Cohomology of group number 1827 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 8.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 2.
  • 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 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    1
    (t  −  1)4 · (t2  +  1)2
  • The a-invariants are -∞,-∞,-4,-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 10:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_2, a nilpotent element of degree 1
  3. b_1_1, an element of degree 1
  4. b_1_3, an element of degree 1
  5. a_3_8, a nilpotent element of degree 3
  6. a_3_6, a nilpotent element of degree 3
  7. a_4_10, a nilpotent element of degree 4
  8. b_4_16, an element of degree 4
  9. c_4_17, a Duflot regular element of degree 4
  10. a_5_14, a nilpotent element of degree 5
  11. a_5_15, a nilpotent element of degree 5
  12. b_5_26, an element of degree 5
  13. a_6_24, a nilpotent element of degree 6
  14. a_7_34, a nilpotent element of degree 7
  15. a_7_31, a nilpotent element of degree 7
  16. a_8_40, a nilpotent element of degree 8
  17. c_8_66, a Duflot regular element of degree 8
  18. a_10_67, a nilpotent element of degree 10

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

Ring relations

There are 107 minimal relations of maximal degree 20:

  1. a_1_0·a_1_2
  2. a_1_0·b_1_1 + a_1_22
  3. a_1_22·b_1_1
  4. a_1_2·b_1_32 + a_1_03
  5. a_1_2·a_3_8
  6. a_1_0·a_3_6
  7. b_1_1·a_3_8 + a_1_2·b_1_12·b_1_3 + a_1_2·a_3_6
  8. a_1_03·b_1_32
  9. b_1_32·a_3_6 + b_1_1·b_1_3·a_3_6 + a_4_10·b_1_1 + a_1_2·b_1_3·a_3_6 + a_1_02·a_3_8
  10. a_1_0·b_1_3·a_3_8 + a_1_02·b_1_33 + a_4_10·a_1_0
  11. a_1_2·b_1_3·a_3_6 + a_4_10·a_1_2
  12. b_1_32·a_3_8 + a_1_0·b_1_34 + b_4_16·a_1_0 + a_1_0·b_1_3·a_3_8
  13. a_1_2·b_1_13·b_1_3 + b_4_16·a_1_2 + a_1_2·b_1_3·a_3_6 + a_1_2·b_1_1·a_3_6
       + a_1_02·a_3_8
  14. a_3_82 + a_1_02·b_1_34 + c_4_17·a_1_02
  15. a_3_8·a_3_6 + a_4_10·a_1_2·b_1_1
  16. b_4_16·a_1_2·b_1_1 + a_3_62 + a_3_8·a_3_6 + c_4_17·a_1_22
  17. a_1_2·a_5_14 + c_4_17·a_1_22
  18. a_1_0·a_5_15
  19. b_1_1·a_5_14 + b_4_16·a_1_0·b_1_3 + a_4_10·b_1_32 + a_4_10·b_1_1·b_1_3 + a_1_2·a_5_15
       + a_1_02·b_1_34 + a_4_10·a_1_0·b_1_3 + a_4_10·a_1_02 + c_4_17·a_1_2·b_1_1
       + c_4_17·a_1_22
  20. b_1_1·a_5_14 + a_1_0·b_5_26 + a_1_0·b_1_35 + b_4_16·a_1_0·b_1_3 + a_4_10·b_1_32
       + a_4_10·b_1_1·b_1_3 + a_3_82 + a_4_10·a_1_0·b_1_3 + c_4_17·a_1_2·b_1_1
       + c_4_17·a_1_0·b_1_3
  21. b_1_1·a_5_15 + b_1_12·b_1_3·a_3_6 + a_1_2·b_5_26 + a_4_10·b_1_12 + c_4_17·a_1_2·b_1_3
       + c_4_17·a_1_2·b_1_1
  22. a_4_10·a_3_8 + a_4_10·a_1_0·b_1_32 + c_4_17·a_1_02·b_1_3
  23. a_4_10·a_3_6 + a_4_10·a_1_2·b_1_12 + c_4_17·a_1_22·b_1_3
  24. b_4_16·a_3_8 + b_4_16·a_1_0·b_1_32 + a_4_10·a_3_8 + a_4_10·a_1_02·b_1_3
       + c_4_17·a_1_0·b_1_32
  25. b_1_32·a_5_15 + b_1_13·b_1_3·a_3_6 + a_4_10·b_1_1·b_1_32 + a_4_10·b_1_12·b_1_3
       + a_4_10·b_1_13 + a_4_10·a_1_2·b_1_12 + a_1_02·a_5_14 + a_4_10·a_1_02·b_1_3
       + c_4_17·a_1_03
  26. a_1_22·b_5_26 + a_4_10·a_1_02·b_1_3 + c_4_17·a_1_22·b_1_3
  27. a_6_24·b_1_1 + b_4_16·a_3_6 + b_4_16·a_3_8 + a_4_10·b_1_33 + a_4_10·b_1_1·b_1_32
       + a_4_10·b_1_12·b_1_3 + a_1_2·b_1_3·a_5_15 + a_1_02·b_1_35
       + c_4_17·a_1_2·b_1_1·b_1_3 + c_4_17·a_1_0·b_1_32 + c_4_17·a_1_22·b_1_3
       + c_4_17·a_1_02·b_1_3 + c_4_17·a_1_03
  28. a_1_0·b_1_3·a_5_14 + a_1_02·b_1_35 + a_6_24·a_1_0 + a_4_10·a_3_8
  29. a_6_24·a_1_2 + a_4_10·a_1_2·b_1_12 + c_4_17·a_1_22·b_1_3
  30. a_4_102 + c_4_17·a_1_02·b_1_32
  31. b_1_12·b_1_36 + b_1_16·b_1_32 + b_4_162 + b_1_12·a_3_62 + a_1_02·b_1_36
       + c_4_17·b_1_34 + c_4_17·a_1_02·b_1_32
  32. a_3_6·a_5_14 + c_4_17·a_1_2·a_3_6
  33. a_3_8·a_5_15 + a_4_10·a_1_02·b_1_32
  34. a_3_8·b_5_26 + a_1_2·b_1_1·b_1_3·b_5_26 + a_1_0·b_1_37 + b_4_16·a_1_0·b_1_33
       + a_3_6·a_5_15 + a_1_02·b_1_36 + a_4_10·a_1_0·b_1_33 + c_4_17·b_1_3·a_3_8
       + c_4_17·a_1_2·a_3_6 + c_4_17·a_1_0·a_3_8 + c_4_17·a_1_03·b_1_3
  35. b_1_33·a_5_14 + a_1_0·b_1_37 + a_6_24·b_1_32 + b_4_16·b_1_3·a_3_6
       + b_4_16·a_1_0·b_1_33 + a_4_10·b_1_1·b_1_33 + a_4_10·b_4_16
       + a_4_10·a_1_02·b_1_32 + c_4_17·a_1_02·b_1_32
  36. b_1_1·a_7_34 + b_1_14·b_1_3·a_3_6 + b_4_16·b_1_3·a_3_6 + a_4_10·b_1_1·b_1_33
       + a_4_10·b_1_13·b_1_3 + a_4_10·b_1_14 + a_4_10·b_4_16 + a_3_6·a_5_15
       + a_4_10·a_1_2·b_1_13 + a_4_10·a_1_0·b_1_33 + a_4_10·a_1_02·b_1_32
