Cohomology of group number 6665 of order 256

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 256

General information on the group

  • The group is also known as Syl2(Ly), the Sylow 2-group of 2A_11 and of Ly.
  • The group has 3 minimal generators and exponent 8.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 1.
  • It has 4 conjugacy classes of maximal elementary abelian subgroups, which are of rank 3, 3, 3 and 4, respectively.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 2.
  • The depth exceeds the Duflot bound, which is 1.
  • The Poincaré series is
    ( − 1) · (t9  −  t8  −  t2  −  1)
    (t  +  1) · (t  −  1)4 · (t2  +  1)2 · (t4  +  1)
  • The a-invariants are -∞,-∞,-5,-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 256

Ring generators

The cohomology ring has 15 minimal generators of maximal degree 8:

  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. a_2_4, a nilpotent element of degree 2
  5. b_2_5, an element of degree 2
  6. b_3_8, an element of degree 3
  7. b_3_9, an element of degree 3
  8. b_4_12, an element of degree 4
  9. b_4_14, an element of degree 4
  10. b_5_19, an element of degree 5
  11. b_5_20, an element of degree 5
  12. b_6_27, an element of degree 6
  13. b_7_35, an element of degree 7
  14. b_8_44, an element of degree 8
  15. c_8_46, a Duflot regular element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 256

Ring relations

There are 65 minimal relations of maximal degree 16:

