Cohomology of group number 1653 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
    t8  −  t7  +  t5  +  1
    (t  −  1)4 · (t2  +  1)2 · (t4  +  1)
  • 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 16 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_10, a nilpotent element of degree 3
  6. a_3_11, a nilpotent element of degree 3
  7. c_4_16, a Duflot regular element of degree 4
  8. a_5_23, a nilpotent element of degree 5
  9. b_5_22, an element of degree 5
  10. b_5_24, an element of degree 5
  11. a_6_28, a nilpotent element of degree 6
  12. b_6_35, an element of degree 6
  13. a_7_35, a nilpotent element of degree 7
  14. c_8_58, a Duflot regular element of degree 8
  15. b_9_76, an element of degree 9
  16. a_10_68, 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 78 minimal relations of maximal degree 20:

  1. a_1_02
  2. a_1_0·b_1_1 + a_1_22
  3. a_1_22·b_1_1
  4. a_1_2·b_1_12 + a_1_0·b_1_32
  5. a_1_0·a_3_10
  6. a_1_2·a_3_10 + a_1_0·a_3_11
  7. a_1_0·b_1_34
  8. b_1_32·a_3_10 + b_1_12·a_3_11 + b_1_12·a_3_10
  9. a_3_102
  10. a_3_10·a_3_11 + c_4_16·a_1_0·a_1_2
  11. a_1_2·b_1_1·b_1_34 + a_3_112 + a_1_0·b_1_32·a_3_11 + c_4_16·a_1_22
  12. a_3_10·a_3_11 + a_1_0·a_5_23 + a_1_0·b_1_32·a_3_11 + a_1_22·b_1_3·a_3_11
  13. a_1_0·b_5_22
  14. a_1_2·b_5_22
  15. a_1_0·b_5_24 + a_1_2·a_5_23 + a_1_2·b_1_1·b_1_3·a_3_11 + a_1_22·b_1_3·a_3_11
  16. b_1_1·a_5_23 + b_1_12·b_1_3·a_3_11 + b_1_12·b_1_3·a_3_10 + a_1_2·b_5_24
       + a_1_0·b_1_32·a_3_11
  17. b_1_32·b_5_22 + b_1_12·b_5_24 + b_1_32·a_5_23 + b_1_1·b_1_33·a_3_11
       + a_1_2·b_1_33·a_3_11 + a_1_2·b_1_1·b_1_32·a_3_11 + c_4_16·b_1_13
       + c_4_16·a_1_2·b_1_32
  18. a_1_2·b_1_1·b_5_24 + a_1_0·b_1_33·a_3_11 + a_1_22·b_1_32·a_3_11
       + c_4_16·a_1_0·b_1_32
  19. a_1_0·b_1_33·a_3_11 + a_6_28·a_1_0 + a_1_22·b_1_32·a_3_11
  20. a_1_2·b_1_3·a_5_23 + a_1_2·b_1_1·b_1_32·a_3_11 + a_1_22·b_5_24
       + a_1_0·b_1_33·a_3_11 + a_6_28·a_1_2 + c_4_16·a_1_22·b_1_3 + c_4_16·a_1_0·a_1_2·b_1_3
       + c_4_16·a_1_23
  21. b_6_35·a_1_0 + a_1_2·b_1_3·a_5_23 + a_1_2·b_1_1·b_1_32·a_3_11 + c_4_16·a_1_0·b_1_32
       + c_4_16·a_1_22·b_1_3 + c_4_16·a_1_23
  22. b_1_32·a_5_23 + b_1_1·b_1_33·a_3_11 + b_1_13·b_1_3·a_3_11 + b_1_13·b_1_3·a_3_10
       + a_1_2·b_1_3·b_5_24 + b_6_35·a_1_2 + a_1_2·b_1_33·a_3_11 + a_1_22·b_5_24
       + a_1_0·b_1_33·a_3_11 + a_1_22·b_1_32·a_3_11 + c_4_16·a_1_2·b_1_1·b_1_3
       + c_4_16·a_1_0·a_1_2·b_1_3 + c_4_16·a_1_23
  23. a_3_10·a_5_23 + c_4_16·a_1_0·a_3_11 + c_4_16·a_1_23·b_1_3
  24. a_3_11·b_5_22 + a_3_10·b_5_24 + b_1_14·b_1_3·a_3_11 + b_1_15·a_3_11 + b_1_15·a_3_10
       + a_6_28·b_1_12 + a_3_11·a_5_23 + c_4_16·b_1_1·a_3_10 + c_4_16·a_1_2·a_3_11
       + c_4_16·a_1_23·b_1_3
  25. a_3_11·b_5_22 + a_3_10·b_5_24 + a_3_10·b_5_22 + a_3_11·a_5_23 + a_6_28·a_1_22
       + c_4_16·b_1_1·a_3_10 + c_4_16·a_1_2·a_3_11 + c_4_16·a_1_23·b_1_3
  26. a_3_11·b_5_22 + a_3_10·b_5_22 + b_1_12·b_1_33·a_3_11 + b_1_13·b_1_32·a_3_11
       + b_1_15·a_3_11 + b_1_15·a_3_10 + b_6_35·a_1_2·b_1_3 + a_6_28·b_1_32
       + a_1_2·b_1_34·a_3_11 + a_6_28·a_1_2·b_1_1 + c_4_16·a_1_2·b_1_33
       + c_4_16·a_1_0·b_1_33 + c_4_16·a_1_22·b_1_32
  27. a_1_0·a_7_35 + c_4_16·a_1_0·a_3_11 + c_4_16·a_1_23·b_1_3
  28. a_3_11·a_5_23 + a_1_2·a_7_35 + c_4_16·a_1_22·b_1_32 + c_4_16·a_1_23·b_1_3
  29. a_6_28·a_3_10
  30. b_1_3·a_3_11·b_5_24 + b_1_32·a_7_35 + b_1_12·b_1_34·a_3_11 + b_1_14·b_1_32·a_3_11
       + b_1_16·a_3_11 + b_1_16·a_3_10 + b_6_35·a_3_11 + b_6_35·a_3_10 + b_6_35·a_1_2·b_1_32
       + a_6_28·b_1_33 + a_1_2·b_1_35·a_3_11 + a_6_28·a_3_11 + a_3_113
       + c_4_16·b_1_1·b_1_3·a_3_11 + c_4_16·b_1_12·a_3_11 + c_4_16·b_1_12·a_3_10