       + c_4_17·a_1_2·b_1_12·b_1_3 + c_4_17·a_1_2·b_1_13 + c_4_17·a_1_0·b_1_33
       + c_4_17·a_1_2·a_3_6 + c_4_17·a_1_02·b_1_32
  37. a_3_8·a_5_14 + a_1_0·a_7_34 + a_1_02·b_1_36 + a_6_24·a_1_0·b_1_3
       + c_4_17·a_1_02·b_1_32 + c_4_17·a_1_03·b_1_3
  38. a_1_2·a_7_34
  39. a_3_6·b_5_26 + a_3_8·b_5_26 + b_1_1·a_7_31 + a_1_2·b_1_12·b_5_26 + a_1_0·b_1_37
       + b_4_16·b_1_3·a_3_6 + b_4_16·b_1_1·a_3_6 + a_4_10·b_1_34 + a_4_10·b_1_1·b_1_33
       + a_4_10·b_1_13·b_1_3 + a_4_10·b_1_14 + a_3_6·a_5_15 + a_4_10·a_1_2·b_1_13
       + c_4_17·b_1_3·a_3_6 + c_4_17·b_1_3·a_3_8 + c_4_17·a_1_2·b_1_12·b_1_3
       + c_4_17·a_1_2·b_1_13 + c_4_17·a_1_2·a_3_6 + c_4_17·a_1_0·a_3_8
  40. a_1_0·a_7_31 + a_6_24·a_1_0·b_1_3 + c_4_17·a_1_03·b_1_3
  41. a_3_6·a_5_15 + a_1_2·a_7_31 + a_4_10·a_1_02·b_1_32 + c_4_17·a_1_2·a_3_6
  42. a_6_24·a_3_8 + a_6_24·a_1_0·b_1_32 + a_4_10·a_5_14 + a_4_10·a_1_0·b_1_34
       + c_4_17·a_1_02·b_1_33 + a_4_10·c_4_17·a_1_2 + a_4_10·c_4_17·a_1_0
  43. a_6_24·a_3_6 + a_4_10·c_4_17·a_1_2
  44. b_1_32·a_7_34 + b_1_15·b_1_3·a_3_6 + b_4_16·a_5_14 + b_4_16·b_1_1·b_1_3·a_3_6
       + a_4_10·b_1_35 + a_4_10·b_1_12·b_1_33 + a_4_10·b_1_13·b_1_32
       + a_4_10·b_1_14·b_1_3 + a_4_10·b_1_15 + a_4_10·b_4_16·b_1_1 + a_6_24·a_3_8 + a_3_63
       + a_6_24·a_1_02·b_1_3 + b_4_16·c_4_17·a_1_2 + c_4_17·a_1_02·b_1_33
       + a_4_10·c_4_17·a_1_0
  45. a_1_0·b_1_3·a_7_34 + a_4_10·a_5_14 + a_4_10·a_1_0·b_1_34 + a_4_10·c_4_17·a_1_2
  46. b_1_32·a_7_31 + b_1_1·b_1_3·a_7_31 + a_1_2·b_1_12·b_1_3·b_5_26 + a_6_24·b_1_33
       + b_4_16·b_1_1·b_1_3·a_3_6 + a_4_10·b_5_26 + a_4_10·b_1_35 + a_4_10·b_1_12·b_1_33
       + a_4_10·b_1_14·b_1_3 + a_1_02·b_1_37 + a_4_10·a_5_15 + a_1_02·a_7_34
       + a_6_24·a_1_02·b_1_3 + b_4_16·c_4_17·a_1_2 + a_4_10·c_4_17·b_1_3
       + c_4_17·a_1_2·b_1_1·a_3_6 + c_4_17·a_1_02·b_1_33 + a_4_10·c_4_17·a_1_0
       + c_4_17·a_1_02·a_3_8
  47. a_1_2·b_1_3·a_7_31 + a_4_10·a_5_15 + a_4_10·c_4_17·a_1_2
  48. a_1_2·b_1_12·b_1_3·b_5_26 + b_4_16·a_5_15 + b_4_16·b_1_1·b_1_3·a_3_6
       + a_4_10·b_4_16·b_1_1 + a_1_2·b_1_1·a_7_31 + a_4_10·a_5_15 + a_1_02·a_7_34
       + b_4_16·c_4_17·a_1_2 + a_4_10·c_4_17·a_1_2
  49. b_1_32·a_7_31 + b_1_12·a_7_31 + a_1_2·b_1_13·b_5_26 + a_8_40·b_1_1 + a_6_24·b_1_33
       + b_4_16·b_1_12·a_3_6 + b_4_16·a_1_0·b_1_34 + a_4_10·b_1_35
       + a_4_10·b_1_1·b_1_34 + a_4_10·b_1_12·b_1_33 + a_4_10·b_1_13·b_1_32
       + a_4_10·b_1_15 + a_4_10·a_1_0·b_1_34 + a_1_02·a_7_34 + a_6_24·a_1_02·b_1_3
       + c_4_17·b_1_1·b_1_3·a_3_6 + c_4_17·b_1_12·a_3_6 + b_4_16·c_4_17·a_1_2
       + a_4_10·c_4_17·b_1_1 + c_4_17·a_1_2·b_1_1·a_3_6 + c_4_17·a_1_02·b_1_33
       + c_4_17·a_1_02·a_3_8
  50. a_8_40·a_1_0 + a_6_24·a_1_02·b_1_3 + c_4_17·a_1_02·b_1_33 + c_4_17·a_1_02·a_3_8
  51. a_1_2·b_1_12·b_1_3·b_5_26 + b_4_16·a_5_15 + b_4_16·b_1_1·b_1_3·a_3_6
       + a_4_10·b_4_16·b_1_1 + a_8_40·a_1_2 + a_4_10·a_5_15 + a_1_02·a_7_34
       + b_4_16·c_4_17·a_1_2 + c_4_17·a_1_2·b_1_1·a_3_6 + a_4_10·c_4_17·a_1_2
  52. a_5_14·a_5_15 + c_4_17·a_1_2·a_5_15
  53. a_4_10·b_1_3·a_5_14 + a_4_10·a_1_0·b_1_35 + a_4_10·a_6_24 + c_4_17·a_1_02·b_1_34
       + a_4_10·c_4_17·a_1_0·b_1_3
  54. b_4_16·b_1_3·a_5_14 + b_4_16·a_1_0·b_1_35 + b_4_16·a_6_24 + a_4_10·b_1_12·b_1_34
       + a_4_10·b_1_13·b_1_33 + a_4_10·b_1_14·b_1_32 + a_4_10·b_1_15·b_1_3
       + a_4_10·b_4_16·b_1_1·b_1_3 + b_1_1·a_3_63 + c_4_17·b_1_12·b_1_3·a_3_6
       + c_4_17·a_1_0·b_1_35 + a_4_10·c_4_17·b_1_32 + a_4_10·c_4_17·b_1_1·b_1_3
       + a_4_10·c_4_17·b_1_12 + a_4_10·c_4_17·a_1_2·b_1_1 + a_4_10·c_4_17·a_1_0·b_1_3
       + a_4_10·c_4_17·a_1_02
  55. a_3_8·a_7_34 + a_4_10·b_1_3·a_5_14 + a_4_10·a_1_0·b_1_35 + c_4_17·a_1_0·a_5_14
       + c_4_17·a_1_02·b_1_34 + a_4_10·c_4_17·a_1_02
  56. a_3_6·a_7_34 + c_4_17·a_1_2·b_1_12·a_3_6 + a_4_10·c_4_17·a_1_2·b_1_1
  57. a_3_8·a_7_31 + a_6_24·a_1_0·b_1_33 + a_4_10·b_1_3·a_5_14 + a_4_10·a_1_2·b_5_26
       + a_4_10·a_1_0·b_1_35 + c_4_17·a_1_02·b_1_34 + a_4_10·c_4_17·a_1_0·b_1_3
       + a_4_10·c_4_17·a_1_02
  58. b_5_262 + b_1_310 + b_1_12·b_1_33·b_5_26 + b_1_15·b_1_35 + b_1_18·b_1_32
       + b_4_16·b_1_12·b_1_34 + b_4_16·b_1_13·b_1_33 + b_4_16·b_1_15·b_1_3
       + b_4_16·b_1_16 + b_4_162·b_1_32 + b_4_162·b_1_1·b_1_3 + b_4_162·b_1_12
       + a_5_15·b_5_26 + b_1_16·b_1_3·a_3_6 + b_4_16·b_1_13·a_3_6 + a_4_10·b_1_1·b_5_26
       + a_4_10·b_1_12·b_1_34 + a_4_10·b_1_14·b_1_32 + a_4_10·b_1_15·b_1_3