  1. b_1_0·b_1_1
  2. b_1_0·b_1_2
  3. a_2_4·b_1_2
  4. a_2_4·b_1_0
  5. b_2_5·b_1_1
  6. a_2_4·b_2_5
  7. b_1_0·b_3_8
  8. b_1_2·b_3_8 + b_1_1·b_3_8 + a_2_4·b_1_12
  9. b_1_2·b_3_9 + b_1_2·b_3_8
  10. b_1_2·b_3_8 + b_1_1·b_3_9 + a_2_42
  11. b_2_5·b_3_8
  12. a_2_4·b_3_8 + a_2_42·b_1_1
  13. a_2_4·b_3_9
  14. b_4_12·b_1_2
  15. b_4_12·b_1_1
  16. b_4_14·b_1_2 + b_4_14·b_1_1 + a_2_42·b_1_1
  17. b_3_8·b_3_9 + b_3_82 + a_2_42·b_1_12
  18. a_2_4·b_4_12
  19. b_3_82 + b_4_14·b_1_12
  20. b_1_2·b_5_19 + b_1_13·b_3_8 + a_2_4·b_1_14
  21. b_3_92 + b_3_82 + b_1_0·b_5_19 + b_1_03·b_3_9 + b_4_14·b_1_02 + b_2_5·b_1_0·b_3_9
       + b_2_5·b_4_14 + a_2_4·b_4_14 + a_2_42·b_1_12
  22. b_1_1·b_5_19 + b_1_13·b_3_8
  23. b_3_92 + b_3_82 + b_1_0·b_5_20 + b_2_5·b_1_0·b_3_9 + b_2_5·b_4_14 + a_2_4·b_4_14
       + a_2_42·b_1_12
  24. b_4_12·b_3_8
  25. a_2_4·b_5_19 + a_2_42·b_1_13
  26. a_2_4·b_5_20 + a_2_42·b_1_13
  27. b_6_27·b_1_2 + b_4_14·b_1_13 + b_2_5·b_5_20 + b_2_5·b_5_19 + b_2_5·b_1_02·b_3_9
       + b_2_5·b_4_14·b_1_0 + a_2_42·b_1_13
  28. b_6_27·b_1_0 + b_4_14·b_1_03 + b_4_12·b_3_9 + b_4_12·b_1_03 + b_2_5·b_5_19
       + b_2_5·b_1_02·b_3_9
  29. b_6_27·b_1_1 + b_4_14·b_1_13 + a_2_4·b_1_15 + a_2_42·b_1_13
  30. b_4_14·b_1_04 + b_4_122 + b_2_5·b_4_12·b_1_02 + b_2_52·b_1_0·b_3_9
       + b_2_52·b_4_14
  31. b_3_8·b_5_19 + b_4_14·b_1_14
  32. b_3_9·b_5_20 + b_3_9·b_5_19 + b_3_8·b_5_20 + b_1_03·b_5_19 + b_1_05·b_3_9
       + b_4_14·b_1_14 + b_4_14·b_1_0·b_3_9 + b_4_14·b_1_04 + b_2_5·b_1_03·b_3_9
       + b_2_5·b_4_14·b_1_02
  33. a_2_4·b_6_27 + a_2_42·b_1_14
  34. b_3_8·b_5_20 + b_1_2·b_7_35 + b_1_23·b_5_20 + b_1_12·b_1_2·b_5_20 + b_1_15·b_3_8
       + b_4_14·b_1_1·b_3_8 + a_2_4·b_1_16 + a_2_42·b_1_14
  35. b_1_0·b_7_35 + b_1_03·b_5_19 + b_4_14·b_1_0·b_3_9 + b_4_14·b_1_04
       + b_4_12·b_1_0·b_3_9 + b_2_5·b_1_0·b_5_19 + b_2_5·b_1_03·b_3_9 + b_2_5·b_4_14·b_1_02
       + b_2_5·b_4_12·b_1_02 + b_2_52·b_1_0·b_3_9
  36. b_3_8·b_5_20 + b_1_1·b_7_35 + b_1_1·b_1_22·b_5_20 + b_1_13·b_5_20 + b_1_15·b_3_8
       + b_4_14·b_1_1·b_3_8 + a_2_4·b_1_16 + a_2_42·b_1_14
  37. b_4_12·b_5_20 + b_4_12·b_5_19 + b_4_12·b_1_02·b_3_9 + b_4_12·b_4_14·b_1_0
  38. b_6_27·b_3_8 + b_4_14·b_1_12·b_3_8 + a_2_42·b_1_15
  39. b_2_5·b_7_35 + b_2_5·b_1_22·b_5_20 + b_2_5·b_1_02·b_5_19 + b_2_5·b_4_14·b_3_9
       + b_2_5·b_4_14·b_1_03 + b_2_5·b_4_12·b_3_9 + b_2_52·b_5_19 + b_2_52·b_1_02·b_3_9
       + b_2_52·b_4_14·b_1_0 + b_2_52·b_4_12·b_1_0 + b_2_53·b_3_9
  40. a_2_4·b_7_35 + a_2_42·b_1_15
  41. b_1_24·b_5_20 + b_1_1·b_1_23·b_5_20 + b_1_12·b_1_22·b_5_20 + b_1_13·b_1_2·b_5_20
       + b_1_16·b_3_8 + b_8_44·b_1_2 + b_4_14·b_1_15 + a_2_4·b_1_17 + a_2_42·b_1_15
  42. b_1_0·b_3_9·b_5_19 + b_1_06·b_3_9 + b_8_44·b_1_0 + b_4_12·b_5_19 + b_4_12·b_1_02·b_3_9
       + b_4_12·b_1_05 + b_2_5·b_1_04·b_3_9 + b_2_5·b_4_14·b_3_9 + b_2_5·b_4_12·b_1_03
       + b_2_52·b_4_14·b_1_0
  43. b_1_1·b_1_23·b_5_20 + b_1_12·b_1_22·b_5_20 + b_1_13·b_1_2·b_5_20 + b_1_14·b_5_20
       + b_1_16·b_3_8 + b_8_44·b_1_1 + b_4_14·b_1_15 + a_2_4·b_1_17 + a_2_42·b_1_15
  44. b_3_8·b_7_35 + b_4_14·b_1_1·b_5_20 + b_4_14·b_1_16 + b_4_142·b_1_12
  45. b_5_19·b_5_20 + b_5_192 + b_3_9·b_7_35 + b_1_13·b_7_35 + b_1_13·b_1_22·b_5_20
       + b_1_15·b_5_20 + b_1_17·b_3_8 + b_4_14·b_1_1·b_5_20 + b_4_14·b_1_13·b_3_8
       + b_4_142·b_1_12 + b_4_142·b_1_02 + b_4_12·b_1_0·b_5_19 + b_4_12·b_1_03·b_3_9
       + b_4_12·b_4_14·b_1_02 + b_2_5·b_3_9·b_5_19 + b_2_5·b_1_03·b_5_19
       + b_2_5·b_1_05·b_3_9 + b_2_5·b_4_142 + b_2_5·b_4_12·b_4_14 + b_2_5·b_4_122
       + b_2_52·b_1_0·b_5_19 + b_2_52·b_4_12·b_1_02 + a_2_4·b_1_18 + a_2_4·b_4_142
  46. b_5_192 + b_4_14·b_1_16 + b_4_14·b_1_0·b_5_19 + b_4_12·b_1_0·b_5_19
       + b_4_12·b_1_03·b_3_9 + b_4_12·b_1_06 + b_2_5·b_4_14·b_1_0·b_3_9 + b_2_5·b_4_142
       + b_2_5·b_4_12·b_1_0·b_3_9 + b_2_52·b_1_0·b_5_19 + b_2_52·b_1_03·b_3_9
       + a_2_4·b_4_142 + c_8_46·b_1_02
  47. b_4_14·b_1_03·b_3_9 + b_4_12·b_6_27 + b_4_12·b_4_14·b_1_02 + b_4_122·b_1_02
       + b_2_5·b_3_9·b_5_19 + b_2_5·b_1_23·b_5_20 + b_2_5·b_1_05·b_3_9 + b_2_5·b_8_44
       + b_2_5·b_4_12·b_1_0·b_3_9 + b_2_5·b_4_12·b_1_04 + b_2_52·b_1_0·b_5_19