       + c_4_16·a_1_2·b_1_1·b_1_33 + c_4_16·a_1_2·b_1_1·a_3_11
  31. b_1_12·a_7_35 + b_1_12·b_1_34·a_3_11 + b_1_13·b_1_33·a_3_11 + b_1_16·a_3_11
       + b_1_16·a_3_10 + b_6_35·a_3_10 + b_6_35·a_1_2·b_1_32 + a_6_28·b_1_33
       + a_1_2·b_1_3·a_7_35 + a_1_2·b_1_35·a_3_11 + c_4_16·b_1_12·a_3_10
       + c_4_16·a_1_2·b_1_34 + c_4_16·a_1_2·b_1_3·a_3_11 + c_4_16·a_1_22·b_1_33
       + c_4_16·a_1_22·a_3_11
  32. a_1_2·b_1_3·a_7_35 + a_1_2·b_1_1·a_7_35 + a_6_28·a_3_11 + c_4_16·a_1_2·b_1_3·a_3_11
       + c_4_16·a_1_2·b_1_1·a_3_11 + c_4_16·a_1_22·b_1_33 + c_4_16·a_1_0·b_1_3·a_3_11
       + c_4_16·a_1_22·a_3_11
  33. a_5_232 + c_4_162·a_1_22
  34. b_5_222 + c_4_16·b_1_16
  35. b_5_22·b_5_24 + a_5_23·b_5_22 + c_4_16·b_1_1·b_5_22 + c_4_16·b_1_14·b_1_32
       + c_4_16·a_3_112 + c_4_16·a_1_0·b_1_32·a_3_11 + c_4_162·a_1_22
  36. a_5_23·b_5_22 + b_1_13·b_1_34·a_3_11 + b_1_14·b_1_33·a_3_11 + b_1_16·b_1_3·a_3_11
       + b_1_16·b_1_3·a_3_10 + b_6_35·a_1_2·b_1_1·b_1_32 + a_6_28·b_1_1·b_1_33
       + b_1_3·a_3_113 + c_4_16·a_3_112 + c_4_16·a_1_0·b_1_32·a_3_11
       + c_4_16·a_1_22·b_1_3·a_3_11 + c_4_162·a_1_22
  37. a_3_10·a_7_35 + c_4_16·a_1_22·b_1_3·a_3_11 + c_4_162·a_1_0·a_1_2
  38. a_5_23·b_5_22 + b_1_13·b_1_34·a_3_11 + b_1_14·b_1_33·a_3_11 + b_1_16·b_1_3·a_3_11
       + b_1_16·b_1_3·a_3_10 + a_6_28·b_1_1·b_1_33 + a_3_11·a_7_35 + b_1_3·a_3_113
       + c_4_16·a_3_112 + c_4_16·a_1_2·a_5_23 + c_4_16·a_1_2·b_1_32·a_3_11
       + c_4_16·a_1_0·b_1_32·a_3_11 + c_4_162·a_1_22
  39. a_5_23·b_5_24 + b_1_1·b_1_32·a_7_35 + b_1_14·b_1_33·a_3_11 + b_1_15·b_1_32·a_3_11
       + b_1_16·b_1_3·a_3_11 + b_1_16·b_1_3·a_3_10 + b_1_17·a_3_11 + b_1_17·a_3_10
       + b_6_35·b_1_1·a_3_11 + b_6_35·b_1_1·a_3_10 + c_4_16·b_1_12·b_1_3·a_3_11
       + c_4_16·b_1_12·b_1_3·a_3_10 + c_4_16·b_1_13·a_3_11 + c_4_16·b_1_13·a_3_10
       + c_8_58·a_1_0·a_1_2 + c_4_16·a_1_22·b_1_3·a_3_11 + c_4_162·a_1_2·b_1_1
       + c_4_162·a_1_0·a_1_2
  40. b_5_242 + c_4_16·b_1_12·b_1_34 + c_8_58·a_1_22 + c_4_16·a_1_22·b_1_3·a_3_11
       + c_4_162·b_1_12 + c_4_162·a_1_22
  41. a_1_0·b_9_76 + c_4_16·a_1_2·a_5_23 + c_4_16·a_1_2·b_1_1·b_1_3·a_3_11
       + c_4_16·a_1_0·b_1_32·a_3_11 + c_4_16·a_1_22·b_1_3·a_3_11 + c_4_162·a_1_0·b_1_3
       + c_4_162·a_1_0·a_1_2
  42. a_1_2·b_9_76 + b_6_35·a_1_2·b_1_33 + a_6_28·b_1_3·a_3_11 + a_6_28·b_1_1·a_3_11
       + c_4_16·a_1_2·b_5_24 + c_4_16·a_3_112 + c_4_16·a_1_2·b_1_32·a_3_11
       + c_4_16·a_1_22·b_1_3·a_3_11 + c_4_162·a_1_2·b_1_3
  43. b_1_14·b_1_34·a_3_11 + b_1_18·a_3_11 + b_1_18·a_3_10 + a_6_28·b_5_22
       + a_6_28·b_1_12·b_1_33 + a_6_28·b_1_13·b_1_32 + a_6_28·b_1_14·b_1_3
       + c_4_16·b_1_14·a_3_10 + c_4_16·a_1_22·b_1_32·a_3_11
  44. a_6_28·a_5_23 + a_6_28·b_1_1·b_1_3·a_3_11 + c_4_16·a_6_28·a_1_2 + c_4_16·a_6_28·a_1_0
  45. b_6_35·a_5_23 + b_6_35·b_1_1·b_1_3·a_3_11 + b_6_35·b_1_1·b_1_3·a_3_10 + a_6_28·a_5_23
       + a_6_28·b_1_32·a_3_11 + c_4_16·a_1_2·b_1_3·b_5_24 + c_4_16·a_1_2·b_1_36
       + c_8_58·a_1_0·a_1_2·b_1_3 + c_4_16·b_1_3·a_3_112 + c_4_16·a_1_2·b_1_33·a_3_11
       + c_4_16·a_6_28·a_1_2 + c_4_16·a_6_28·a_1_0 + c_4_162·a_1_2·b_1_32
       + c_4_162·a_1_2·b_1_1·b_1_3 + c_4_162·a_1_22·b_1_3 + c_4_162·a_1_23
  46. b_1_12·b_1_36·a_3_11 + b_1_16·b_1_32·a_3_11 + b_1_18·a_3_11 + b_1_18·a_3_10
       + b_6_35·a_5_23 + b_6_35·b_1_1·b_1_3·a_3_11 + b_6_35·b_1_1·b_1_3·a_3_10
       + b_6_35·a_1_2·b_1_34 + a_6_28·b_5_24 + a_6_28·b_1_35 + a_6_28·b_1_1·b_1_34
       + a_6_28·b_1_12·b_1_33 + b_1_3·a_3_11·a_7_35 + a_1_2·b_1_37·a_3_11 + a_6_28·a_5_23
       + b_1_32·a_3_113 + c_4_16·b_1_14·a_3_11 + c_4_16·b_1_14·a_3_10