       + a_4_10·b_1_16 + a_4_10·b_4_16·b_1_1·b_1_3 + a_3_6·a_7_31 + b_1_14·a_3_62
       + a_1_02·b_1_38 + a_4_10·a_1_2·b_5_26 + b_1_1·a_3_63 + a_6_24·a_1_02·b_1_32
       + c_8_66·b_1_12 + c_4_17·b_1_36 + c_4_17·b_1_1·b_1_35 + c_4_17·b_1_12·b_1_34
       + c_4_17·b_1_13·b_1_33 + c_4_17·b_1_14·b_1_32 + c_4_17·b_1_15·b_1_3
       + c_8_66·a_1_2·b_1_1 + c_4_17·b_1_3·a_5_15 + c_4_17·b_1_13·a_3_6 + c_4_17·a_1_2·b_5_26
       + a_4_10·c_4_17·b_1_1·b_1_3 + a_4_10·c_4_17·b_1_12 + c_4_17·a_1_2·a_5_15
       + c_4_17·a_1_02·b_1_34 + a_4_10·c_4_17·a_1_2·b_1_1 + c_4_172·b_1_32
       + c_4_172·a_1_2·b_1_3 + c_4_172·a_1_22 + c_4_172·a_1_02
  59. a_5_142 + a_1_02·b_1_38 + a_6_24·a_1_0·b_1_33 + a_4_10·a_1_0·b_1_35
       + a_4_10·a_1_0·a_5_14 + c_8_66·a_1_02 + c_4_17·a_1_02·b_1_34
       + a_4_10·c_4_17·a_1_02 + c_4_172·a_1_22
  60. a_5_152 + c_8_66·a_1_22 + c_4_172·a_1_22
  61. a_5_14·b_5_26 + a_1_0·b_1_39 + a_8_40·b_1_32 + a_6_24·b_1_34
       + b_4_16·b_1_12·b_1_3·a_3_6 + b_4_16·a_1_0·b_1_35 + a_4_10·b_1_13·b_1_33
       + a_4_10·b_4_16·b_1_1·b_1_3 + a_4_10·b_4_16·b_1_12 + a_5_152 + a_1_02·b_1_38
       + a_6_24·a_1_0·b_1_33 + a_4_10·a_1_0·b_1_35 + a_4_10·a_1_0·a_5_14
       + c_4_17·b_1_3·a_5_14 + c_4_17·a_1_2·b_5_26 + b_4_16·c_4_17·a_1_0·b_1_3
       + a_4_10·c_4_17·b_1_32 + a_4_10·c_4_17·b_1_1·b_1_3 + c_4_17·a_1_0·a_5_14
       + c_4_17·a_1_02·b_1_34 + a_4_10·c_4_17·a_1_02 + c_4_172·a_1_2·b_1_3
       + c_4_172·a_1_22
  62. b_5_262 + b_1_310 + b_1_12·b_1_33·b_5_26 + b_1_15·b_1_35 + b_1_18·b_1_32
       + b_4_16·b_1_12·b_1_34 + b_4_16·b_1_13·b_1_33 + b_4_16·b_1_15·b_1_3
       + b_4_16·b_1_16 + b_4_162·b_1_32 + b_4_162·b_1_1·b_1_3 + b_4_162·b_1_12
       + b_1_13·a_7_31 + b_1_16·b_1_3·a_3_6 + a_1_2·b_1_14·b_5_26 + a_8_40·b_1_12
       + b_4_16·b_1_12·b_1_3·a_3_6 + a_4_10·b_1_1·b_5_26 + a_4_10·b_1_1·b_1_35
       + a_4_10·b_1_12·b_1_34 + a_4_10·b_1_14·b_1_32 + a_4_10·b_1_15·b_1_3
       + a_4_10·b_4_16·b_1_1·b_1_3 + a_4_10·b_4_16·b_1_12 + a_3_6·a_7_31 + a_1_02·b_1_38
       + a_4_10·a_1_2·b_5_26 + c_8_66·b_1_12 + c_4_17·b_1_36 + c_4_17·b_1_1·b_1_35
       + c_4_17·b_1_12·b_1_34 + c_4_17·b_1_13·b_1_33 + c_4_17·b_1_14·b_1_32
       + c_4_17·b_1_15·b_1_3 + c_4_17·b_1_12·b_1_3·a_3_6 + a_4_10·c_4_17·b_1_1·b_1_3
       + c_4_17·a_1_2·a_5_15 + c_4_17·a_1_2·b_1_12·a_3_6 + c_4_17·a_1_02·b_1_34
       + a_4_10·c_4_17·a_1_2·b_1_1 + c_4_172·b_1_32 + c_4_172·a_1_22 + c_4_172·a_1_02
  63. b_4_16·a_1_2·b_5_26 + a_3_6·a_7_31 + a_8_40·a_1_2·b_1_1 + b_1_1·a_3_63
       + c_4_17·a_1_2·a_5_15 + a_4_10·c_4_17·a_1_2·b_1_1 + a_4_10·c_4_17·a_1_02
       + c_4_172·a_1_22
  64. a_6_24·a_5_15 + a_4_10·a_1_2·b_1_1·b_5_26 + c_4_17·a_1_2·b_1_3·a_5_15
       + a_4_10·c_4_17·a_1_2·b_1_12
  65. a_4_10·a_7_34 + c_4_17·a_6_24·a_1_0 + a_4_10·c_4_17·a_1_2·b_1_12
       + a_4_10·c_4_17·a_1_0·b_1_32 + a_4_10·c_4_17·a_1_02·b_1_3 + c_4_172·a_1_02·b_1_3
  66. b_4_16·a_7_34 + b_4_16·b_1_13·b_1_3·a_3_6 + a_4_10·b_1_1·b_1_36
       + a_4_10·b_1_12·b_1_35 + a_4_10·b_1_13·b_1_34 + a_4_10·b_1_14·b_1_33
       + a_4_10·b_4_16·b_1_33 + a_4_10·b_4_16·b_1_12·b_1_3 + a_4_10·b_4_16·b_1_13
       + a_4_10·a_1_2·b_1_1·b_5_26 + a_4_10·a_6_24·b_1_3 + a_4_10·a_6_24·a_1_0
       + c_4_17·b_1_32·a_5_14 + c_4_17·b_1_13·b_1_3·a_3_6 + a_4_10·c_4_17·b_1_1·b_1_32
       + a_4_10·c_4_17·b_1_12·b_1_3 + a_4_10·c_4_17·b_1_13 + c_4_17·b_1_1·a_3_62
       + c_4_17·a_6_24·a_1_0 + a_4_10·c_4_17·a_1_2·b_1_12 + a_4_10·c_4_17·a_1_0·b_1_32
       + c_4_172·a_1_02·b_1_3 + c_4_172·a_1_03
  67. a_4_10·a_7_31 + a_4_10·a_6_24·b_1_3 + c_4_17·a_1_2·b_1_3·a_5_15
       + a_4_10·c_4_17·a_1_2·b_1_12 + a_4_10·c_4_17·a_1_02·b_1_3 + c_4_172·a_1_22·b_1_3
  68. a_6_24·a_5_14 + a_4_10·a_1_0·b_1_36 + a_4_10·a_6_24·b_1_3 + a_6_24·a_1_02·b_1_33
       + a_4_10·a_6_24·a_1_0 + c_8_66·a_1_02·b_1_3 + c_4_17·a_6_24·a_1_0
       + a_4_10·c_4_17·a_1_2·b_1_12 + c_4_172·a_1_22·b_1_3 + c_4_172·a_1_02·b_1_3
  69. a_8_40·a_3_8 + a_4_10·a_1_2·b_1_1·b_5_26 + a_6_24·a_1_02·b_1_33
       + a_4_10·a_6_24·a_1_0 + c_4_17·a_1_02·b_1_35 + a_4_10·c_4_17·a_1_2·b_1_12
       + a_4_10·c_4_17·a_1_0·b_1_32 + a_4_10·c_4_17·a_1_02·b_1_3 + c_4_172·a_1_03
  70. a_8_40·b_1_33 + a_6_24·b_5_26 + a_6_24·b_1_35 + b_4_16·a_7_31
       + b_4_16·b_1_13·b_1_3·a_3_6 + b_4_16·a_6_24·b_1_3 + a_4_10·b_1_1·b_1_3·b_5_26
       + a_4_10·b_1_14·b_1_33 + a_4_10·b_1_15·b_1_32 + a_4_10·b_1_16·b_1_3