       + b_2_52·b_4_14·b_1_02 + b_2_52·b_4_12·b_1_02 + b_2_53·b_1_0·b_3_9
  48. b_5_202 + b_5_192 + b_1_13·b_1_22·b_5_20 + b_1_14·b_1_2·b_5_20 + b_1_17·b_3_8
       + b_1_05·b_5_19 + b_1_07·b_3_9 + b_8_44·b_1_1·b_1_2 + b_4_14·b_1_16
       + b_4_142·b_1_12 + b_4_142·b_1_02 + b_4_122·b_1_02 + b_2_5·b_1_23·b_5_20
       + b_2_5·b_1_05·b_3_9 + b_2_5·b_4_12·b_1_04 + b_2_5·b_4_122 + b_2_52·b_1_2·b_5_20
       + b_2_52·b_1_03·b_3_9 + b_2_52·b_4_14·b_1_02 + b_2_52·b_4_12·b_1_02
       + b_2_53·b_1_0·b_3_9 + b_2_53·b_4_14 + a_2_4·b_1_18 + a_2_42·b_1_16
       + c_8_46·b_1_22
  49. a_2_4·b_8_44 + a_2_42·b_1_16
  50. b_5_19·b_5_20 + b_5_192 + b_1_13·b_7_35 + b_1_13·b_1_22·b_5_20 + b_1_15·b_5_20
       + b_1_17·b_3_8 + b_1_07·b_3_9 + b_8_44·b_1_02 + b_4_14·b_1_13·b_3_8
       + b_4_14·b_1_16 + b_4_14·b_1_0·b_5_19 + b_4_12·b_1_0·b_5_19 + b_4_12·b_1_03·b_3_9
       + b_4_12·b_1_06 + b_2_5·b_1_05·b_3_9 + b_2_5·b_4_14·b_1_0·b_3_9
       + b_2_5·b_4_12·b_1_04 + b_2_52·b_4_14·b_1_02 + a_2_4·b_1_18 + a_2_42·b_1_16
  51. b_4_12·b_7_35 + b_4_12·b_1_02·b_5_19 + b_4_12·b_4_14·b_3_9 + b_4_12·b_4_14·b_1_03
       + b_4_122·b_3_9 + b_2_5·b_4_12·b_5_19 + b_2_5·b_4_12·b_1_02·b_3_9
       + b_2_5·b_4_12·b_4_14·b_1_0 + b_2_5·b_4_122·b_1_0 + b_2_52·b_4_12·b_3_9
  52. b_6_27·b_5_20 + b_6_27·b_5_19 + b_4_14·b_1_12·b_5_20 + b_4_14·b_1_14·b_3_8
       + b_4_142·b_1_03 + b_4_12·b_1_02·b_5_19 + b_4_12·b_4_14·b_3_9 + b_4_122·b_3_9
       + b_2_5·b_1_04·b_5_19 + b_2_5·b_8_44·b_1_0 + b_2_5·b_4_14·b_5_19
       + b_2_5·b_4_14·b_1_02·b_3_9 + b_2_5·b_4_12·b_5_19 + b_2_5·b_4_12·b_1_02·b_3_9
       + b_2_5·b_4_12·b_1_05 + b_2_5·b_4_12·b_4_14·b_1_0 + b_2_5·b_4_122·b_1_0
       + b_2_52·b_1_22·b_5_20 + b_2_52·b_1_02·b_5_19 + b_2_52·b_1_04·b_3_9
       + b_2_53·b_5_20 + b_2_53·b_5_19 + b_2_53·b_1_02·b_3_9 + b_2_5·c_8_46·b_1_2
  53. b_8_44·b_3_8 + b_4_14·b_1_14·b_3_8 + b_4_14·b_1_17
  54. b_1_06·b_5_19 + b_8_44·b_3_9 + b_8_44·b_1_03 + b_6_27·b_5_19 + b_4_14·b_1_17
       + b_4_14·b_1_02·b_5_19 + b_4_12·b_4_14·b_1_03 + b_4_122·b_1_03
       + b_2_5·b_1_04·b_5_19 + b_2_5·b_1_06·b_3_9 + b_2_5·b_4_14·b_5_19
       + b_2_5·b_4_14·b_1_02·b_3_9 + b_2_5·b_4_12·b_5_19 + b_2_5·b_4_12·b_1_05
       + b_2_5·b_4_12·b_4_14·b_1_0 + b_2_52·b_1_02·b_5_19 + b_2_52·b_1_04·b_3_9
       + b_2_52·b_4_14·b_3_9 + b_2_52·b_4_14·b_1_03 + b_2_52·b_4_12·b_3_9
       + b_2_53·b_5_19 + b_2_53·b_1_02·b_3_9 + c_8_46·b_1_03 + b_2_5·c_8_46·b_1_0
  55. b_6_272 + b_4_14·b_1_03·b_5_19 + b_4_142·b_1_14 + b_4_122·b_1_0·b_3_9
       + b_4_122·b_1_04 + b_2_5·b_4_142·b_1_02 + b_2_5·b_4_12·b_1_0·b_5_19
       + b_2_5·b_4_12·b_6_27 + b_2_5·b_4_122·b_1_02 + b_2_52·b_3_9·b_5_19
       + b_2_52·b_1_03·b_5_19 + b_2_52·b_1_05·b_3_9 + b_2_52·b_4_14·b_1_0·b_3_9
       + b_2_52·b_4_142 + b_2_52·b_4_12·b_1_04 + b_2_52·b_4_12·b_4_14
       + b_2_52·b_4_122 + b_2_53·b_1_2·b_5_20 + b_2_53·b_1_03·b_3_9 + b_2_53·b_6_27
       + b_2_54·b_1_0·b_3_9 + b_2_54·b_4_14 + a_2_42·b_1_18 + b_2_52·c_8_46
  56. b_5_20·b_7_35 + b_1_15·b_7_35 + b_1_15·b_1_22·b_5_20 + b_1_17·b_5_20 + b_1_09·b_3_9
       + b_8_44·b_1_1·b_1_23 + b_8_44·b_1_04 + b_4_14·b_3_9·b_5_19 + b_4_14·b_1_1·b_7_35
       + b_4_14·b_1_15·b_3_8 + b_4_14·b_1_18 + b_4_142·b_1_14 + b_4_142·b_1_0·b_3_9
       + b_4_12·b_3_9·b_5_19 + b_4_12·b_1_03·b_5_19 + b_4_12·b_1_05·b_3_9
       + b_4_12·b_4_14·b_1_0·b_3_9 + b_4_123 + b_2_5·b_1_05·b_5_19 + b_2_5·b_8_44·b_1_22
       + b_2_5·b_4_14·b_1_0·b_5_19 + b_2_5·b_4_142·b_1_02 + b_2_5·b_4_12·b_6_27
       + b_2_5·b_4_12·b_4_14·b_1_02 + b_2_5·b_4_122·b_1_02 + b_2_52·b_8_44
       + b_2_52·b_4_142 + b_2_52·b_4_12·b_1_0·b_3_9 + b_2_52·b_4_12·b_4_14
       + b_2_52·b_4_122 + b_2_53·b_1_03·b_3_9 + b_2_53·b_4_14·b_1_02 + b_2_54·b_4_14
       + c_8_46·b_1_24 + c_8_46·b_1_1·b_3_8 + c_8_46·b_1_12·b_1_22 + c_8_46·b_1_04
       + b_2_5·c_8_46·b_1_02 + a_2_4·c_8_46·b_1_12
  57. b_5_19·b_7_35 + b_4_14·b_3_9·b_5_19 + b_4_14·b_1_13·b_5_20 + b_4_14·b_1_18
       + b_4_12·b_3_9·b_5_19 + b_4_12·b_1_03·b_5_19 + b_4_12·b_1_05·b_3_9 + b_4_12·b_1_08
       + b_2_5·b_1_07·b_3_9 + b_2_5·b_8_44·b_1_02 + b_2_5·b_4_142·b_1_02