       + c_4_16·a_1_2·b_1_3·b_5_24 + c_4_16·a_6_28·b_1_1 + c_4_16·b_1_3·a_3_112
       + c_4_16·a_1_22·b_5_24 + c_4_16·a_6_28·a_1_2 + c_8_58·a_1_23
       + c_4_16·a_1_22·b_1_32·a_3_11 + c_4_162·a_1_2·b_1_32
       + c_4_162·a_1_2·b_1_1·b_1_3 + c_4_162·a_1_0·a_1_2·b_1_3
  47. b_1_32·b_9_76 + b_1_36·b_5_24 + b_1_1·b_1_35·b_5_24 + b_1_13·b_1_33·b_5_24
       + b_1_15·b_1_3·b_5_24 + b_1_16·b_5_24 + b_6_35·b_5_24 + b_6_35·b_1_35
       + b_6_35·b_1_1·b_1_34 + b_6_35·b_1_12·b_1_33 + b_1_1·b_1_37·a_3_11
       + b_1_13·b_1_35·a_3_11 + b_1_14·b_1_34·a_3_11 + b_1_16·b_1_32·a_3_11
       + b_6_35·a_5_23 + b_6_35·b_1_32·a_3_11 + b_6_35·b_1_1·b_1_3·a_3_11
       + b_6_35·b_1_1·b_1_3·a_3_10 + b_6_35·a_1_2·b_1_34 + a_6_28·b_5_24 + a_6_28·b_1_35
       + a_6_28·b_1_12·b_1_33 + a_6_28·b_1_13·b_1_32 + b_1_3·a_3_11·a_7_35
       + a_6_28·a_5_23 + a_6_28·b_1_32·a_3_11 + b_1_32·a_3_113 + c_4_16·b_1_12·b_5_24
       + c_4_16·b_1_12·b_1_35 + c_4_16·b_1_14·b_1_33 + c_4_16·b_1_16·b_1_3
       + c_4_16·b_1_17 + c_4_16·b_6_35·b_1_1 + c_8_58·a_1_0·b_1_32
       + c_4_16·b_1_13·b_1_3·a_3_11 + c_4_16·b_1_13·b_1_3·a_3_10 + c_4_16·a_1_2·b_1_36
       + c_4_16·b_6_35·a_1_2 + c_4_16·a_6_28·b_1_1 + c_8_58·a_1_22·b_1_3
       + c_4_16·b_1_3·a_3_112 + c_4_16·a_1_2·b_1_33·a_3_11 + c_4_16·a_6_28·a_1_0
       + c_4_16·a_1_22·b_1_32·a_3_11 + c_4_162·b_1_33 + c_4_162·b_1_1·b_1_32
       + c_4_162·b_1_13 + c_4_162·a_1_2·b_1_32 + c_4_162·a_1_0·b_1_32
       + c_4_162·a_1_22·b_1_3 + c_4_162·a_1_0·a_1_2·b_1_3 + c_4_162·a_1_23
  48. b_1_12·b_9_76 + b_1_12·b_1_34·b_5_24 + b_1_13·b_1_33·b_5_24
       + b_1_15·b_1_3·b_5_24 + b_1_15·b_1_3·b_5_22 + b_1_16·b_5_22 + b_6_35·b_5_22
       + b_6_35·b_1_12·b_1_33 + b_6_35·b_1_13·b_1_32 + b_6_35·b_1_14·b_1_3
       + b_1_13·b_1_35·a_3_11 + b_1_14·b_1_34·a_3_11 + b_1_15·b_1_33·a_3_11
       + b_1_16·b_1_32·a_3_11 + b_1_17·b_1_3·a_3_10 + b_1_18·a_3_11
       + b_6_35·b_1_1·b_1_3·a_3_10 + b_6_35·b_1_12·a_3_11 + a_6_28·b_1_13·b_1_32
       + a_6_28·b_1_15 + c_4_16·b_1_12·b_5_22 + c_4_16·b_1_14·b_1_33
       + c_4_16·b_1_16·b_1_3 + c_4_16·b_1_14·a_3_10 + c_4_16·a_1_2·b_1_3·b_5_24
       + c_4_16·a_1_2·b_1_36 + c_4_16·b_6_35·a_1_2 + c_4_16·b_1_3·a_3_112
       + c_4_16·a_1_2·b_1_1·b_1_32·a_3_11 + c_4_16·a_1_22·b_5_24 + c_4_16·a_6_28·a_1_0
       + c_4_16·a_1_22·b_1_32·a_3_11 + c_4_162·b_1_12·b_1_3 + c_4_162·b_1_13
       + c_4_162·a_1_2·b_1_32 + c_4_162·a_1_2·b_1_1·b_1_3 + c_4_162·a_1_0·b_1_32
       + c_4_162·a_1_22·b_1_3 + c_4_162·a_1_0·a_1_2·b_1_3 + c_4_162·a_1_23
  49. b_6_35·a_5_23 + b_6_35·b_1_1·b_1_3·a_3_11 + b_6_35·b_1_1·b_1_3·a_3_10 + a_10_68·a_1_0
       + a_6_28·a_5_23 + a_6_28·b_1_32·a_3_11 + c_4_16·a_1_2·b_1_3·b_5_24
       + c_4_16·a_1_2·b_1_36 + c_4_16·b_1_3·a_3_112 + c_4_16·a_1_2·b_1_33·a_3_11
       + c_4_16·a_6_28·a_1_2 + c_4_16·a_6_28·a_1_0 + c_4_162·a_1_2·b_1_32
       + c_4_162·a_1_2·b_1_1·b_1_3 + c_4_162·a_1_22·b_1_3
  50. b_1_12·b_1_36·a_3_11 + b_1_16·b_1_32·a_3_11 + b_1_18·a_3_11 + b_1_18·a_3_10
       + b_6_35·a_5_23 + b_6_35·b_1_1·b_1_3·a_3_11 + b_6_35·b_1_1·b_1_3·a_3_10
       + b_6_35·a_1_2·b_1_34 + a_6_28·b_5_24 + a_6_28·b_1_35 + a_6_28·b_1_1·b_1_34
       + a_6_28·b_1_12·b_1_33 + b_1_3·a_3_11·a_7_35 + a_1_2·b_1_37·a_3_11 + a_10_68·a_1_2
       + a_6_28·a_5_23 + b_1_32·a_3_113 + c_4_16·b_1_14·a_3_11 + c_4_16·b_1_14·a_3_10
       + c_4_16·a_1_2·b_1_3·b_5_24 + c_4_16·a_6_28·b_1_1 + c_8_58·a_1_22·b_1_3
       + c_4_16·b_1_3·a_3_112 + c_4_16·a_1_2·b_1_1·b_1_32·a_3_11 + c_4_16·a_6_28·a_1_2
       + c_4_16·a_6_28·a_1_0 + c_4_162·a_1_2·b_1_32 + c_4_162·a_1_2·b_1_1·b_1_3
       + c_4_162·a_1_23
  51. a_6_282
  52. a_5_23·a_7_35 + c_4_16·a_1_2·b_1_34·a_3_11 + c_4_16·a_1_2·b_1_1·b_1_33·a_3_11