       + b_1_1·a_3_6·a_7_31 + a_1_02·b_1_39 + a_8_40·a_1_2·b_1_12 + a_6_24·a_1_0·b_1_34
       + a_4_10·a_1_2·b_1_1·b_5_26 + a_4_10·a_1_0·b_1_36 + c_4_17·b_1_13·b_1_3·a_3_6
       + c_4_17·a_1_2·b_1_3·b_5_26 + c_4_17·a_1_0·b_1_36 + c_4_17·a_6_24·b_1_3
       + b_4_16·c_4_17·a_1_0·b_1_32 + a_4_10·c_4_17·b_1_33
       + a_4_10·c_4_17·b_1_1·b_1_32 + a_4_10·c_4_17·b_1_12·b_1_3 + a_4_10·c_4_17·b_1_13
       + c_8_66·a_1_22·b_1_3 + c_4_17·b_1_1·a_3_62 + c_4_17·a_1_02·b_1_35
       + c_4_17·a_6_24·a_1_0 + a_4_10·c_4_17·a_1_0·b_1_32 + c_4_17·a_1_02·a_5_14
       + c_4_172·a_1_03
  71. a_8_40·b_1_33 + a_6_24·b_5_26 + a_6_24·b_1_35 + b_4_16·a_7_31
       + b_4_16·b_1_13·b_1_3·a_3_6 + b_4_16·a_6_24·b_1_3 + a_4_10·b_1_1·b_1_3·b_5_26
       + a_4_10·b_1_14·b_1_33 + a_4_10·b_1_15·b_1_32 + a_4_10·b_1_16·b_1_3
       + a_1_02·b_1_39 + a_8_40·a_3_6 + a_6_24·a_1_0·b_1_34 + a_4_10·a_1_2·b_1_1·b_5_26
       + a_4_10·a_1_0·b_1_36 + b_1_12·a_3_63 + c_4_17·b_1_13·b_1_3·a_3_6
       + c_4_17·a_1_2·b_1_3·b_5_26 + c_4_17·a_1_0·b_1_36 + c_4_17·a_6_24·b_1_3
       + b_4_16·c_4_17·a_1_0·b_1_32 + a_4_10·c_4_17·b_1_33
       + a_4_10·c_4_17·b_1_1·b_1_32 + a_4_10·c_4_17·b_1_12·b_1_3 + a_4_10·c_4_17·b_1_13
       + c_8_66·a_1_22·b_1_3 + c_4_17·a_1_2·b_1_13·a_3_6 + c_4_17·a_1_02·b_1_35
       + c_4_17·a_6_24·a_1_0 + a_4_10·c_4_17·a_1_0·b_1_32 + c_4_17·a_1_02·a_5_14
       + c_4_172·a_1_03
  72. b_1_17·b_1_3·a_3_6 + a_10_67·b_1_1 + a_8_40·b_1_33 + a_8_40·b_1_13 + a_6_24·b_5_26
       + a_6_24·b_1_35 + b_4_16·b_1_14·a_3_6 + a_4_10·b_1_32·b_5_26 + a_4_10·b_1_37
       + a_4_10·b_1_1·b_1_36 + a_4_10·b_1_12·b_5_26 + a_4_10·b_1_12·b_1_35
       + a_4_10·b_1_15·b_1_32 + a_4_10·b_1_16·b_1_3 + a_4_10·b_1_17
       + a_4_10·b_4_16·b_1_1·b_1_32 + a_4_10·b_4_16·b_1_13 + b_1_1·a_3_6·a_7_31
       + a_1_02·b_1_39 + a_6_24·a_1_0·b_1_34 + a_4_10·a_1_2·b_1_1·b_5_26
       + b_1_12·a_3_63 + a_4_10·a_6_24·a_1_0 + c_8_66·a_1_2·b_1_12
       + c_4_17·b_1_13·b_1_3·a_3_6 + c_4_17·a_1_2·b_1_1·b_5_26 + c_4_17·a_1_2·b_1_16
       + c_4_17·a_1_0·b_1_36 + c_4_17·a_6_24·b_1_3 + b_4_16·c_4_17·a_3_6
       + a_4_10·c_4_17·b_1_33 + a_4_10·c_4_17·b_1_13 + c_4_17·b_1_1·a_3_62
       + c_4_17·a_6_24·a_1_0 + a_4_10·c_4_17·a_1_02·b_1_3 + c_4_172·a_1_2·b_1_1·b_1_3
       + c_4_172·a_1_2·b_1_12 + c_4_172·a_1_22·b_1_3 + c_4_172·a_1_03
  73. a_10_67·a_1_0 + a_6_24·a_5_14 + a_6_24·a_1_02·b_1_33 + a_4_10·a_6_24·a_1_0
       + c_4_17·a_1_02·b_1_35 + a_4_10·c_4_17·a_1_2·b_1_12 + c_4_172·a_1_22·b_1_3
  74. a_8_40·b_1_33 + a_6_24·b_5_26 + a_6_24·b_1_35 + b_4_16·a_7_31
       + b_4_16·b_1_13·b_1_3·a_3_6 + b_4_16·a_6_24·b_1_3 + a_4_10·b_1_1·b_1_3·b_5_26
       + a_4_10·b_1_14·b_1_33 + a_4_10·b_1_15·b_1_32 + a_4_10·b_1_16·b_1_3
       + b_1_1·a_3_6·a_7_31 + a_1_02·b_1_39 + a_10_67·a_1_2 + a_6_24·a_1_0·b_1_34
       + a_4_10·a_1_2·b_1_1·b_5_26 + a_4_10·a_1_0·b_1_36 + b_1_12·a_3_63
       + c_4_17·b_1_13·b_1_3·a_3_6 + c_4_17·a_1_2·b_1_3·b_5_26 + c_4_17·a_1_0·b_1_36
       + c_4_17·a_6_24·b_1_3 + b_4_16·c_4_17·a_1_0·b_1_32 + a_4_10·c_4_17·b_1_33
       + a_4_10·c_4_17·b_1_1·b_1_32 + a_4_10·c_4_17·b_1_12·b_1_3 + a_4_10·c_4_17·b_1_13
       + c_8_66·a_1_22·b_1_3 + c_4_17·b_1_1·a_3_62 + c_4_17·a_1_2·b_1_3·a_5_15
       + c_4_17·a_1_02·b_1_35 + c_4_17·a_6_24·a_1_0 + a_4_10·c_4_17·a_1_2·b_1_12
       + a_4_10·c_4_17·a_1_0·b_1_32 + c_4_17·a_1_02·a_5_14 + a_4_10·c_4_17·a_1_02·b_1_3
       + c_4_172·a_1_22·b_1_3 + c_4_172·a_1_03
  75. a_5_15·a_7_34 + a_4_10·c_4_17·a_1_02·b_1_32
  76. a_5_14·a_7_31 + a_6_24·a_1_0·b_1_35 + a_6_242 + a_4_10·a_6_24·b_1_32
       + c_4_17·a_1_2·a_7_31 + c_4_17·a_6_24·a_1_0·b_1_3 + c_4_17·a_6_24·a_1_02
       + a_4_10·c_4_17·a_1_02·b_1_32 + c_4_172·a_1_03·b_1_3
  77. a_5_14·a_7_34 + a_6_24·a_1_0·b_1_35 + a_6_242 + a_4_10·a_1_0·b_1_37
       + a_6_24·a_1_02·b_1_34 + a_4_10·a_6_24·a_1_0·b_1_3 + c_8_66·a_1_0·a_3_8
       + c_4_172·a_1_02·b_1_32 + c_4_172·a_1_03·b_1_3
  78. a_6_24·a_1_0·b_1_35 + a_6_242 + a_4_10·a_1_0·b_1_37 + a_4_10·a_6_24·a_1_0·b_1_3
       + c_8_66·a_1_02·b_1_32 + c_4_172·a_1_02·b_1_32
  79. a_5_15·a_7_31 + b_1_13·a_3_63 + c_8_66·a_1_2·a_3_6 + c_4_17·a_1_2·a_7_31
       + a_4_10·c_4_17·a_1_2·b_1_13
  80. a_4_10·a_1_2·b_1_12·b_5_26 + a_4_10·a_8_40 + a_4_10·a_6_24·a_1_0·b_1_3
       + a_4_10·c_4_17·a_1_0·b_1_33 + a_4_10·c_4_17·a_1_02·b_1_32
       + c_4_172·a_1_03·b_1_3
  81. b_5_26·a_7_34 + b_1_15·a_7_31 + a_1_2·b_1_16·b_5_26 + a_8_40·b_1_14