       + b_2_5·b_4_12·b_1_0·b_5_19 + b_2_5·b_4_12·b_1_03·b_3_9 + b_2_5·b_4_12·b_6_27
       + b_2_5·b_4_12·b_4_14·b_1_02 + b_2_5·b_4_122·b_1_02 + b_2_52·b_1_23·b_5_20
       + b_2_52·b_1_03·b_5_19 + b_2_52·b_1_05·b_3_9 + b_2_52·b_8_44 + b_2_52·b_4_142
       + b_2_53·b_1_03·b_3_9 + b_2_53·b_4_12·b_1_02 + b_2_54·b_1_0·b_3_9
       + c_8_46·b_1_04 + b_2_5·c_8_46·b_1_02
  58. b_4_14·b_1_03·b_5_19 + b_4_12·b_3_9·b_5_19 + b_4_12·b_1_05·b_3_9 + b_4_12·b_8_44
       + b_4_122·b_1_0·b_3_9 + b_4_122·b_1_04 + b_2_5·b_4_14·b_6_27
       + b_2_5·b_4_142·b_1_02 + b_2_5·b_4_12·b_1_0·b_5_19 + b_2_5·b_4_12·b_1_03·b_3_9
       + b_2_5·b_4_12·b_4_14·b_1_02 + b_2_5·b_4_122·b_1_02 + b_2_52·b_3_9·b_5_19
       + b_2_52·b_4_14·b_1_0·b_3_9 + b_2_52·b_4_12·b_4_14
  59. b_6_27·b_7_35 + b_4_14·b_1_12·b_7_35 + b_4_14·b_6_27·b_3_9 + b_4_142·b_1_12·b_3_8
       + b_4_12·b_1_04·b_5_19 + b_4_12·b_1_06·b_3_9 + b_4_12·b_8_44·b_1_0 + b_4_122·b_5_19
       + b_4_122·b_1_02·b_3_9 + b_4_122·b_1_05 + b_4_123·b_1_0 + b_2_5·b_1_08·b_3_9
       + b_2_5·b_8_44·b_1_03 + b_2_5·b_4_14·b_1_02·b_5_19 + b_2_5·b_4_12·b_4_14·b_1_03
       + b_2_5·b_4_122·b_1_03 + b_2_52·b_1_04·b_5_19 + b_2_52·b_1_06·b_3_9
       + b_2_52·b_8_44·b_1_2 + b_2_52·b_8_44·b_1_0 + b_2_52·b_6_27·b_3_9
       + b_2_52·b_4_14·b_5_19 + b_2_52·b_4_12·b_5_19 + b_2_52·b_4_12·b_1_02·b_3_9
       + b_2_52·b_4_12·b_1_05 + b_2_52·b_4_12·b_4_14·b_1_0 + b_2_52·b_4_122·b_1_0
       + b_2_53·b_1_22·b_5_20 + b_2_53·b_1_02·b_5_19 + b_2_53·b_1_04·b_3_9
       + b_2_53·b_4_14·b_3_9 + b_2_53·b_4_12·b_3_9 + b_2_54·b_5_19 + a_2_42·b_1_19
       + b_2_5·c_8_46·b_1_23 + b_2_5·c_8_46·b_1_03 + b_2_52·c_8_46·b_1_0
  60. b_1_010·b_3_9 + b_8_44·b_5_19 + b_8_44·b_1_05 + b_4_14·b_1_19 + b_4_14·b_8_44·b_1_1
       + b_4_14·b_8_44·b_1_0 + b_4_14·b_6_27·b_3_9 + b_4_142·b_1_12·b_3_8
       + b_4_142·b_1_15 + b_4_142·b_1_02·b_3_9 + b_4_12·b_1_04·b_5_19
       + b_4_12·b_1_06·b_3_9 + b_4_12·b_1_09 + b_4_12·b_4_14·b_5_19
       + b_4_12·b_4_14·b_1_02·b_3_9 + b_4_12·b_4_142·b_1_0 + b_4_122·b_5_19
       + b_4_122·b_1_05 + b_2_5·b_8_44·b_1_03 + b_2_5·b_4_12·b_1_02·b_5_19
       + b_2_5·b_4_12·b_4_14·b_1_03 + b_2_5·b_4_122·b_3_9 + b_2_52·b_8_44·b_1_0
       + b_2_52·b_4_14·b_5_19 + b_2_52·b_4_142·b_1_0 + b_2_52·b_4_12·b_1_02·b_3_9
       + b_2_52·b_4_12·b_4_14·b_1_0 + b_2_52·b_4_122·b_1_0 + b_2_53·b_1_04·b_3_9
       + b_2_53·b_4_14·b_3_9 + b_2_53·b_4_14·b_1_03 + b_2_54·b_1_02·b_3_9
       + c_8_46·b_1_02·b_3_9 + b_4_12·c_8_46·b_1_0
  61. b_1_16·b_7_35 + b_1_16·b_1_22·b_5_20 + b_1_18·b_5_20 + b_1_110·b_3_8
       + b_8_44·b_5_20 + b_8_44·b_5_19 + b_8_44·b_1_1·b_1_24 + b_8_44·b_1_12·b_1_23
       + b_8_44·b_1_02·b_3_9 + b_4_14·b_1_14·b_5_20 + b_4_14·b_1_19 + b_4_14·b_8_44·b_1_0
       + b_2_5·b_8_44·b_1_23 + b_2_52·b_8_44·b_1_2 + a_2_4·b_1_111 + a_2_42·b_1_19
       + c_8_46·b_1_25 + c_8_46·b_1_1·b_1_24 + c_8_46·b_1_12·b_1_23
       + c_8_46·b_1_13·b_1_22
  62. b_7_352 + b_8_44·b_1_1·b_1_25 + b_8_44·b_1_13·b_1_23 + b_4_14·b_1_110
       + b_4_142·b_1_16 + b_4_142·b_1_0·b_5_19 + b_4_143·b_1_02 + b_4_12·b_1_05·b_5_19
       + b_4_12·b_1_07·b_3_9 + b_4_12·b_1_010 + b_4_12·b_4_14·b_6_27
       + b_4_12·b_4_142·b_1_02 + b_4_122·b_1_03·b_3_9 + b_4_122·b_4_14·b_1_02
       + b_2_5·b_8_44·b_1_24 + b_2_5·b_4_14·b_3_9·b_5_19 + b_2_5·b_4_14·b_8_44
       + b_2_5·b_4_142·b_1_0·b_3_9 + b_2_5·b_4_143 + b_2_5·b_4_12·b_1_03·b_5_19
       + b_2_5·b_4_12·b_1_05·b_3_9 + b_2_5·b_4_12·b_4_14·b_1_0·b_3_9
       + b_2_5·b_4_122·b_1_0·b_3_9 + b_2_52·b_1_07·b_3_9 + b_2_52·b_8_44·b_1_22
       + b_2_52·b_8_44·b_1_02 + b_2_52·b_4_14·b_1_0·b_5_19 + b_2_52·b_4_142·b_1_02
       + b_2_52·b_4_12·b_6_27 + b_2_52·b_4_12·b_4_14·b_1_02 + b_2_52·b_4_122·b_1_02
       + b_2_53·b_3_9·b_5_19 + b_2_53·b_1_23·b_5_20 + b_2_53·b_1_05·b_3_9
       + b_2_53·b_8_44 + b_2_53·b_4_12·b_1_04 + b_2_53·b_4_122 + b_2_54·b_1_0·b_5_19
       + b_2_54·b_1_03·b_3_9 + b_2_55·b_1_0·b_3_9 + a_2_4·b_4_143 + c_8_46·b_1_26
       + c_8_46·b_1_14·b_1_22 + c_8_46·b_1_06 + b_4_14·c_8_46·b_1_12
       + b_2_52·c_8_46·b_1_02 + a_2_42·c_8_46·b_1_12