       + c_4_162·a_1_2·a_3_11 + c_4_162·a_1_22·b_1_32 + c_4_162·a_1_23·b_1_3
  53. b_5_22·a_7_35 + b_1_17·b_1_32·a_3_11 + b_1_18·b_1_3·a_3_11 + b_1_18·b_1_3·a_3_10
       + b_6_35·b_1_12·b_1_3·a_3_11 + b_6_35·b_1_13·a_3_11 + b_6_35·b_1_13·a_3_10
       + a_6_28·b_1_1·b_5_22 + a_6_28·b_1_15·b_1_3 + a_6_28·b_6_35 + a_6_28·b_1_33·a_3_11
       + c_4_16·b_1_14·b_1_3·a_3_10 + c_4_16·b_1_15·a_3_11 + c_4_16·a_1_2·b_1_37
       + c_4_16·b_6_35·a_1_2·b_1_3 + c_4_16·a_6_28·b_1_12 + c_4_16·a_1_2·b_1_34·a_3_11
       + c_4_16·a_1_2·b_1_1·b_1_33·a_3_11 + c_4_16·a_6_28·a_1_2·b_1_1
       + c_8_58·a_1_23·b_1_3 + c_4_162·a_1_2·b_1_33 + c_4_162·a_1_0·b_1_33
       + c_4_162·a_1_22·b_1_32
  54. b_1_12·b_1_35·b_5_24 + b_1_15·b_1_32·b_5_24 + b_1_16·b_1_3·b_5_22
       + b_1_17·b_5_24 + b_6_35·b_1_12·b_1_34 + b_6_35·b_1_14·b_1_32 + b_6_352
       + b_5_22·a_7_35 + b_1_16·b_1_33·a_3_11 + b_1_18·b_1_3·a_3_11 + b_1_18·b_1_3·a_3_10
       + b_1_19·a_3_11 + b_6_35·b_1_12·b_1_3·a_3_11 + b_6_35·b_1_12·b_1_3·a_3_10
       + b_6_35·b_1_13·a_3_11 + b_6_35·b_1_13·a_3_10 + a_6_28·b_1_1·b_5_24
       + a_6_28·b_1_1·b_1_35 + a_6_28·b_1_12·b_1_34 + a_6_28·b_1_14·b_1_32
       + a_6_28·b_1_15·b_1_3 + a_6_28·b_6_35 + b_6_35·a_3_112 + a_6_28·b_1_33·a_3_11
       + a_6_28·b_1_1·b_1_32·a_3_11 + b_1_33·a_3_113 + c_8_58·b_1_14 + c_4_16·b_1_38
       + c_4_16·b_1_13·b_1_35 + c_4_16·b_1_16·b_1_32 + c_4_16·b_1_14·b_1_3·a_3_10
       + c_4_16·a_1_2·b_1_37 + c_4_16·b_6_35·a_1_2·b_1_3 + c_8_58·a_1_22·b_1_32
       + c_4_16·b_1_32·a_3_112 + c_4_16·a_1_2·b_1_34·a_3_11
       + c_4_16·a_1_2·b_1_1·b_1_33·a_3_11 + c_4_16·a_6_28·a_1_2·b_1_1
       + c_4_16·a_6_28·a_1_22 + c_4_162·b_1_34 + c_4_162·b_1_14
       + c_4_162·a_1_2·b_1_33 + c_4_162·a_1_0·b_1_33 + c_4_162·a_1_23·b_1_3
  55. a_3_10·b_9_76 + b_1_16·b_1_33·a_3_11 + b_1_18·b_1_3·a_3_10 + a_6_28·b_1_3·b_5_24
       + a_6_28·b_1_3·b_5_22 + a_6_28·b_1_14·b_1_32 + a_6_28·b_1_15·b_1_3
       + a_6_28·b_1_16 + a_6_28·b_6_35 + a_6_28·b_1_33·a_3_11
       + c_4_16·b_1_13·b_1_32·a_3_11 + c_4_16·a_1_2·b_1_37 + c_4_16·b_6_35·a_1_2·b_1_3
       + c_4_16·a_6_28·b_1_1·b_1_3 + c_4_16·a_6_28·b_1_12 + c_4_16·b_1_32·a_3_112
       + c_4_16·a_1_2·a_7_35 + c_4_162·b_1_3·a_3_10 + c_4_162·b_1_1·a_3_10
       + c_4_162·a_1_2·b_1_33 + c_4_162·a_1_0·b_1_33 + c_4_162·a_1_2·a_3_11
       + c_4_162·a_1_22·b_1_32 + c_4_162·a_1_0·a_3_11
  56. b_5_24·a_7_35 + b_5_22·a_7_35 + a_3_11·b_9_76 + b_1_35·a_7_35 + b_1_1·b_1_34·a_7_35
       + b_1_16·b_1_33·a_3_11 + b_1_18·b_1_3·a_3_11 + b_1_19·a_3_11 + b_1_19·a_3_10
       + b_6_35·b_1_12·b_1_3·a_3_10 + b_6_35·b_1_13·a_3_11 + b_6_35·b_1_13·a_3_10
       + a_6_28·b_1_3·b_5_24 + a_6_28·b_1_1·b_5_24 + a_6_28·b_1_1·b_5_22
       + a_6_28·b_1_1·b_1_35 + a_6_28·b_1_12·b_1_34 + a_6_28·b_1_13·b_1_33
       + a_6_28·b_1_14·b_1_32 + a_6_28·b_1_16 + a_6_28·b_1_1·b_1_32·a_3_11
       + c_4_16·b_1_1·a_7_35 + c_4_16·b_1_1·b_1_34·a_3_11 + c_4_16·b_1_13·b_1_32·a_3_11
       + c_4_16·b_1_15·a_3_10 + c_4_16·a_1_2·b_1_37 + c_4_16·b_6_35·a_1_2·b_1_1
       + c_4_16·a_6_28·b_1_1·b_1_3 + c_4_16·a_6_28·b_1_12 + c_8_58·a_1_0·a_3_11
       + c_4_16·a_1_2·b_1_1·b_1_33·a_3_11 + c_4_162·b_1_3·a_3_11 + c_4_162·b_1_1·a_3_11
       + c_4_162·a_1_2·b_1_1·b_1_32 + c_4_162·a_1_2·a_3_11 + c_4_162·a_1_22·b_1_32
       + c_4_162·a_1_0·a_3_11
  57. b_5_24·a_7_35 + b_1_1·b_1_34·a_7_35 + b_1_18·b_1_3·a_3_11 + b_1_18·b_1_3·a_3_10
       + a_10_68·b_1_32 + b_6_35·b_1_1·b_1_32·a_3_11 + b_6_35·b_1_12·b_1_3·a_3_11
       + b_6_35·b_1_12·b_1_3·a_3_10 + b_6_35·a_1_2·b_1_35 + a_6_28·b_1_3·b_5_22
       + a_6_28·b_1_36 + a_6_28·b_1_1·b_5_22 + a_6_28·b_1_12·b_1_34
