_1_0·b_3_10
       + c_4_26·b_1_03·b_1_2 + c_4_26·b_1_04 + c_2_7·b_1_23·b_3_10 + c_2_7·b_1_13·b_3_15
       + c_2_7·b_1_13·b_3_13 + c_2_7·b_1_0·b_5_44 + c_2_7·b_1_03·b_3_15
       + c_2_7·b_1_03·b_3_14 + c_2_7·b_1_03·b_3_13 + c_2_7·b_1_03·b_3_12
       + c_2_7·b_1_03·b_3_10 + c_2_7·b_1_06 + c_2_7·c_4_27·b_1_22 + c_2_7·c_4_27·b_1_12
       + c_2_7·c_4_27·b_1_0·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_1·b_1_3
       + c_2_7·c_4_26·b_1_12 + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_7·c_4_26·b_1_0·b_1_1
       + c_2_7·c_4_26·b_1_02 + c_2_72·b_1_1·b_3_15 + c_2_72·b_1_1·b_3_13
       + c_2_72·b_1_1·b_3_12 + c_2_72·b_1_1·b_3_11 + c_2_72·b_1_13·b_1_3
       + c_2_72·b_1_0·b_3_15 + c_2_72·b_1_0·b_3_14 + c_2_72·b_1_0·b_3_10
       + c_2_72·b_1_03·b_1_2 + c_2_72·b_1_04 + c_2_73·b_1_0·b_1_1
  54. b_3_14·b_5_43 + b_3_12·b_5_44 + b_3_12·b_5_43 + b_3_10·b_5_43 + b_1_25·b_3_14
       + b_1_15·b_3_15 + b_1_15·b_3_13 + b_1_15·b_3_11 + b_1_05·b_3_15 + b_1_05·b_3_14
       + b_1_05·b_3_11 + b_1_07·b_1_2 + c_4_27·b_1_2·b_3_14 + c_4_27·b_1_24
       + c_4_27·b_1_1·b_3_15 + c_4_27·b_1_1·b_3_13 + c_4_27·b_1_1·b_3_12 + c_4_27·b_1_1·b_3_11
       + c_4_27·b_1_0·b_3_13 + c_4_26·b_1_2·b_3_14 + c_4_26·b_1_2·b_3_10 + c_4_26·b_1_24
       + c_4_26·b_1_1·b_3_12 + c_4_26·b_1_13·b_1_3 + c_4_26·b_1_0·b_3_15
       + c_4_26·b_1_0·b_3_14 + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_12 + c_4_26·b_1_0·b_3_11
       + c_4_26·b_1_03·b_1_3 + c_4_26·b_1_03·b_1_2 + c_2_7·b_1_23·b_3_10
       + c_2_7·b_1_1·b_5_44 + c_2_7·b_1_13·b_3_11 + c_2_7·b_1_03·b_3_14
       + c_2_7·b_1_03·b_3_13 + c_2_7·b_1_03·b_3_12 + c_2_7·b_1_03·b_3_11
       + c_2_7·b_1_03·b_3_10 + c_2_7·b_1_05·b_1_2 + c_2_7·c_4_27·b_1_22
       + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_1·b_1_3
       + c_2_7·c_4_26·b_1_12 + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_7·c_4_26·b_1_0·b_1_1
       + c_2_7·c_4_26·b_1_02 + c_2_72·b_1_1·b_3_13 + c_2_72·b_1_1·b_3_11
       + c_2_72·b_1_0·b_3_15 + c_2_72·b_1_0·b_3_14 + c_2_72·b_1_0·b_3_13
       + c_2_72·b_1_0·b_3_11 + c_2_72·b_1_03·b_1_2 + c_2_72·b_1_04 + c_2_73·b_1_1·b_1_3
       + c_2_73·b_1_0·b_1_2 + c_2_73·b_1_02
  55. b_5_432 + b_1_25·b_5_43 + b_1_04·b_1_2·b_5_43 + b_1_07·b_3_15 + b_1_07·b_3_12
       + b_1_07·b_3_10 + b_1_09·b_1_2 + c_4_27·b_1_23·b_3_14 + c_4_27·b_1_23·b_3_10
       + c_4_27·b_1_26 + c_4_27·b_1_03·b_3_13 + c_4_27·b_1_05·b_1_2
       + c_4_26·b_1_23·b_3_10 + c_4_26·b_1_03·b_3_13 + c_4_26·b_1_05·b_1_2
       + c_4_26·b_1_06 + c_2_7·b_1_25·b_3_10 + c_2_7·b_1_05·b_3_15 + c_2_7·b_1_05·b_3_14
       + c_2_7·b_1_05·b_3_13 + c_2_7·b_1_05·b_3_12 + c_2_7·b_1_05·b_3_10
       + c_2_7·b_1_07·b_1_3 + c_4_26·c_4_27·b_1_22 + c_4_262·b_1_22
       + c_2_7·c_4_27·b_1_03·b_1_2 + c_2_7·c_4_26·b_1_03·b_1_2 + c_2_7·c_4_26·b_1_04
       + c_2_72·b_1_23·b_3_10 + c_2_72·b_1_13·b_3_15 + c_2_72·b_1_13·b_3_13
       + c_2_72·b_1_13·b_3_12 + c_2_72·b_1_03·b_3_13 + c_2_72·b_1_06
       + c_2_72·c_4_27·b_1_22 + c_2_72·c_4_27·b_1_12 + c_2_72·c_4_26·b_1_12
       + c_2_73·b_1_13·b_1_3 + c_2_74·b_1_0·b_1_2