       + b_4_16·b_1_1·a_7_31 + b_4_16·b_1_14·b_1_3·a_3_6 + b_4_16·b_1_15·a_3_6
       + b_4_16·a_1_0·b_1_37 + b_4_16·a_8_40 + b_4_16·a_6_24·b_1_32
       + a_4_10·b_1_33·b_5_26 + a_4_10·b_1_12·b_1_3·b_5_26 + a_4_10·b_1_13·b_1_35
       + a_4_10·b_1_14·b_1_34 + a_4_10·b_1_15·b_1_33 + a_4_10·b_1_16·b_1_32
       + a_4_10·b_1_17·b_1_3 + a_4_10·b_1_18 + a_4_10·b_4_16·b_1_34
       + a_4_10·b_4_16·b_1_1·b_1_33 + a_5_15·a_7_31 + a_8_40·b_1_1·a_3_6
       + a_6_24·a_1_0·b_1_35 + b_1_13·a_3_63 + a_4_10·a_6_24·a_1_0·b_1_3
       + c_4_17·b_1_3·a_7_34 + c_4_17·b_1_15·a_3_6 + c_4_17·a_1_2·b_1_1·b_1_3·b_5_26
       + c_4_17·a_1_2·b_1_12·b_5_26 + b_4_16·c_4_17·b_1_3·a_3_6 + b_4_16·c_4_17·b_1_1·a_3_6
       + a_4_10·c_4_17·b_1_34 + a_4_10·c_4_17·b_1_13·b_1_3 + a_4_10·b_4_16·c_4_17
       + c_4_17·a_1_2·a_7_31 + c_4_17·a_1_0·a_7_34 + c_4_17·a_1_02·b_1_36
       + a_4_10·c_4_17·a_1_0·b_1_33 + c_4_17·a_6_24·a_1_02
       + c_4_172·a_1_2·b_1_12·b_1_3 + c_4_172·a_1_0·b_1_33
  82. b_5_26·a_7_31 + b_5_26·a_7_34 + a_10_67·b_1_32 + a_6_24·b_1_36 + b_4_16·b_1_3·a_7_31
       + b_4_16·b_1_1·a_7_31 + b_4_16·b_1_15·a_3_6 + b_4_16·a_1_0·b_1_37
       + b_4_16·a_6_24·b_1_32 + a_4_10·b_1_33·b_5_26 + a_4_10·b_1_38
       + a_4_10·b_1_13·b_5_26 + a_4_10·b_1_17·b_1_3 + a_5_15·a_7_31 + b_1_16·a_3_62
       + a_8_40·b_1_1·a_3_6 + a_6_24·a_1_02·b_1_34 + c_8_66·b_1_1·a_3_6
       + c_8_66·a_1_2·b_1_12·b_1_3 + c_8_66·a_1_2·b_1_13 + c_8_66·a_1_0·b_1_33
       + c_4_17·b_1_3·a_7_31 + c_4_17·b_1_3·a_7_34 + c_4_17·a_1_2·b_1_1·b_1_3·b_5_26
       + c_4_17·a_6_24·b_1_32 + b_4_16·c_4_17·a_1_0·b_1_33 + a_4_10·c_4_17·b_1_34
       + a_4_10·c_4_17·b_1_14 + c_4_17·a_1_2·a_7_31 + c_4_17·a_1_2·b_1_14·a_3_6
       + c_4_17·a_1_0·a_7_34 + c_4_17·a_1_02·b_1_36 + c_4_17·a_6_24·a_1_0·b_1_3
       + a_4_10·c_4_17·a_1_2·b_1_13 + a_4_10·c_4_17·a_1_0·b_1_33
       + c_4_17·a_6_24·a_1_02 + a_4_10·c_4_17·a_1_02·b_1_32 + c_4_172·a_1_0·b_1_33
       + c_4_172·a_1_03·b_1_3
  83. b_5_26·a_7_31 + b_1_15·a_7_31 + a_1_2·b_1_16·b_5_26 + a_10_67·b_1_12
       + a_6_24·b_1_3·b_5_26 + b_4_16·b_1_14·b_1_3·a_3_6 + b_4_16·b_1_15·a_3_6
       + b_4_16·a_1_0·b_1_37 + a_4_10·b_1_38 + a_4_10·b_1_12·b_1_3·b_5_26
       + a_4_10·b_1_13·b_1_35 + a_4_10·b_1_14·b_1_34 + a_4_10·b_1_15·b_1_33
       + a_4_10·b_1_18 + a_4_10·b_4_16·b_1_12·b_1_32 + a_4_10·b_4_16·b_1_13·b_1_3
       + a_4_10·b_4_16·b_1_14 + a_4_10·b_4_162 + b_1_16·a_3_62 + a_8_40·b_1_1·a_3_6
       + a_8_40·a_1_2·b_1_13 + a_4_10·a_1_2·b_1_12·b_5_26 + a_4_10·a_1_0·b_1_37
       + a_6_24·a_1_02·b_1_34 + a_4_10·a_6_24·a_1_0·b_1_3 + c_8_66·b_1_1·a_3_6
       + c_8_66·a_1_2·b_1_12·b_1_3 + c_4_17·b_1_3·a_7_31 + c_4_17·b_1_15·a_3_6
       + c_4_17·a_1_2·b_1_1·b_1_3·b_5_26 + c_4_17·a_1_2·b_1_17 + c_4_17·a_6_24·b_1_32
       + b_4_16·c_4_17·b_1_1·a_3_6 + a_4_10·c_4_17·b_1_34 + a_4_10·c_4_17·b_1_1·b_1_33
       + a_4_10·c_4_17·b_1_12·b_1_32 + a_4_10·c_4_17·b_1_13·b_1_3
       + a_4_10·c_4_17·b_1_14 + c_4_17·b_1_12·a_3_62 + c_4_17·a_1_02·b_1_36
       + c_4_172·a_1_2·b_1_13 + c_4_172·a_1_03·b_1_3
  84. a_6_24·a_7_31 + a_6_242·b_1_3 + a_3_62·a_7_31 + a_6_242·a_1_0 + a_4_10·c_4_17·a_5_15
       + c_4_17·a_3_63 + c_4_17·a_6_24·a_1_02·b_1_3 + a_4_10·c_4_172·a_1_2
  85. a_6_24·a_7_34 + a_4_10·a_6_24·b_1_33 + a_6_242·a_1_0 + a_4_10·a_6_24·a_1_0·b_1_32
       + c_4_17·a_1_02·b_1_37 + c_4_17·a_6_24·a_1_0·b_1_32 + a_4_10·c_8_66·a_1_0
       + a_4_10·c_4_17·a_5_14 + a_4_10·c_4_17·a_1_0·b_1_34 + c_4_17·a_3_63
       + c_4_172·a_1_02·b_1_33 + a_4_10·c_4_172·a_1_2
  86. a_8_40·b_5_26 + a_6_24·b_1_32·b_5_26 + a_6_24·b_1_37 + b_4_16·b_1_12·a_7_31
       + b_4_16·b_1_16·a_3_6 + b_4_16·a_8_40·b_1_1 + a_4_10·b_1_1·b_1_33·b_5_26
       + a_4_10·b_1_12·b_1_32·b_5_26 + a_4_10·b_1_13·b_1_3·b_5_26
       + a_4_10·b_1_14·b_1_35 + a_4_10·b_1_17·b_1_32 + a_4_10·b_1_18·b_1_3
       + a_4_10·b_4_16·b_5_26 + a_4_10·b_4_16·b_1_12·b_1_33 + a_4_10·b_4_162·b_1_1
       + a_1_02·b_1_311 + a_8_40·b_1_12·a_3_6 + a_6_242·b_1_3 + a_3_62·a_7_31
       + b_1_14·a_3_63 + c_8_66·b_1_1·b_1_3·a_3_6 + c_8_66·b_1_12·a_3_6
       + c_4_17·a_1_2·b_1_13·b_5_26 + c_4_17·a_8_40·b_1_3 + c_4_17·a_8_40·b_1_1
       + c_4_17·a_6_24·b_1_33 + b_4_16·c_8_66·a_1_2 + b_4_16·c_4_17·a_5_15
       + b_4_16·c_4_17·b_1_12·a_3_6 + b_4_16·c_4_17·a_1_0·b_1_34 + a_4_10·c_8_66·b_1_1
       + a_4_10·c_4_17·b_1_35 + a_4_10·c_4_17·b_1_1·b_1_34
       + a_4_10·c_4_17·b_1_12·b_1_33 + a_4_10·c_4_17·b_1_13·b_1_32