  63. b_7_352 + b_8_44·b_1_1·b_1_25 + b_8_44·b_1_13·b_1_23 + b_6_27·b_8_44
       + b_4_14·b_1_110 + b_4_14·b_8_44·b_1_12 + b_4_142·b_1_16 + b_4_142·b_1_0·b_5_19
       + b_4_143·b_1_02 + b_4_12·b_1_07·b_3_9 + b_4_12·b_1_010
       + b_4_12·b_4_14·b_1_0·b_5_19 + b_4_12·b_4_14·b_6_27 + b_4_12·b_4_142·b_1_02
       + b_4_122·b_1_0·b_5_19 + b_4_122·b_6_27 + b_4_122·b_4_14·b_1_02
       + b_4_123·b_1_02 + b_2_5·b_1_09·b_3_9 + b_2_5·b_8_44·b_1_24
       + b_2_5·b_8_44·b_1_0·b_3_9 + b_2_5·b_8_44·b_1_04 + b_2_5·b_4_14·b_3_9·b_5_19
       + b_2_5·b_4_143 + b_2_5·b_4_12·b_1_03·b_5_19 + b_2_5·b_4_12·b_1_08
       + b_2_5·b_4_12·b_4_14·b_1_0·b_3_9 + b_2_5·b_4_122·b_1_0·b_3_9
       + b_2_5·b_4_122·b_4_14 + b_2_5·b_4_123 + b_2_52·b_1_05·b_5_19
       + b_2_52·b_1_07·b_3_9 + b_2_52·b_8_44·b_1_02 + b_2_52·b_4_142·b_1_02
       + b_2_52·b_4_12·b_1_0·b_5_19 + b_2_53·b_3_9·b_5_19 + b_2_53·b_1_03·b_5_19
       + b_2_53·b_1_05·b_3_9 + b_2_53·b_8_44 + b_2_53·b_4_142 + b_2_53·b_4_12·b_4_14
       + b_2_54·b_4_12·b_1_02 + b_2_55·b_4_14 + a_2_4·b_4_143 + a_2_42·b_1_110
       + c_8_46·b_1_26 + c_8_46·b_1_14·b_1_22 + c_8_46·b_1_06 + b_4_14·c_8_46·b_1_12
       + b_4_12·c_8_46·b_1_02 + b_2_5·c_8_46·b_1_24 + b_2_5·c_8_46·b_1_0·b_3_9
       + b_2_5·b_4_12·c_8_46 + a_2_42·c_8_46·b_1_12
  64. b_8_44·b_7_35 + b_8_44·b_1_1·b_1_26 + b_8_44·b_1_12·b_1_25
       + b_8_44·b_1_13·b_1_24 + b_8_44·b_1_14·b_1_23 + b_8_44·b_1_02·b_5_19
       + b_4_14·b_1_14·b_7_35 + b_4_14·b_1_16·b_5_20 + b_4_14·b_1_111
       + b_4_14·b_6_27·b_5_19 + b_4_142·b_1_14·b_3_8 + b_4_142·b_1_17
       + b_4_142·b_1_02·b_5_19 + b_4_12·b_8_44·b_3_9 + b_4_12·b_4_142·b_1_03
       + b_4_122·b_1_02·b_5_19 + b_4_122·b_4_14·b_1_03 + b_2_5·b_8_44·b_5_19
       + b_2_5·b_8_44·b_1_25 + b_2_5·b_8_44·b_1_02·b_3_9 + b_2_5·b_4_14·b_8_44·b_1_0
       + b_2_5·b_4_142·b_5_19 + b_2_5·b_4_142·b_1_02·b_3_9 + b_2_5·b_4_12·b_1_04·b_5_19
       + b_2_5·b_4_12·b_8_44·b_1_0 + b_2_5·b_4_12·b_4_14·b_5_19
       + b_2_5·b_4_12·b_4_142·b_1_0 + b_2_5·b_4_122·b_5_19 + b_2_5·b_4_122·b_1_02·b_3_9
       + b_2_5·b_4_123·b_1_0 + b_2_52·b_1_08·b_3_9 + b_2_52·b_8_44·b_3_9
       + b_2_52·b_8_44·b_1_23 + b_2_52·b_8_44·b_1_03 + b_2_52·b_4_142·b_3_9
       + b_2_52·b_4_142·b_1_03 + b_2_52·b_4_12·b_1_07 + b_2_52·b_4_12·b_4_14·b_3_9
       + b_2_52·b_4_122·b_3_9 + b_2_52·b_4_122·b_1_03 + b_2_53·b_1_04·b_5_19
       + b_2_53·b_1_06·b_3_9 + b_2_53·b_8_44·b_1_0 + b_2_53·b_4_14·b_1_02·b_3_9
       + b_2_53·b_4_12·b_5_19 + b_2_53·b_4_12·b_1_02·b_3_9 + b_2_53·b_4_12·b_4_14·b_1_0
       + b_2_53·b_4_122·b_1_0 + b_2_54·b_1_02·b_5_19 + b_2_54·b_1_04·b_3_9
       + b_2_54·b_4_14·b_1_03 + b_2_55·b_4_14·b_1_0 + c_8_46·b_1_27
       + c_8_46·b_1_1·b_1_26 + c_8_46·b_1_14·b_1_23 + c_8_46·b_1_15·b_1_22
       + b_4_14·c_8_46·b_1_03 + b_2_5·b_4_14·c_8_46·b_1_0
  65. b_8_44·b_1_1·b_1_27 + b_8_44·b_1_15·b_1_23 + b_8_44·b_1_03·b_5_19
       + b_8_44·b_1_05·b_3_9 + b_8_442 + b_4_14·b_1_112 + b_4_142·b_1_18
       + b_4_12·b_1_012 + b_4_12·b_8_44·b_1_04 + b_4_12·b_4_14·b_3_9·b_5_19
       + b_4_12·b_4_14·b_8_44 + b_4_122·b_3_9·b_5_19 + b_4_122·b_1_05·b_3_9
       + b_4_122·b_8_44 + b_4_122·b_4_14·b_1_0·b_3_9 + b_4_123·b_1_0·b_3_9
       + b_4_123·b_1_04 + b_2_5·b_8_44·b_1_26 + b_2_5·b_8_44·b_1_0·b_5_19
       + b_2_5·b_8_44·b_1_03·b_3_9 + b_2_5·b_4_142·b_6_27 + b_2_5·b_4_12·b_1_010
       + b_2_5·b_4_12·b_8_44·b_1_02 + b_2_5·b_4_12·b_4_142·b_1_02
       + b_2_5·b_4_122·b_1_03·b_3_9 + b_2_52·b_8_44·b_1_24 + b_2_52·b_8_44·b_1_0·b_3_9
       + b_2_52·b_4_14·b_3_9·b_5_19 + b_2_52·b_4_142·b_1_0·b_3_9
       + b_2_52·b_4_12·b_1_03·b_5_19 + b_2_52·b_4_12·b_1_05·b_3_9
       + b_2_52·b_4_12·b_8_44 + b_2_52·b_4_12·b_4_142 + b_2_52·b_4_122·b_1_04
       + b_2_52·b_4_123 + b_2_53·b_8_44·b_1_02 + b_2_53·b_4_12·b_1_0·b_5_19
       + b_2_54·b_1_05·b_3_9 + b_2_54·b_4_142 + b_2_54·b_4_12·b_1_04
       + b_2_54·b_4_12·b_4_14 + b_2_55·b_4_14·b_1_02 + c_8_46·b_1_28
       + c_8_46·b_1_12·b_1_26 + c_8_46·b_1_14·b_1_24 + c_8_46·b_1_16·b_1_22
       + c_8_46·b_1_03·b_5_19 + c_8_46·b_1_08 + b_4_122·c_8_46 + b_2_5·c_8_46·b_1_06
       + b_2_5·b_4_14·c_8_46·b_1_02 + b_2_5·b_4_12·c_8_46·b_1_02