  56. b_5_442 + b_1_14·b_1_3·b_5_44 + b_1_15·b_5_44 + b_1_17·b_3_15 + b_1_17·b_3_12
       + b_1_07·b_3_15 + b_1_07·b_3_12 + b_1_07·b_3_10 + b_1_09·b_1_2
       + c_4_27·b_1_13·b_3_13 + c_4_27·b_1_13·b_3_12 + c_4_27·b_1_13·b_3_11
       + c_4_27·b_1_16 + c_4_27·b_1_05·b_1_2 + c_4_26·b_1_13·b_3_15
       + c_4_26·b_1_13·b_3_11 + c_4_26·b_1_15·b_1_3 + c_4_26·b_1_16 + c_4_26·b_1_05·b_1_2
       + c_4_26·b_1_06 + c_2_7·b_1_15·b_3_13 + c_2_7·b_1_15·b_3_11 + c_2_7·b_1_05·b_3_15
       + c_2_7·b_1_05·b_3_12 + c_2_7·b_1_05·b_3_10 + c_2_7·b_1_07·b_1_3 + c_2_7·b_1_08
       + c_4_272·b_1_22 + c_4_272·b_1_12 + c_4_26·c_4_27·b_1_12 + c_4_262·b_1_12
       + c_4_262·b_1_0·b_1_2 + c_4_262·b_1_02 + c_2_7·c_4_27·b_1_13·b_1_3
       + c_2_7·c_4_26·b_1_03·b_1_2 + c_2_7·c_4_26·b_1_04 + c_2_72·b_1_23·b_3_14
       + c_2_72·b_1_23·b_3_10 + c_2_72·b_1_13·b_3_13 + c_2_72·b_1_13·b_3_12
       + c_2_72·b_1_13·b_3_11 + c_2_72·b_1_15·b_1_3 + c_2_72·b_1_03·b_3_14
       + c_2_72·b_1_03·b_3_13 + c_2_72·b_1_05·b_1_3 + c_2_72·c_4_26·b_1_22
       + c_2_72·c_4_26·b_1_12 + c_2_72·c_4_26·b_1_0·b_1_2 + c_2_73·b_1_13·b_1_3
       + c_2_73·b_1_03·b_1_3 + c_2_73·b_1_03·b_1_2 + c_2_73·b_1_04
  57. b_5_43·b_5_44 + b_1_05·b_5_43 + b_1_07·b_3_13 + c_4_27·b_1_2·b_5_43
       + c_4_27·b_1_03·b_3_14 + c_4_27·b_1_03·b_3_13 + c_4_27·b_1_05·b_1_2
       + c_4_26·b_1_0·b_5_44 + c_4_26·b_1_03·b_3_13 + c_4_26·b_1_03·b_3_10
       + c_4_26·b_1_05·b_1_3 + c_4_26·b_1_05·b_1_2 + c_4_26·b_1_06 + c_2_7·b_1_25·b_3_14
       + c_2_7·b_1_25·b_3_10 + c_2_7·b_1_12·b_1_3·b_5_44 + c_2_7·b_1_13·b_5_44
       + c_2_7·b_1_15·b_3_13 + c_2_7·b_1_15·b_3_12 + c_2_7·b_1_15·b_3_11
       + c_2_7·b_1_02·b_1_2·b_5_43 + c_2_7·b_1_03·b_5_44 + c_2_7·b_1_03·b_5_43
       + c_2_7·b_1_05·b_3_14 + c_2_7·b_1_05·b_3_13 + c_2_7·b_1_05·b_3_12
       + c_2_7·b_1_05·b_3_11 + c_2_7·b_1_05·b_3_10 + c_2_7·b_1_08
       + c_4_26·c_4_27·b_1_0·b_1_2 + c_4_26·c_4_27·b_1_0·b_1_1 + c_4_262·b_1_0·b_1_3
       + c_4_262·b_1_02 + c_2_7·c_4_27·b_1_1·b_3_11 + c_2_7·c_4_27·b_1_13·b_1_3
       + c_2_7·c_4_27·b_1_14 + c_2_7·c_4_27·b_1_03·b_1_3 + c_2_7·c_4_26·b_1_2·b_3_14
       + c_2_7·c_4_26·b_1_24 + c_2_7·c_4_26·b_1_1·b_3_15 + c_2_7·c_4_26·b_1_1·b_3_12
       + c_2_7·c_4_26·b_1_14 + c_2_7·c_4_26·b_1_0·b_3_15 + c_2_7·c_4_26·b_1_0·b_3_13
       + c_2_7·c_4_26·b_1_0·b_3_10 + c_2_7·c_4_26·b_1_03·b_1_3 + c_2_72·b_1_2·b_5_43
       + c_2_72·b_1_23·b_3_14 + c_2_72·b_1_1·b_5_44 + c_2_72·b_1_13·b_3_13
       + c_2_72·b_1_13·b_3_11 + c_2_72·b_1_0·b_5_44 + c_2_72·b_1_0·b_5_43
       + c_2_72·b_1_03·b_3_13 + c_2_72·b_1_03·b_3_12 + c_2_72·b_1_05·b_1_3
       + c_2_72·b_1_05·b_1_2 + c_2_72·c_4_27·b_1_12 + c_2_72·c_4_27·b_1_0·b_1_2
       + c_2_72·c_4_27·b_1_0·b_1_1 + c_2_72·c_4_26·b_1_22 + c_2_72·c_4_26·b_1_0·b_1_3
       + c_2_72·c_4_26·b_1_0·b_1_2 + c_2_72·c_4_26·b_1_02 + c_2_73·b_1_2·b_3_10
       + c_2_73·b_1_1·b_3_13 + c_2_73·b_1_1·b_3_11 + c_2_73·b_1_0·b_3_15
       + c_2_73·b_1_0·b_3_14 + c_2_73·b_1_0·b_3_10 + c_2_73·b_1_03·b_1_2
       + c_2_73·b_1_04 + c_2_74·b_1_1·b_1_3 + c_2_74·b_1_0·b_1_3 + c_2_74·b_1_0·b_1_1