       + a_4_10·c_4_17·b_1_14·b_1_3 + a_4_10·c_4_17·b_1_15 + a_4_10·b_4_16·c_4_17·b_1_3
       + a_4_10·b_4_16·c_4_17·b_1_1 + c_8_66·a_1_2·b_1_1·a_3_6 + c_8_66·a_1_02·b_1_33
       + c_4_17·a_1_2·b_1_15·a_3_6 + c_4_17·a_8_40·a_1_2 + c_4_17·a_6_24·a_1_0·b_1_32
       + a_4_10·c_4_17·a_5_15 + c_8_66·a_1_02·a_3_8 + c_4_17·a_3_63 + c_4_17·a_1_02·a_7_34
       + c_4_17·a_6_24·a_1_02·b_1_3 + c_4_172·b_1_1·b_1_3·a_3_6 + c_4_172·b_1_12·a_3_6
       + c_4_172·a_1_2·b_1_14 + a_4_10·c_4_172·b_1_1 + c_4_172·a_1_02·b_1_33
       + a_4_10·c_4_172·a_1_2
  87. a_8_40·a_5_15 + b_1_14·a_3_63 + c_8_66·a_1_2·b_1_1·a_3_6 + c_4_17·a_3_63
       + c_4_172·a_1_2·b_1_1·a_3_6
  88. a_8_40·a_5_14 + a_6_242·a_1_0 + a_4_10·a_6_24·a_1_0·b_1_32
       + c_4_17·a_1_02·b_1_37 + c_4_17·a_8_40·a_1_2 + c_4_17·a_6_24·a_1_0·b_1_32
       + a_4_10·c_4_17·a_1_0·b_1_34 + c_4_17·a_1_02·a_7_34 + c_4_17·a_6_24·a_1_02·b_1_3
       + c_4_172·a_1_02·b_1_33
  89. a_10_67·a_3_8 + a_6_24·a_7_34 + a_4_10·a_1_0·b_1_38 + a_3_62·a_7_31 + a_6_242·a_1_0
       + a_4_10·a_6_24·a_1_0·b_1_32 + c_8_66·a_1_02·b_1_33 + c_4_17·a_1_02·b_1_37
       + c_4_17·a_6_24·a_1_0·b_1_32 + a_4_10·c_4_17·a_1_0·b_1_34
       + c_4_172·a_1_02·b_1_33
  90. a_10_67·a_3_6 + a_8_40·b_1_12·a_3_6 + c_8_66·a_1_2·b_1_1·a_3_6
       + c_4_17·a_1_2·b_1_15·a_3_6 + c_4_17·a_8_40·a_1_2 + a_4_10·c_4_17·a_5_15
       + c_4_17·a_3_63 + a_4_10·c_4_172·a_1_2
  91. a_7_312 + a_6_242·b_1_32 + c_8_66·a_3_62
  92. a_7_342 + c_4_17·a_6_24·a_1_0·b_1_33 + a_4_10·c_4_17·a_1_0·b_1_35
       + a_4_10·c_4_17·a_1_0·a_5_14 + c_4_17·c_8_66·a_1_02 + c_4_172·a_1_02·b_1_34
       + a_4_10·c_4_172·a_1_02
  93. a_7_34·a_7_31 + a_4_10·a_6_24·b_1_34 + a_6_242·a_1_0·b_1_3
       + c_4_17·a_1_02·b_1_38 + c_4_17·a_8_40·a_1_2·b_1_1 + c_4_17·a_6_24·a_1_0·b_1_33
       + a_4_10·c_8_66·a_1_0·b_1_3 + a_4_10·c_4_17·a_1_2·b_5_26 + a_4_10·c_4_17·a_6_24
       + a_4_10·c_4_17·a_1_0·a_5_14 + c_4_172·a_1_2·b_1_12·a_3_6
       + a_4_10·c_4_172·a_1_0·b_1_3
  94. a_6_24·a_8_40 + c_4_17·a_6_24·a_1_0·b_1_33 + a_4_10·c_4_17·a_1_2·b_5_26
       + c_4_17·b_1_1·a_3_63 + a_4_10·c_4_17·a_1_0·a_5_14 + a_4_10·c_4_172·a_1_2·b_1_1
       + a_4_10·c_4_172·a_1_02
  95. a_4_10·a_10_67 + a_8_40·a_3_62 + c_4_17·a_1_02·b_1_38
       + c_4_17·a_6_24·a_1_0·b_1_33 + a_4_10·c_8_66·a_1_2·b_1_1
       + a_4_10·c_8_66·a_1_0·b_1_3 + a_4_10·c_4_17·a_1_2·b_5_26
       + a_4_10·c_4_17·a_1_0·b_1_35 + a_4_10·c_4_17·a_6_24 + a_4_10·c_4_172·a_1_2·b_1_1
       + a_4_10·c_4_172·a_1_0·b_1_3
  96. b_4_16·b_1_16·b_1_3·a_3_6 + b_4_16·a_10_67 + b_4_16·a_8_40·b_1_32
       + b_4_16·a_8_40·b_1_12 + a_4_10·b_1_1·b_1_34·b_5_26
       + a_4_10·b_1_12·b_1_33·b_5_26 + a_4_10·b_1_13·b_1_32·b_5_26
       + a_4_10·b_1_14·b_1_3·b_5_26 + a_4_10·b_1_15·b_1_35 + a_4_10·b_1_19·b_1_3
       + a_4_10·b_4_16·b_1_1·b_5_26 + a_4_10·b_4_16·b_1_12·b_1_34
       + a_4_10·b_4_16·b_1_13·b_1_33 + a_4_10·b_4_16·b_1_14·b_1_32
       + a_4_10·b_4_16·b_1_15·b_1_3 + a_4_10·b_4_16·b_1_16 + a_4_10·b_4_162·b_1_32
       + a_4_10·b_4_162·b_1_1·b_1_3 + a_7_312 + a_7_34·a_7_31 + a_6_242·b_1_32
       + a_4_10·a_1_0·b_1_39 + a_4_10·a_6_24·b_1_34 + b_1_15·a_3_63
       + c_4_17·b_1_13·a_7_31 + c_4_17·a_1_2·b_1_14·b_5_26 + c_4_17·a_1_0·b_1_39
       + c_4_17·a_8_40·b_1_32 + c_4_17·a_8_40·b_1_12 + c_4_17·a_6_24·b_1_34
       + b_4_16·c_8_66·a_1_0·b_1_3 + b_4_16·c_4_17·b_1_12·b_1_3·a_3_6
       + b_4_16·c_4_17·b_1_13·a_3_6 + b_4_16·c_4_17·a_1_0·b_1_35 + b_4_16·c_4_17·a_6_24
       + a_4_10·c_4_17·b_1_12·b_1_34 + a_4_10·c_4_17·b_1_13·b_1_33
       + a_4_10·c_4_17·b_1_14·b_1_32 + a_4_10·c_4_17·b_1_16
       + a_4_10·b_4_16·c_4_17·b_1_32 + a_4_10·b_4_16·c_4_17·b_1_1·b_1_3
       + a_4_10·b_4_16·c_4_17·b_1_12 + c_4_17·a_3_6·a_7_31 + c_4_17·b_1_14·a_3_62
       + c_4_17·a_1_02·b_1_38 + c_4_17·a_6_24·a_1_0·b_1_33 + a_4_10·c_8_66·a_1_2·b_1_1
       + a_4_10·c_8_66·a_1_0·b_1_3 + a_4_10·c_4_17·a_6_24 + c_4_17·b_1_1·a_3_63
       + c_4_17·a_6_24·a_1_02·b_1_32 + c_4_172·b_1_12·b_1_3·a_3_6
       + c_4_172·b_1_13·a_3_6 + a_4_10·c_4_172·b_1_32 + a_4_10·c_4_172·b_1_1·b_1_3
       + a_4_10·c_4_172·b_1_12 + c_4_17·c_8_66·a_1_22 + c_4_172·a_1_2·a_5_15
       + c_4_172·a_1_02·b_1_34 + a_4_10·c_4_172·a_1_2·b_1_1
       + a_4_10·c_4_172·a_1_0·b_1_3 + c_4_173·a_1_22
  97. a_8_40·a_7_34 + c_4_17·a_8_40·a_1_2·b_1_12 + a_4_10·c_4_17·a_1_2·b_1_1·b_5_26
       + a_4_10·c_4_17·a_6_24·b_1_3 + c_4_17·a_6_24·a_1_02·b_1_33