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 256

Data used for Benson′s test

  • Benson′s completion test succeeded in degree 16.
  • The completion test was perfect: It applied in the last degree in which a generator or relation was found.
  • The following is a filter regular homogeneous system of parameters:
    1. c_8_46, a Duflot regular element of degree 8
    2. b_1_24 + b_1_12·b_1_22 + b_1_14 + b_1_04 + b_4_14 + b_2_52, an element of degree 4
    3. b_1_12·b_1_24 + b_1_14·b_1_22 + b_4_14·b_1_12 + b_4_14·b_1_02 + b_2_5·b_4_14
         + b_2_52·b_1_22 + b_2_52·b_1_02, an element of degree 6
    4. b_1_0, an element of degree 1
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 7, 14, 15].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].
  • We found that there exists some filter regular HSOP formed by the first 2 terms of the above HSOP, together with 2 elements of degree 2.

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 256

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 1

  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. a_2_4 → 0, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → 0, an element of degree 3
  8. b_4_12 → 0, an element of degree 4
  9. b_4_14 → 0, an element of degree 4
  10. b_5_19 → 0, an element of degree 5
  11. b_5_20 → 0, an element of degree 5
  12. b_6_27 → 0, an element of degree 6
  13. b_7_35 → 0, an element of degree 7
  14. b_8_44 → 0, an element of degree 8
  15. c_8_46 → c_1_08, an element of degree 8

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

  1. b_1_0 → 0, an element of degree 1
  2. b_1_1 → c_1_1, an element of degree 1
  3. b_1_2 → c_1_2, an element of degree 1
  4. a_2_4 → 0, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → 0, an element of degree 3
  8. b_4_12 → 0, an element of degree 4
  9. b_4_14 → 0, an element of degree 4
  10. b_5_19 → 0, an element of degree 5
  11. b_5_20 → c_1_0·c_1_1·c_1_23 + c_1_0·c_1_12·c_1_22 + c_1_02·c_1_23
       + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_2, an element of degree 5
  12. b_6_27 → 0, an element of degree 6
  13. b_7_35 → c_1_0·c_1_1·c_1_25 + c_1_0·c_1_12·c_1_24 + c_1_0·c_1_13·c_1_23
       + c_1_0·c_1_14·c_1_22 + c_1_02·c_1_25 + c_1_02·c_1_1·c_1_24
       + c_1_02·c_1_13·c_1_22 + c_1_02·c_1_14·c_1_2 + c_1_04·c_1_23
       + c_1_04·c_1_12·c_1_2, an element of degree 7
  14. b_8_44 → c_1_0·c_1_1·c_1_26 + c_1_0·c_1_15·c_1_22 + c_1_02·c_1_26
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_13·c_1_23 + c_1_02·c_1_15·c_1_2
       + c_1_04·c_1_24 + c_1_04·c_1_1·c_1_23 + c_1_04·c_1_12·c_1_22
       + c_1_04·c_1_13·c_1_2, an element of degree 8
  15. c_8_46 → c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_23 + c_1_02·c_1_1·c_1_25
       + c_1_02·c_1_12·c_1_24 + c_1_04·c_1_24 + c_1_04·c_1_1·c_1_23
       + c_1_04·c_1_14 + c_1_08, an element of degree 8