       + a_6_28·b_1_15·b_1_3 + b_1_36·a_3_112 + a_6_28·b_1_1·b_1_32·a_3_11
       + b_1_33·a_3_113 + c_8_58·a_1_2·b_1_33 + c_4_16·a_3_11·b_5_24
       + c_4_16·b_1_1·a_7_35 + c_4_16·b_1_12·b_1_33·a_3_11 + c_4_16·b_1_13·b_1_32·a_3_11
       + c_4_16·b_1_14·b_1_3·a_3_10 + c_4_16·b_1_15·a_3_11 + c_4_16·a_1_2·b_1_37
       + c_4_16·b_6_35·a_1_2·b_1_3 + c_4_16·a_6_28·b_1_32 + c_8_58·a_1_22·b_1_32
       + c_8_58·a_1_0·a_3_11 + c_4_16·a_1_2·b_1_34·a_3_11
       + c_4_16·a_1_2·b_1_1·b_1_33·a_3_11 + c_4_16·a_6_28·a_1_2·b_1_1
       + c_4_162·b_1_1·a_3_11 + c_4_162·a_1_2·b_1_33 + c_4_162·a_1_2·b_1_1·b_1_32
       + c_4_162·a_1_0·a_3_11
  58. b_1_16·b_1_33·a_3_11 + b_1_19·a_3_10 + a_10_68·b_1_12
       + b_6_35·b_1_12·b_1_3·a_3_11 + b_6_35·b_1_12·b_1_3·a_3_10 + b_6_35·b_1_13·a_3_11
       + a_6_28·b_1_3·b_5_22 + a_6_28·b_1_1·b_5_24 + a_6_28·b_1_1·b_5_22
       + a_6_28·b_1_12·b_1_34 + a_6_28·b_1_14·b_1_32 + a_6_28·b_1_15·b_1_3
       + a_6_28·b_6_35 + a_6_28·b_1_33·a_3_11 + c_8_58·a_1_0·b_1_33
       + c_4_16·b_1_12·b_1_33·a_3_11 + c_4_16·b_1_13·b_1_32·a_3_11
       + c_4_16·b_1_15·a_3_10 + c_4_16·a_1_2·b_1_37 + c_4_16·a_6_28·b_1_32
       + c_4_16·a_1_2·b_1_34·a_3_11 + c_4_16·a_1_2·b_1_1·b_1_33·a_3_11
       + c_4_16·a_6_28·a_1_2·b_1_1 + c_4_162·a_1_22·b_1_32
  59. a_6_28·a_7_35 + c_4_16·a_1_2·b_1_35·a_3_11 + c_4_16·a_6_28·a_3_11 + c_4_16·a_3_113
       + c_4_162·a_1_22·a_3_11
  60. a_10_68·a_3_10 + c_8_58·a_1_0·b_1_3·a_3_11 + c_4_162·a_1_22·a_3_11
  61. b_1_1·b_1_35·a_7_35 + b_1_110·a_3_10 + a_10_68·b_1_33 + a_10_68·b_1_13
       + b_6_35·a_7_35 + b_6_35·b_1_1·b_1_33·a_3_11 + b_6_35·b_1_14·a_3_11
       + b_6_35·a_1_2·b_1_36 + a_6_28·b_1_32·b_5_24 + a_6_28·b_1_37
       + a_6_28·b_1_1·b_1_3·b_5_22 + a_6_28·b_1_12·b_1_35 + a_6_28·b_1_13·b_1_34
       + a_6_28·b_1_15·b_1_32 + a_6_28·b_1_16·b_1_3 + a_6_28·b_6_35·b_1_1
       + b_1_37·a_3_112 + a_3_112·a_7_35 + b_1_34·a_3_113 + c_8_58·b_1_12·a_3_10
       + c_8_58·a_1_2·b_1_34 + c_4_16·b_1_32·a_7_35 + c_4_16·b_1_36·a_3_11
       + c_4_16·b_1_12·b_1_34·a_3_11 + c_4_16·b_1_13·b_1_33·a_3_11
       + c_4_16·b_1_14·b_1_32·a_3_11 + c_4_16·b_1_16·a_3_11 + c_4_16·a_1_2·b_1_38
       + c_4_16·b_6_35·a_3_11 + c_4_16·a_6_28·b_1_33 + c_4_16·a_6_28·b_1_13
       + c_8_58·a_1_0·b_1_3·a_3_11 + c_4_16·a_1_2·b_1_35·a_3_11 + c_4_16·a_1_2·b_1_1·a_7_35
       + c_4_162·b_1_32·a_3_11 + c_4_162·b_1_12·a_3_10 + c_4_162·a_1_2·b_1_1·b_1_33
       + c_4_162·a_1_2·b_1_1·a_3_11 + c_4_162·a_1_0·b_1_3·a_3_11 + c_4_162·a_1_22·a_3_11
  62. a_10_68·a_3_11 + b_1_34·a_3_113 + c_8_58·a_1_2·b_1_3·a_3_11
       + c_4_16·a_1_2·b_1_1·a_7_35 + c_8_58·a_1_22·a_3_11 + c_4_16·a_3_113
       + c_4_162·a_1_0·b_1_3·a_3_11
  63. a_7_352 + c_4_16·b_1_34·a_3_112 + c_4_162·a_3_112
  64. b_5_24·b_9_76 + b_6_35·b_1_33·b_5_24 + b_6_35·b_1_1·b_1_32·b_5_24
       + b_6_35·b_1_12·b_1_3·b_5_24 + a_10_68·b_1_34 + a_10_68·b_1_1·b_1_33
       + a_10_68·b_1_12·b_1_32 + b_6_35·b_1_1·a_7_35 + b_6_35·b_1_12·b_1_33·a_3_11
       + b_6_35·b_1_13·b_1_32·a_3_11 + b_6_35·a_1_2·b_1_37 + a_6_28·b_1_38
       + a_6_28·b_1_1·b_1_37 + a_6_28·b_1_12·b_1_3·b_5_24 + a_6_28·b_1_12·b_1_36
       + a_6_28·b_1_14·b_1_34 + a_6_28·b_1_15·b_1_33 + a_6_28·b_1_17·b_1_3
       + b_1_38·a_3_112 + b_6_35·b_1_32·a_3_112 + b_1_35·a_3_113
       + c_4_16·b_1_1·b_9_76 + c_4_16·b_1_1·b_1_34·b_5_24 + c_4_16·b_1_12·b_1_38
       + c_4_16·b_1_13·b_1_37 + c_4_16·b_1_15·b_1_35 + c_4_16·b_1_17·b_1_33
       + c_4_16·b_1_18·b_1_32 + c_4_16·b_6_35·b_1_1·b_1_33
       + c_4_16·b_6_35·b_1_13·b_1_3 + c_8_58·b_1_13·a_3_10 + c_8_58·a_1_2·b_1_35
       + c_4_16·b_1_33·a_7_35 + c_4_16·b_1_1·b_1_32·a_7_35 + c_4_16·b_1_1·b_1_36·a_3_11