       + a_4_10·c_8_66·a_1_02·b_1_3 + a_4_10·c_4_17·a_6_24·a_1_0
       + c_4_172·a_1_02·b_1_35 + a_4_10·c_4_172·a_1_2·b_1_12
       + a_4_10·c_4_172·a_1_0·b_1_32 + c_4_172·a_1_02·a_5_14
       + a_4_10·c_4_172·a_1_02·b_1_3
  98. a_8_40·a_7_31 + a_8_40·a_7_34 + b_1_16·a_3_63 + a_8_40·b_1_1·a_3_62
       + c_8_66·b_1_1·a_3_62 + c_8_66·a_1_2·b_1_13·a_3_6 + c_4_17·a_8_40·a_3_6
       + c_4_17·a_6_24·a_1_0·b_1_34 + a_4_10·c_4_17·a_1_2·b_1_1·b_5_26
       + a_4_10·c_4_17·a_6_24·b_1_3 + c_4_17·b_1_12·a_3_63
       + c_4_17·a_6_24·a_1_02·b_1_33 + a_4_10·c_8_66·a_1_02·b_1_3
       + c_4_172·b_1_1·a_3_62 + c_4_172·a_1_2·b_1_13·a_3_6 + c_4_172·a_1_02·b_1_35
       + a_4_10·c_4_172·a_1_2·b_1_12 + a_4_10·c_4_172·a_1_0·b_1_32
       + c_4_172·a_1_02·a_5_14 + a_4_10·c_4_172·a_1_02·b_1_3
  99. b_1_18·a_7_31 + a_1_2·b_1_19·b_5_26 + a_10_67·b_5_26 + a_8_40·b_1_17
       + a_6_24·b_1_34·b_5_26 + a_6_24·b_1_39 + b_4_16·a_1_0·b_1_310
       + b_4_16·a_8_40·b_1_13 + b_4_16·a_6_24·b_1_35 + a_4_10·b_1_12·b_1_34·b_5_26
       + a_4_10·b_1_13·b_1_33·b_5_26 + a_4_10·b_1_16·b_1_35 + a_4_10·b_1_17·b_1_34
       + a_4_10·b_1_18·b_1_33 + a_4_10·b_1_19·b_1_32 + a_4_10·b_1_110·b_1_3
       + a_4_10·b_1_111 + a_4_10·b_4_16·b_1_32·b_5_26 + a_4_10·b_4_16·b_1_37
       + a_4_10·b_4_16·b_1_1·b_1_3·b_5_26 + a_4_10·b_4_16·b_1_1·b_1_36
       + a_4_10·b_4_16·b_1_12·b_1_35 + a_4_10·b_4_16·b_1_13·b_1_34
       + a_4_10·b_4_16·b_1_14·b_1_33 + a_4_10·b_4_162·b_1_13 + a_6_242·b_1_33
       + a_4_10·a_1_0·b_1_310 + a_4_10·a_6_24·b_1_35 + a_8_40·b_1_1·a_3_62
       + a_6_242·a_1_0·b_1_32 + a_4_10·a_6_24·a_1_0·b_1_34 + c_8_66·b_1_13·b_1_3·a_3_6
       + c_8_66·b_1_14·a_3_6 + c_8_66·a_1_2·b_1_1·b_5_26 + c_8_66·a_1_0·b_1_36
       + c_4_17·b_1_14·a_7_31 + c_4_17·b_1_18·a_3_6 + c_4_17·a_1_2·b_1_15·b_5_26
       + c_4_17·a_1_0·b_1_310 + c_4_17·a_10_67·b_1_3 + c_4_17·a_6_24·b_5_26
       + c_4_17·a_6_24·b_1_35 + b_4_16·c_8_66·a_3_6 + b_4_16·c_4_17·a_1_0·b_1_36
       + a_4_10·c_8_66·b_1_1·b_1_32 + a_4_10·c_8_66·b_1_12·b_1_3 + a_4_10·c_4_17·b_1_37
       + a_4_10·c_4_17·b_1_1·b_1_36 + a_4_10·c_4_17·b_1_13·b_1_34
       + a_4_10·c_4_17·b_1_15·b_1_32 + a_4_10·c_4_17·b_1_16·b_1_3
       + a_4_10·b_4_16·c_4_17·b_1_33 + c_8_66·a_1_2·b_1_3·a_5_15 + c_8_66·a_1_02·b_1_35
       + c_4_17·a_1_2·b_1_17·a_3_6 + c_4_17·a_1_02·b_1_39 + c_4_17·a_6_24·a_1_0·b_1_34
       + a_4_10·c_8_66·a_1_2·b_1_12 + a_4_10·c_4_17·a_6_24·b_1_3 + c_4_17·b_1_12·a_3_63
       + c_4_17·c_8_66·a_1_2·b_1_12 + c_4_172·a_1_2·b_1_3·b_5_26
       + c_4_172·a_1_2·b_1_1·b_5_26 + c_4_172·a_1_2·b_1_16 + c_4_172·a_1_0·b_1_36
       + c_4_172·a_6_24·b_1_3 + c_4_17·c_8_66·a_1_02·b_1_3 + c_4_172·a_1_2·b_1_3·a_5_15
       + c_4_172·a_1_2·b_1_13·a_3_6 + c_4_172·a_1_02·b_1_35 + c_4_17·c_8_66·a_1_03
       + c_4_173·a_1_2·b_1_1·b_1_3 + c_4_173·a_1_22·b_1_3 + c_4_173·a_1_02·b_1_3
       + c_4_173·a_1_03
  100. a_10_67·a_5_15 + b_1_16·a_3_63 + a_8_40·b_1_1·a_3_62 + c_8_66·a_1_2·b_1_13·a_3_6
       + a_4_10·c_4_17·a_1_2·b_1_1·b_5_26 + c_4_17·b_1_12·a_3_63
       + a_4_10·c_8_66·a_1_02·b_1_3 + c_4_17·c_8_66·a_1_22·b_1_3
       + c_4_172·a_1_2·b_1_3·a_5_15 + c_4_172·a_1_2·b_1_13·a_3_6
       + a_4_10·c_4_172·a_1_2·b_1_12 + c_4_173·a_1_22·b_1_3
  101. a_10_67·a_5_14 + a_8_40·a_7_34 + a_4_10·a_1_0·b_1_310 + a_4_10·a_6_24·b_1_35
       + a_6_242·a_1_0·b_1_32 + c_8_66·a_1_02·b_1_35 + a_6_24·c_8_66·a_1_0
       + c_4_17·a_1_02·b_1_39 + a_4_10·c_4_17·a_1_2·b_1_1·b_5_26
       + a_4_10·c_4_17·a_1_0·b_1_36 + a_4_10·c_4_17·a_6_24·b_1_3 + c_4_17·b_1_12·a_3_63
       + c_4_17·a_6_24·a_1_02·b_1_33 + a_4_10·c_8_66·a_1_02·b_1_3
       + c_4_172·a_1_2·b_1_3·a_5_15 + c_4_172·a_1_02·b_1_35
       + a_4_10·c_4_172·a_1_0·b_1_32 + c_4_172·a_1_02·a_5_14 + c_4_173·a_1_22·b_1_3
  102. a_8_402 + c_8_66·b_1_12·a_3_62 + c_4_172·b_1_12·a_3_62
       + c_4_172·a_1_02·b_1_36
  103. a_6_24·a_10_67 + a_6_242·a_1_0·b_1_33 + a_4_10·a_6_242
       + a_6_24·c_8_66·a_1_0·b_1_3 + c_4_17·a_1_02·b_1_310 + a_4_10·c_8_66·a_1_2·b_1_13
       + a_4_10·c_8_66·a_1_0·b_1_33 + a_4_10·c_4_17·a_1_0·b_1_37
       + c_4_17·a_6_24·a_1_02·b_1_34 + a_4_10·c_8_66·a_1_02·b_1_32
       + a_4_10·c_4_17·a_6_24·a_1_0·b_1_3 + c_4_17·c_8_66·a_1_02·b_1_32
       + c_4_172·a_6_24·a_1_0·b_1_3 + a_4_10·c_4_172·a_1_0·b_1_33
       + c_4_173·a_1_02·b_1_32
  104. a_10_67·a_7_34 + c_4_17·a_8_40·a_1_2·b_1_14 + a_4_10·c_8_66·a_5_14