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 10.
  • 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_2_7, a Duflot regular element of degree 2
    2. c_4_26, a Duflot regular element of degree 4
    3. c_4_27, a Duflot regular element of degree 4
    4. b_1_32 + b_1_22 + b_1_12 + b_1_02, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 5, 8].
  • 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. b_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. c_2_7 → c_1_22, an element of degree 2
  6. b_3_10 → 0, an element of degree 3
  7. b_3_11 → 0, an element of degree 3
  8. b_3_12 → 0, an element of degree 3
  9. b_3_13 → 0, an element of degree 3
  10. b_3_14 → 0, an element of degree 3
  11. b_3_15 → 0, an element of degree 3
  12. c_4_26 → c_1_14 + c_1_04, an element of degree 4
  13. c_4_27 → c_1_04, an element of degree 4
  14. b_5_43 → 0, an element of degree 5
  15. b_5_44 → 0, an element of degree 5

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

  1. b_1_0 → c_1_3, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. c_2_7 → c_1_22, an element of degree 2
  6. b_3_10 → c_1_2·c_1_32 + c_1_22·c_1_3, an element of degree 3
  7. b_3_11 → 0, an element of degree 3
  8. b_3_12 → c_1_2·c_1_32 + c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  9. b_3_13 → 0, an element of degree 3
  10. b_3_14 → 0, an element of degree 3
  11. b_3_15 → c_1_22·c_1_3, an element of degree 3
  12. c_4_26 → c_1_1·c_1_33 + c_1_14 + c_1_0·c_1_33 + c_1_04, an element of degree 4
  13. c_4_27 → c_1_2·c_1_33 + c_1_02·c_1_32 + c_1_04, an element of degree 4
  14. b_5_43 → c_1_22·c_1_33 + c_1_1·c_1_34 + c_1_1·c_1_2·c_1_33 + c_1_12·c_1_33
       + c_1_12·c_1_2·c_1_32 + c_1_0·c_1_34 + c_1_0·c_1_2·c_1_33 + c_1_02·c_1_33
       + c_1_02·c_1_2·c_1_32, an element of degree 5
  15. b_5_44 → c_1_2·c_1_34 + c_1_23·c_1_32 + c_1_1·c_1_2·c_1_33 + c_1_12·c_1_33
       + c_1_12·c_1_2·c_1_32 + c_1_14·c_1_3 + c_1_0·c_1_2·c_1_33 + c_1_02·c_1_33
       + c_1_02·c_1_2·c_1_32 + c_1_04·c_1_3, an element of degree 5