       + c_4_16·b_1_12·b_1_35·a_3_11 + c_4_16·b_1_14·b_1_33·a_3_11
       + c_4_16·b_1_15·b_1_32·a_3_11 + c_4_16·b_1_17·a_3_10 + c_4_16·a_1_2·b_1_39
       + c_4_16·b_6_35·b_1_3·a_3_11 + c_4_16·b_6_35·b_1_3·a_3_10
       + c_4_16·b_6_35·b_1_1·a_3_11 + c_4_16·a_6_28·b_1_13·b_1_3 + c_8_58·a_3_112
       + c_4_16·a_3_11·a_7_35 + c_4_16·a_6_28·b_1_3·a_3_11 + c_4_16·a_6_28·b_1_1·a_3_11
       + c_8_58·a_1_22·b_1_3·a_3_11 + c_4_16·b_1_3·a_3_113 + c_4_162·b_1_3·b_5_24
       + c_4_162·b_1_1·b_5_24 + c_4_162·b_1_12·b_1_34 + c_4_162·b_1_14·b_1_32
       + c_4_162·b_1_1·b_1_32·a_3_11 + c_4_162·b_1_12·b_1_3·a_3_11
       + c_4_162·b_1_12·b_1_3·a_3_10 + c_4_162·b_1_13·a_3_10 + c_4_162·a_1_2·b_5_24
       + c_4_162·a_1_2·b_1_35 + c_4_162·a_1_2·a_5_23 + c_4_162·a_1_2·b_1_32·a_3_11
       + c_4_162·a_1_2·b_1_1·b_1_3·a_3_11 + c_4_162·a_1_0·b_1_32·a_3_11
       + c_4_163·b_1_1·b_1_3 + c_4_163·b_1_12 + c_4_163·a_1_2·b_1_1 + c_4_163·a_1_22
  65. b_5_24·b_9_76 + b_5_22·b_9_76 + b_6_35·b_1_33·b_5_24 + b_6_35·b_1_1·b_1_32·b_5_24
       + b_6_35·b_1_12·b_1_3·b_5_22 + b_6_35·b_1_13·b_5_24 + a_10_68·b_1_34
       + a_10_68·b_1_13·b_1_3 + b_6_35·a_3_11·b_5_24 + b_6_35·b_1_3·a_7_35
       + b_6_35·b_1_12·b_1_33·a_3_11 + b_6_35·a_1_2·b_1_37 + a_6_28·b_1_38
       + a_6_28·b_1_12·b_1_3·b_5_24 + a_6_28·b_1_12·b_1_3·b_5_22 + a_6_28·b_1_13·b_5_22
       + a_6_28·b_1_13·b_1_35 + a_6_28·b_1_14·b_1_34 + a_6_28·b_1_16·b_1_32
       + a_6_28·b_1_17·b_1_3 + a_6_28·b_1_18 + a_6_28·b_6_35·b_1_32
       + a_6_28·b_6_35·b_1_12 + b_1_38·a_3_112 + a_6_28·b_1_35·a_3_11
       + b_1_3·a_3_112·a_7_35 + b_1_35·a_3_113 + c_4_16·b_1_1·b_9_76
       + c_4_16·b_1_1·b_1_34·b_5_24 + c_4_16·b_1_12·b_1_38
       + c_4_16·b_1_13·b_1_32·b_5_24 + c_4_16·b_1_13·b_1_37 + c_4_16·b_1_14·b_1_36
       + c_4_16·b_1_18·b_1_32 + c_4_16·b_1_19·b_1_3 + c_4_16·b_1_110
       + c_4_16·b_6_35·b_1_1·b_1_33 + c_8_58·b_1_12·b_1_3·a_3_10 + c_8_58·a_1_2·b_1_35
       + c_4_16·b_1_33·a_7_35 + c_4_16·b_1_37·a_3_11 + c_4_16·b_1_12·b_1_35·a_3_11
       + c_4_16·b_1_13·b_1_34·a_3_11 + c_4_16·b_1_14·b_1_33·a_3_11
       + c_4_16·b_1_15·b_1_32·a_3_11 + c_4_16·b_1_16·b_1_3·a_3_10 + c_4_16·b_1_17·a_3_11
       + c_4_16·b_1_17·a_3_10 + c_4_16·a_1_2·b_1_39 + c_4_16·b_6_35·b_1_3·a_3_11
       + c_4_16·b_6_35·b_1_1·a_3_11 + c_4_16·a_6_28·b_1_34
       + c_4_16·a_6_28·b_1_12·b_1_32 + c_4_16·a_6_28·b_1_14
       + c_8_58·a_1_0·b_1_32·a_3_11 + c_4_16·a_3_11·a_7_35 + c_8_58·a_1_22·b_1_3·a_3_11
       + c_4_16·b_1_3·a_3_113 + c_4_162·b_1_3·b_5_24 + c_4_162·b_1_3·b_5_22
       + c_4_162·b_1_1·b_5_24 + c_4_162·b_1_1·b_5_22 + c_4_162·b_1_12·b_1_34
       + c_4_162·b_1_16 + c_4_162·b_1_33·a_3_11 + c_4_162·b_1_12·b_1_3·a_3_10
       + c_4_162·a_1_2·b_5_24 + c_4_16·c_8_58·a_1_22 + c_4_162·a_1_2·a_5_23
       + c_4_162·a_1_2·b_1_32·a_3_11 + c_4_162·a_1_0·b_1_32·a_3_11
       + c_4_162·a_1_22·b_1_3·a_3_11 + c_4_163·b_1_1·b_1_3 + c_4_163·b_1_12
       + c_4_163·a_1_2·b_1_1 + c_4_163·a_1_22
  66. a_5_23·b_9_76 + b_1_111·a_3_10 + a_10_68·b_1_34 + a_10_68·b_1_1·b_1_33
       + a_10_68·b_1_14 + b_6_35·a_3_11·b_5_24 + b_6_35·b_1_1·b_1_34·a_3_11
       + b_6_35·b_1_12·b_1_33·a_3_11 + b_6_35·b_1_13·b_1_32·a_3_11
       + b_6_35·b_1_15·a_3_10 + b_6_35·a_1_2·b_1_37 + a_6_28·b_1_38
       + a_6_28·b_1_1·b_1_32·b_5_24 + a_6_28·b_1_1·b_1_37 + a_6_28·b_1_12·b_1_3·b_5_22
       + a_6_28·b_1_13·b_5_24 + a_6_28·b_1_13·b_5_22 + a_6_28·b_1_15·b_1_33
       + a_6_28·b_1_16·b_1_32 + a_6_28·b_1_17·b_1_3 + a_6_28·b_6_35·b_1_32
       + a_6_28·b_6_35·b_1_12 + b_1_38·a_3_112 + b_6_35·b_1_32·a_3_112
       + b_1_35·a_3_113 + c_8_58·a_1_2·b_1_35 + c_4_16·b_1_33·a_7_35