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

  1. 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_1, an element of degree 1
  4. a_2_4 → 0, an element of degree 2
  5. b_2_5 → c_1_22 + c_1_1·c_1_2, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → 0, an element of degree 3
  8. b_4_12 → 0, an element of degree 4
  9. b_4_14 → 0, an element of degree 4
  10. b_5_19 → 0, an element of degree 5
  11. b_5_20 → c_1_0·c_1_12·c_1_22 + c_1_0·c_1_13·c_1_2 + c_1_02·c_1_1·c_1_22
       + c_1_02·c_1_12·c_1_2 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  12. b_6_27 → c_1_0·c_1_1·c_1_24 + c_1_0·c_1_13·c_1_22 + c_1_02·c_1_24
       + c_1_02·c_1_13·c_1_2 + c_1_04·c_1_22 + c_1_04·c_1_1·c_1_2, an element of degree 6
  13. b_7_35 → c_1_0·c_1_14·c_1_22 + c_1_0·c_1_15·c_1_2 + c_1_02·c_1_13·c_1_22
       + c_1_02·c_1_14·c_1_2 + c_1_02·c_1_15 + c_1_04·c_1_13, an element of degree 7
  14. b_8_44 → c_1_0·c_1_15·c_1_22 + c_1_0·c_1_16·c_1_2 + c_1_02·c_1_14·c_1_22
       + c_1_02·c_1_15·c_1_2 + c_1_02·c_1_16 + c_1_04·c_1_14, an element of degree 8
  15. c_8_46 → c_1_0·c_1_1·c_1_26 + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_23
       + c_1_0·c_1_15·c_1_22 + c_1_02·c_1_26 + c_1_02·c_1_1·c_1_25
       + c_1_02·c_1_13·c_1_23 + c_1_02·c_1_15·c_1_2 + c_1_04·c_1_12·c_1_22
       + c_1_04·c_1_13·c_1_2 + c_1_04·c_1_14 + c_1_08, an element of degree 8

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

  1. b_1_0 → 0, an element of degree 1
  2. b_1_1 → c_1_2, an element of degree 1
  3. b_1_2 → c_1_2, an element of degree 1
  4. a_2_4 → 0, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  7. b_3_9 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  8. b_4_12 → 0, an element of degree 4
  9. b_4_14 → c_1_12·c_1_22 + c_1_14, an element of degree 4
  10. b_5_19 → c_1_1·c_1_24 + c_1_12·c_1_23, an element of degree 5
  11. b_5_20 → c_1_1·c_1_24 + c_1_14·c_1_2 + c_1_0·c_1_1·c_1_23 + c_1_0·c_1_12·c_1_22
       + c_1_02·c_1_23 + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_2, an element of degree 5
  12. b_6_27 → c_1_12·c_1_24 + c_1_14·c_1_22, an element of degree 6
  13. b_7_35 → c_1_1·c_1_26 + c_1_14·c_1_23 + c_1_0·c_1_12·c_1_24 + c_1_0·c_1_14·c_1_22
       + c_1_02·c_1_1·c_1_24 + c_1_02·c_1_14·c_1_2 + c_1_04·c_1_1·c_1_22
       + c_1_04·c_1_12·c_1_2, an element of degree 7
  14. b_8_44 → c_1_1·c_1_27 + c_1_14·c_1_24, an element of degree 8
  15. c_8_46 → c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22 + c_1_04·c_1_24
       + c_1_04·c_1_12·c_1_22 + c_1_04·c_1_14 + c_1_08, an element of degree 8