       + a_4_10·c_8_66·a_1_0·b_1_34 + a_4_10·c_4_17·a_6_24·b_1_33
       + c_4_17·a_3_62·a_7_31 + c_4_17·b_1_14·a_3_63 + c_4_17·a_6_242·a_1_0
       + a_4_10·c_4_17·a_6_24·a_1_0·b_1_32 + c_4_17·c_8_66·a_1_02·b_1_33
       + c_4_172·a_1_02·b_1_37 + a_4_10·c_4_17·c_8_66·a_1_2 + a_4_10·c_4_17·c_8_66·a_1_0
       + a_4_10·c_4_172·a_1_0·b_1_34
  105. a_10_67·a_7_31 + b_1_18·a_3_63 + a_6_242·a_1_0·b_1_34 + c_8_66·b_1_13·a_3_62
       + c_8_66·a_1_2·b_1_15·a_3_6 + a_8_40·c_8_66·a_1_2 + a_6_24·c_8_66·a_1_0·b_1_32
       + c_4_17·a_1_02·b_1_311 + c_4_17·a_8_40·b_1_12·a_3_6
       + a_4_10·c_8_66·a_1_0·b_1_34 + a_4_10·c_4_17·a_1_0·b_1_38
       + c_4_17·c_8_66·a_1_02·b_1_33 + c_4_172·b_1_13·a_3_62 + c_4_172·a_8_40·a_1_2
       + c_4_172·a_6_24·a_1_0·b_1_32 + a_4_10·c_4_17·c_8_66·a_1_2
       + a_4_10·c_4_172·a_1_0·b_1_34 + c_4_172·a_6_24·a_1_02·b_1_3
       + c_4_173·a_1_2·b_1_1·a_3_6 + c_4_173·a_1_02·b_1_33
  106. a_8_40·a_10_67 + a_4_10·a_6_242·b_1_32 + c_8_66·b_1_14·a_3_62
       + a_8_40·c_8_66·a_1_2·b_1_1 + c_4_17·a_8_40·a_1_2·b_1_15
       + a_4_10·c_4_17·a_1_0·b_1_39 + a_4_10·c_4_17·a_6_24·b_1_34
       + a_6_24·c_8_66·a_1_02·b_1_32 + c_4_17·a_8_40·a_3_62
       + c_4_17·a_6_242·a_1_0·b_1_3 + c_4_17·c_8_66·a_1_2·b_1_12·a_3_6
       + c_4_17·c_8_66·a_1_02·b_1_34 + c_4_172·b_1_14·a_3_62
       + c_4_172·a_1_02·b_1_38 + c_4_172·a_6_24·a_1_0·b_1_33
       + a_4_10·c_4_17·c_8_66·a_1_2·b_1_1 + a_4_10·c_4_172·a_1_2·b_5_26
       + a_4_10·c_4_17·c_8_66·a_1_02 + a_4_10·c_4_172·a_1_0·a_5_14
       + c_4_173·a_1_2·b_1_12·a_3_6 + c_4_173·a_1_02·b_1_34
  107. a_10_672 + c_8_66·b_1_16·a_3_62 + c_4_17·a_1_02·b_1_314
       + c_4_17·a_6_242·b_1_34 + c_8_662·a_1_02·b_1_32 + c_4_172·b_1_16·a_3_62
       + c_4_172·a_1_02·b_1_310 + c_4_172·a_6_242 + c_4_174·a_1_02·b_1_32

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 20.
  • 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_17, a Duflot regular element of degree 4
    2. c_8_66, a Duflot regular element of degree 8
    3. b_1_32 + b_1_1·b_1_3 + b_1_12, an element of degree 2
    4. b_1_32, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 8, 10, 12].
  • 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 2

  1. a_1_0 → 0, an element of degree 1
  2. a_1_2 → 0, an element of degree 1
  3. b_1_1 → 0, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. a_3_8 → 0, an element of degree 3
  6. a_3_6 → 0, an element of degree 3
  7. a_4_10 → 0, an element of degree 4
  8. b_4_16 → 0, an element of degree 4
  9. c_4_17 → c_1_04, an element of degree 4
  10. a_5_14 → 0, an element of degree 5
  11. a_5_15 → 0, an element of degree 5
  12. b_5_26 → 0, an element of degree 5
  13. a_6_24 → 0, an element of degree 6
  14. a_7_34 → 0, an element of degree 7
  15. a_7_31 → 0, an element of degree 7
  16. a_8_40 → 0, an element of degree 8
  17. c_8_66 → c_1_18 + c_1_08, an element of degree 8
  18. a_10_67 → 0, an element of degree 10

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

  1. a_1_0 → 0, an element of degree 1
  2. a_1_2 → 0, an element of degree 1
  3. b_1_1 → c_1_2, an element of degree 1
  4. b_1_3 → c_1_3, an element of degree 1
  5. a_3_8 → 0, an element of degree 3
  6. a_3_6 → 0, an element of degree 3
  7. a_4_10 → 0, an element of degree 4
  8. b_4_16 → c_1_2·c_1_33 + c_1_23·c_1_3 + c_1_0·c_1_2·c_1_32 + c_1_02·c_1_32, an element of degree 4
  9. c_4_17 → c_1_02·c_1_22 + c_1_04, an element of degree 4
  10. a_5_14 → 0, an element of degree 5
  11. a_5_15 → 0, an element of degree 5
  12. b_5_26 → c_1_35 + c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_24·c_1_3 + c_1_12·c_1_2·c_1_32
       + c_1_14·c_1_2 + 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_02·c_1_23 + c_1_04·c_1_3 + c_1_04·c_1_2, an element of degree 5
  13. a_6_24 → 0, an element of degree 6
  14. a_7_34 → 0, an element of degree 7
  15. a_7_31 → 0, an element of degree 7
  16. a_8_40 → 0, an element of degree 8
  17. c_8_66 → c_1_38 + c_1_2·c_1_37 + c_1_27·c_1_3 + c_1_12·c_1_2·c_1_35 + c_1_14·c_1_34
       + c_1_14·c_1_2·c_1_33 + c_1_18 + c_1_0·c_1_2·c_1_36 + c_1_0·c_1_24·c_1_33
       + c_1_0·c_1_25·c_1_32 + c_1_02·c_1_36 + c_1_02·c_1_23·c_1_33
       + c_1_02·c_1_25·c_1_3 + c_1_04·c_1_22·c_1_32 + c_1_04·c_1_23·c_1_3
       + c_1_04·c_1_24 + c_1_08, an element of degree 8
  18. a_10_67 → 0, an element of degree 10

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