       + c_4_16·b_1_1·b_1_32·a_7_35 + c_4_16·b_1_12·b_1_35·a_3_11
       + c_4_16·b_1_15·b_1_32·a_3_11 + c_4_16·b_1_16·b_1_3·a_3_11
       + c_4_16·b_1_16·b_1_3·a_3_10 + c_4_16·b_1_17·a_3_10 + c_4_16·a_1_2·b_1_39
       + c_4_16·b_6_35·b_1_3·a_3_11 + c_4_16·b_6_35·b_1_3·a_3_10
       + c_4_16·b_6_35·b_1_1·a_3_10 + c_4_16·a_6_28·b_1_34 + c_8_58·a_3_112
       + c_4_16·a_3_11·a_7_35 + c_4_16·b_1_34·a_3_112 + c_4_16·a_1_2·b_1_36·a_3_11
       + c_4_16·a_6_28·b_1_3·a_3_11 + c_8_58·a_1_22·b_1_3·a_3_11 + c_4_16·b_1_3·a_3_113
       + c_4_162·b_1_3·a_5_23 + c_4_162·b_1_13·a_3_11 + c_4_162·b_1_13·a_3_10
       + c_4_16·c_8_58·a_1_22 + c_4_16·c_8_58·a_1_0·a_1_2
       + c_4_162·a_1_2·b_1_1·b_1_3·a_3_11 + c_4_162·a_1_0·b_1_32·a_3_11
       + c_4_163·a_1_2·b_1_1 + c_4_163·a_1_0·a_1_2
  67. b_6_35·b_1_12·b_1_34·a_3_11 + b_6_35·b_1_16·a_3_11 + b_6_35·b_1_16·a_3_10
       + a_6_28·b_9_76 + a_6_28·b_1_34·b_5_24 + a_6_28·b_1_1·b_1_33·b_5_24
       + a_6_28·b_1_13·b_1_3·b_5_24 + a_6_28·b_1_13·b_1_3·b_5_22 + a_6_28·b_1_14·b_5_22
       + a_6_28·b_1_36·a_3_11 + c_4_16·a_1_2·b_1_310 + c_4_16·b_6_35·b_1_12·a_3_10
       + c_4_16·b_6_35·a_1_2·b_1_34 + c_4_16·a_6_28·b_5_22
       + c_4_16·a_6_28·b_1_12·b_1_33 + c_4_16·a_6_28·b_1_14·b_1_3
       + c_4_16·b_1_35·a_3_112 + c_4_16·a_1_2·b_1_37·a_3_11
       + c_4_16·a_6_28·b_1_1·b_1_3·a_3_11 + c_4_16·b_1_32·a_3_113
       + c_4_162·a_1_2·b_1_36 + c_4_162·a_6_28·b_1_3 + c_4_162·a_6_28·b_1_1
       + c_4_16·c_8_58·a_1_0·a_1_2·b_1_3 + c_4_162·b_1_3·a_3_112
       + c_4_162·a_1_2·b_1_1·b_1_32·a_3_11 + c_4_162·a_6_28·a_1_0
       + c_4_16·c_8_58·a_1_23 + c_4_162·a_1_22·b_1_32·a_3_11 + c_4_163·a_1_22·b_1_3
  68. b_6_35·b_9_76 + b_6_35·b_1_34·b_5_24 + b_6_35·b_1_1·b_1_33·b_5_24
       + b_6_35·b_1_12·b_1_32·b_5_24 + b_6_35·b_1_13·b_1_3·b_5_24
       + b_6_35·b_1_13·b_1_3·b_5_22 + b_6_35·b_1_14·b_5_24 + b_6_35·b_1_14·b_5_22
       + b_6_352·b_1_33 + b_6_352·b_1_1·b_1_32 + b_6_352·b_1_12·b_1_3 + a_10_68·b_5_22
       + b_6_35·b_1_1·b_1_35·a_3_11 + b_6_35·b_1_12·b_1_34·a_3_11
       + b_6_35·b_1_13·b_1_33·a_3_11 + b_6_35·b_1_15·b_1_3·a_3_11
       + b_6_35·b_1_15·b_1_3·a_3_10 + b_6_35·b_1_16·a_3_10 + b_6_352·a_3_11
       + b_6_352·a_3_10 + a_6_28·b_1_1·b_1_33·b_5_24 + a_6_28·b_1_12·b_1_32·b_5_24
       + a_6_28·b_1_13·b_1_3·b_5_24 + a_6_28·b_1_14·b_5_22 + a_6_28·b_6_35·b_1_1·b_1_32
       + a_6_28·b_1_36·a_3_11 + c_8_58·b_1_12·b_5_22 + c_4_16·b_1_36·b_5_24
       + c_4_16·b_1_14·b_1_37 + c_4_16·b_1_16·b_5_22 + c_4_16·b_1_17·b_1_34
       + c_4_16·b_1_19·b_1_32 + c_4_16·b_1_110·b_1_3 + c_4_16·b_6_35·b_5_22
       + c_4_16·b_6_35·b_1_12·b_1_33 + c_4_16·b_6_35·b_1_13·b_1_32
       + c_4_16·b_6_35·b_1_14·b_1_3 + c_4_16·b_6_35·b_1_15 + c_8_58·b_1_13·b_1_3·a_3_10
       + c_8_58·b_1_14·a_3_10 + c_4_16·b_1_16·b_1_32·a_3_11 + c_4_16·b_1_17·b_1_3·a_3_11
       + c_4_16·b_1_17·b_1_3·a_3_10 + c_4_16·a_6_28·b_5_24 + c_4_16·a_6_28·b_1_35
       + c_4_16·a_6_28·b_1_1·b_1_34 + c_4_16·a_6_28·b_1_12·b_1_33
       + c_4_16·a_6_28·b_1_14·b_1_3 + c_4_16·b_1_3·a_3_11·a_7_35
       + c_4_16·a_1_2·b_1_37·a_3_11 + c_4_16·a_6_28·b_1_32·a_3_11
       + c_4_16·b_1_32·a_3_113 + c_4_162·b_1_32·b_5_24 + c_4_162·b_1_1·b_1_36
       + c_4_162·b_1_12·b_5_22 + c_4_162·b_6_35·b_1_3 + c_4_162·b_6_35·b_1_1
       + c_4_16·c_8_58·a_1_0·b_1_32 + c_4_162·b_1_12·b_1_32·a_3_11
       + c_4_162·b_1_13·b_1_3·a_3_10 + c_4_162·b_1_14·a_3_11 + c_4_162·b_1_14·a_3_10
       + c_4_162·a_1_2·b_1_36 + c_4_162·b_6_35·a_1_2 + c_4_162·a_6_28·b_1_1
       + c_4_16·c_8_58·a_1_22·b_1_3 + c_4_16·c_8_58·a_1_0·a_1_2·b_1_3
       + c_4_162·a_1_2·b_1_1·b_1_32·a_3_11 + c_4_162·a_1_22·b_5_24