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

  1. b_1_0 → 0, an element of degree 1
  2. b_1_1 → c_1_3, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. c_2_7 → c_1_2·c_1_3 + c_1_22, an element of degree 2
  6. b_3_10 → 0, an element of degree 3
  7. b_3_11 → c_1_1·c_1_32 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  8. b_3_12 → 0, an element of degree 3
  9. b_3_13 → c_1_12·c_1_3, an element of degree 3
  10. b_3_14 → c_1_1·c_1_32 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  11. b_3_15 → c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  12. c_4_26 → c_1_1·c_1_33 + c_1_14 + c_1_0·c_1_33 + c_1_04, an element of degree 4
  13. c_4_27 → c_1_02·c_1_32 + c_1_04, an element of degree 4
  14. b_5_43 → c_1_12·c_1_2·c_1_32 + c_1_12·c_1_22·c_1_3, an element of degree 5
  15. b_5_44 → c_1_1·c_1_2·c_1_33 + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_2·c_1_32
       + c_1_12·c_1_22·c_1_3 + c_1_13·c_1_32 + c_1_14·c_1_3 + c_1_0·c_1_2·c_1_33
       + c_1_0·c_1_22·c_1_32 + c_1_0·c_1_12·c_1_32 + c_1_02·c_1_33
       + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3 + c_1_02·c_1_12·c_1_3
       + c_1_04·c_1_3, an element of degree 5

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

  1. b_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → c_1_3, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. c_2_7 → c_1_2·c_1_3 + c_1_22, an element of degree 2
  6. b_3_10 → c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  7. b_3_11 → c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  8. b_3_12 → c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  9. b_3_13 → c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  10. b_3_14 → c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  11. b_3_15 → c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  12. c_4_26 → c_1_1·c_1_33 + c_1_14 + c_1_0·c_1_33 + c_1_04, an element of degree 4
  13. c_4_27 → c_1_0·c_1_33 + c_1_04, an element of degree 4
  14. b_5_43 → c_1_12·c_1_33 + c_1_14·c_1_3 + c_1_0·c_1_34 + c_1_0·c_1_2·c_1_33
       + c_1_0·c_1_22·c_1_32 + c_1_0·c_1_1·c_1_33 + c_1_0·c_1_12·c_1_32
       + c_1_02·c_1_33 + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3
       + c_1_02·c_1_1·c_1_32 + c_1_02·c_1_12·c_1_3, an element of degree 5
  15. b_5_44 → c_1_1·c_1_2·c_1_33 + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_2·c_1_32
       + c_1_12·c_1_22·c_1_3 + c_1_0·c_1_34 + c_1_0·c_1_2·c_1_33
       + c_1_0·c_1_22·c_1_32 + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3
       + c_1_04·c_1_3, an element of degree 5

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

  1. b_1_0 → c_1_3, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → c_1_3, an element of degree 1
  4. b_1_3 → c_1_3, an element of degree 1
  5. c_2_7 → c_1_2·c_1_3 + c_1_22, an element of degree 2
  6. b_3_10 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  7. b_3_11 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  8. b_3_12 → c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  9. b_3_13 → c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  10. b_3_14 → c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  11. b_3_15 → c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  12. c_4_26 → c_1_34 + c_1_2·c_1_33 + c_1_22·c_1_32 + c_1_1·c_1_33 + c_1_14
       + c_1_02·c_1_32 + c_1_04, an element of degree 4
  13. c_4_27 → c_1_2·c_1_33 + c_1_22·c_1_32 + c_1_02·c_1_32 + c_1_04, an element of degree 4
  14. b_5_43 → c_1_22·c_1_33 + c_1_24·c_1_3 + c_1_1·c_1_34 + c_1_14·c_1_3 + c_1_0·c_1_2·c_1_33
       + c_1_0·c_1_22·c_1_32 + c_1_0·c_1_1·c_1_33 + c_1_0·c_1_12·c_1_32
       + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3 + c_1_02·c_1_1·c_1_32
       + c_1_02·c_1_12·c_1_3, an element of degree 5
  15. b_5_44 → c_1_35 + c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_0·c_1_34 + c_1_04·c_1_3, an element of degree 5

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