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

  1. b_1_0 → c_1_1, 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. a_2_4 → 0, an element of degree 2
  5. b_2_5 → c_1_22 + c_1_1·c_1_2, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_12
       + c_1_02·c_1_1, an element of degree 3
  8. b_4_12 → c_1_22·c_1_32 + c_1_23·c_1_3 + c_1_1·c_1_2·c_1_32 + c_1_12·c_1_32
       + c_1_12·c_1_2·c_1_3 + c_1_13·c_1_3 + c_1_0·c_1_1·c_1_22 + c_1_0·c_1_12·c_1_2, an element of degree 4
  9. b_4_14 → c_1_34 + c_1_22·c_1_32 + c_1_1·c_1_2·c_1_32 + c_1_1·c_1_22·c_1_3
       + c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3, an element of degree 4
  10. b_5_19 → c_1_2·c_1_34 + c_1_23·c_1_32 + c_1_1·c_1_22·c_1_32 + c_1_1·c_1_23·c_1_3
       + c_1_13·c_1_32 + c_1_14·c_1_3 + c_1_0·c_1_12·c_1_22 + c_1_0·c_1_13·c_1_2
       + c_1_0·c_1_14 + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_1, an element of degree 5
  11. b_5_20 → c_1_2·c_1_34 + c_1_23·c_1_32 + c_1_1·c_1_34 + c_1_1·c_1_23·c_1_3
       + c_1_13·c_1_32 + c_1_13·c_1_2·c_1_3 + c_1_0·c_1_12·c_1_22 + c_1_0·c_1_13·c_1_2
       + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  12. b_6_27 → c_1_22·c_1_34 + c_1_25·c_1_3 + c_1_1·c_1_22·c_1_33 + c_1_12·c_1_2·c_1_33
       + c_1_13·c_1_2·c_1_32 + c_1_13·c_1_22·c_1_3 + c_1_14·c_1_32 + c_1_15·c_1_3
       + c_1_0·c_1_23·c_1_32 + c_1_0·c_1_24·c_1_3 + c_1_0·c_1_1·c_1_22·c_1_32
       + c_1_0·c_1_1·c_1_24 + c_1_0·c_1_12·c_1_22·c_1_3 + c_1_0·c_1_13·c_1_32
       + c_1_0·c_1_14·c_1_3 + c_1_0·c_1_14·c_1_2 + c_1_02·c_1_22·c_1_32
       + c_1_02·c_1_23·c_1_3 + c_1_02·c_1_24 + c_1_02·c_1_1·c_1_2·c_1_32
       + c_1_02·c_1_12·c_1_32 + c_1_02·c_1_12·c_1_2·c_1_3 + c_1_02·c_1_12·c_1_22
       + c_1_02·c_1_13·c_1_3 + c_1_03·c_1_1·c_1_22 + c_1_03·c_1_12·c_1_2
       + c_1_04·c_1_22 + c_1_04·c_1_1·c_1_2, an element of degree 6
  13. b_7_35 → c_1_2·c_1_36 + c_1_22·c_1_35 + c_1_23·c_1_34 + c_1_24·c_1_33
       + c_1_25·c_1_32 + c_1_26·c_1_3 + c_1_1·c_1_36 + c_1_12·c_1_35
       + c_1_12·c_1_22·c_1_33 + c_1_12·c_1_23·c_1_32 + c_1_13·c_1_34
       + c_1_13·c_1_2·c_1_33 + c_1_13·c_1_23·c_1_3 + c_1_14·c_1_33
       + c_1_14·c_1_2·c_1_32 + c_1_14·c_1_22·c_1_3 + c_1_15·c_1_32 + c_1_16·c_1_3
       + c_1_0·c_1_1·c_1_23·c_1_32 + c_1_0·c_1_1·c_1_24·c_1_3 + c_1_0·c_1_12·c_1_34
       + c_1_0·c_1_12·c_1_24 + c_1_0·c_1_13·c_1_2·c_1_32 + c_1_0·c_1_14·c_1_2·c_1_3
       + c_1_0·c_1_15·c_1_3 + c_1_0·c_1_15·c_1_2 + c_1_0·c_1_16 + c_1_02·c_1_1·c_1_34
       + c_1_02·c_1_1·c_1_23·c_1_3 + c_1_02·c_1_12·c_1_22·c_1_3
       + c_1_02·c_1_13·c_1_22 + c_1_02·c_1_14·c_1_3 + c_1_02·c_1_14·c_1_2
       + c_1_03·c_1_12·c_1_22 + c_1_03·c_1_13·c_1_2 + c_1_04·c_1_1·c_1_22
       + c_1_04·c_1_12·c_1_2 + c_1_04·c_1_13, an element of degree 7
  14. b_8_44 → c_1_24·c_1_34 + c_1_26·c_1_32 + c_1_1·c_1_2·c_1_36 + c_1_1·c_1_23·c_1_34
       + c_1_1·c_1_25·c_1_32 + c_1_1·c_1_26·c_1_3 + c_1_12·c_1_2·c_1_35
       + c_1_12·c_1_22·c_1_34 + c_1_13·c_1_2·c_1_34 + c_1_13·c_1_23·c_1_32
       + c_1_13·c_1_24·c_1_3 + c_1_14·c_1_34 + c_1_14·c_1_2·c_1_33
       + c_1_14·c_1_22·c_1_32 + c_1_16·c_1_32 + c_1_16·c_1_2·c_1_3
       + c_1_0·c_1_23·c_1_34 + c_1_0·c_1_25·c_1_32 + c_1_0·c_1_12·c_1_24·c_1_3
       + c_1_0·c_1_13·c_1_24 + c_1_0·c_1_14·c_1_22·c_1_3 + c_1_0·c_1_15·c_1_22
       + c_1_0·c_1_17 + c_1_02·c_1_22·c_1_34 + c_1_02·c_1_25·c_1_3
       + c_1_02·c_1_1·c_1_24·c_1_3 + c_1_02·c_1_12·c_1_24
       + c_1_02·c_1_14·c_1_2·c_1_3 + c_1_02·c_1_14·c_1_22 + c_1_03·c_1_1·c_1_24
       + c_1_03·c_1_14·c_1_2 + c_1_03·c_1_15 + c_1_04·c_1_22·c_1_32
       + c_1_04·c_1_23·c_1_3 + c_1_04·c_1_1·c_1_22·c_1_3 + c_1_04·c_1_12·c_1_2·c_1_3
       + c_1_04·c_1_12·c_1_22 + c_1_04·c_1_13·c_1_2 + c_1_05·c_1_1·c_1_22
       + c_1_05·c_1_12·c_1_2 + c_1_05·c_1_13 + c_1_06·c_1_12, an element of degree 8
  15. c_8_46 → c_1_22·c_1_36 + c_1_23·c_1_35 + c_1_25·c_1_33 + c_1_27·c_1_3
       + c_1_1·c_1_2·c_1_36 + c_1_1·c_1_22·c_1_35 + c_1_1·c_1_23·c_1_34
       + c_1_1·c_1_25·c_1_32 + c_1_1·c_1_26·c_1_3 + c_1_12·c_1_36
       + c_1_12·c_1_22·c_1_34 + c_1_12·c_1_24·c_1_32 + c_1_12·c_1_25·c_1_3
       + c_1_13·c_1_35 + c_1_13·c_1_2·c_1_34 + c_1_13·c_1_22·c_1_33
       + c_1_13·c_1_24·c_1_3 + c_1_14·c_1_23·c_1_3 + c_1_15·c_1_33
       + c_1_15·c_1_2·c_1_32 + c_1_16·c_1_2·c_1_3 + c_1_17·c_1_3 + c_1_0·c_1_23·c_1_34
       + c_1_0·c_1_26·c_1_3 + c_1_0·c_1_1·c_1_22·c_1_34 + c_1_0·c_1_1·c_1_24·c_1_32
       + c_1_0·c_1_1·c_1_25·c_1_3 + c_1_0·c_1_1·c_1_26 + c_1_0·c_1_12·c_1_23·c_1_32
       + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_13·c_1_34 + c_1_0·c_1_13·c_1_22·c_1_32
       + c_1_0·c_1_13·c_1_23·c_1_3 + c_1_0·c_1_13·c_1_24 + c_1_0·c_1_14·c_1_2·c_1_32
       + c_1_0·c_1_14·c_1_23 + c_1_0·c_1_15·c_1_32 + c_1_0·c_1_15·c_1_2·c_1_3
       + c_1_0·c_1_15·c_1_22 + c_1_0·c_1_16·c_1_2 + c_1_02·c_1_26
       + c_1_02·c_1_1·c_1_25 + c_1_02·c_1_12·c_1_22·c_1_32
       + c_1_02·c_1_12·c_1_23·c_1_3 + c_1_02·c_1_12·c_1_24
       + c_1_02·c_1_13·c_1_2·c_1_32 + c_1_02·c_1_13·c_1_23
       + c_1_02·c_1_14·c_1_32 + c_1_02·c_1_14·c_1_2·c_1_3 + c_1_02·c_1_15·c_1_3
       + c_1_02·c_1_16 + c_1_03·c_1_13·c_1_22 + c_1_03·c_1_14·c_1_2
       + c_1_04·c_1_34 + c_1_04·c_1_23·c_1_3 + c_1_04·c_1_1·c_1_22·c_1_3
       + c_1_04·c_1_13·c_1_3 + c_1_05·c_1_1·c_1_22 + c_1_05·c_1_12·c_1_2 + c_1_08, an element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 256


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