       + c_4_162·a_6_28·a_1_2 + c_4_163·b_1_1·b_1_32 + c_4_163·a_1_0·b_1_32
       + c_4_163·a_1_23
  69. b_6_35·b_9_76 + b_6_35·b_1_34·b_5_24 + b_6_35·b_1_1·b_1_33·b_5_24
       + b_6_35·b_1_12·b_1_32·b_5_24 + b_6_35·b_1_13·b_1_3·b_5_24
       + b_6_35·b_1_13·b_1_3·b_5_22 + b_6_35·b_1_14·b_5_24 + b_6_35·b_1_14·b_5_22
       + b_6_352·b_1_33 + b_6_352·b_1_1·b_1_32 + b_6_352·b_1_12·b_1_3
       + a_10_68·b_1_12·b_1_33 + a_10_68·b_1_13·b_1_32 + a_10_68·b_1_14·b_1_3
       + b_6_35·b_1_1·b_1_35·a_3_11 + b_6_35·b_1_13·b_1_33·a_3_11
       + b_6_35·b_1_15·b_1_3·a_3_11 + b_6_35·b_1_15·b_1_3·a_3_10 + b_6_35·b_1_16·a_3_11
       + b_6_352·a_3_11 + b_6_352·a_3_10 + a_6_28·b_1_12·b_1_37 + a_6_28·b_1_13·b_1_36
       + a_6_28·b_1_14·b_5_24 + a_6_28·b_1_14·b_5_22 + a_6_28·b_1_14·b_1_35
       + a_6_28·b_1_16·b_1_33 + a_6_28·b_1_17·b_1_32 + a_6_28·b_1_19
       + a_6_28·b_6_35·b_1_33 + a_6_28·b_6_35·b_1_13 + b_6_35·a_3_113
       + c_8_58·b_1_12·b_5_22 + c_4_16·b_1_36·b_5_24 + c_4_16·b_1_14·b_1_37
       + c_4_16·b_1_16·b_5_22 + c_4_16·b_1_17·b_1_34 + c_4_16·b_1_19·b_1_32
       + c_4_16·b_1_110·b_1_3 + c_4_16·b_6_35·b_5_22 + c_4_16·b_6_35·b_1_12·b_1_33
       + c_4_16·b_6_35·b_1_13·b_1_32 + c_4_16·b_6_35·b_1_14·b_1_3
       + c_4_16·b_6_35·b_1_15 + c_8_58·b_1_13·b_1_3·a_3_10 + c_8_58·b_1_14·a_3_10
       + c_4_16·b_1_16·b_1_32·a_3_11 + c_4_16·b_1_17·b_1_3·a_3_11
       + c_4_16·b_1_17·b_1_3·a_3_10 + c_4_16·a_1_2·b_1_310 + c_4_16·b_6_35·b_1_12·a_3_10
       + c_4_16·b_6_35·a_1_2·b_1_34 + c_4_16·a_6_28·b_5_22 + c_4_16·a_6_28·b_1_35
       + c_4_16·a_6_28·b_1_1·b_1_34 + c_4_16·a_6_28·b_1_12·b_1_33
       + c_4_16·a_6_28·b_1_15 + c_4_16·b_1_35·a_3_112 + c_4_16·a_1_2·b_1_37·a_3_11
       + c_4_16·a_6_28·b_1_1·b_1_3·a_3_11 + c_4_16·b_1_32·a_3_113
       + c_4_162·b_1_32·b_5_24 + c_4_162·b_1_1·b_1_36 + c_4_162·b_1_12·b_5_22
       + c_4_162·b_6_35·b_1_3 + c_4_162·b_6_35·b_1_1 + c_4_16·c_8_58·a_1_0·b_1_32
       + c_4_162·b_1_12·b_1_32·a_3_11 + c_4_162·b_1_13·b_1_3·a_3_10
       + c_4_162·b_1_14·a_3_11 + c_4_162·b_1_14·a_3_10 + c_4_162·b_6_35·a_1_2
       + c_4_16·c_8_58·a_1_22·b_1_3 + c_4_162·a_1_2·b_1_33·a_3_11
       + c_4_162·a_1_2·b_1_1·b_1_32·a_3_11 + c_4_162·a_6_28·a_1_2 + c_4_162·a_6_28·a_1_0
       + c_4_16·c_8_58·a_1_23 + c_4_163·b_1_1·b_1_32 + c_4_163·a_1_0·b_1_32
       + c_4_163·a_1_22·b_1_3 + c_4_163·a_1_0·a_1_2·b_1_3
  70. a_10_68·a_5_23 + c_8_58·a_1_2·b_1_1·b_1_32·a_3_11 + c_8_58·a_1_22·b_5_24
       + a_6_28·c_8_58·a_1_2 + a_6_28·c_8_58·a_1_0 + c_4_16·a_6_28·b_1_1·b_1_3·a_3_11
       + c_4_16·c_8_58·a_1_22·b_1_3 + c_4_16·c_8_58·a_1_0·a_1_2·b_1_3
       + c_4_162·a_1_2·b_1_1·b_1_32·a_3_11 + c_4_162·a_6_28·a_1_0
       + c_4_163·a_1_0·a_1_2·b_1_3 + c_4_163·a_1_23
  71. a_10_68·b_5_24 + b_6_35·b_1_15·b_1_3·a_3_11 + b_6_35·b_1_15·b_1_3·a_3_10
       + b_6_35·b_1_16·a_3_11 + b_6_35·b_1_16·a_3_10 + b_6_352·a_3_11
       + a_6_28·b_1_1·b_1_33·b_5_24 + a_6_28·b_1_12·b_1_32·b_5_24
       + a_6_28·b_1_13·b_1_3·b_5_24 + a_6_28·b_1_13·b_1_3·b_5_22 + a_6_28·b_1_14·b_5_24
       + a_6_28·b_1_14·b_5_22 + a_6_28·b_6_35·b_1_33 + a_6_28·b_6_35·b_1_1·b_1_32
       + a_6_28·b_1_36·a_3_11 + c_8_58·b_1_14·a_3_11 + c_8_58·a_1_2·b_1_3·b_5_24
       + c_4_16·b_1_38·a_3_11 + c_4_16·b_1_13·b_1_35·a_3_11
       + c_4_16·b_1_16·b_1_32·a_3_11 + c_4_16·b_1_17·b_1_3·a_3_11 + c_4_16·b_1_18·a_3_11
       + c_4_16·b_1_18·a_3_10 + c_4_16·a_1_2·b_1_310 + c_4_16·a_10_68·b_1_1
       + c_4_16·b_6_35·b_1_12·a_3_11 + c_4_16·b_6_35·b_1_12·a_3_10
       + c_4_16·b_6_35·a_1_2·b_1_34 + c_4_16·a_6_28·b_5_24
       + c_4_16·a_6_28·b_1_13·b_1_32 + c_4_16·a_6_28·b_1_14·b_1_3
       + c_4_16·a_6_28·b_1_15 + c_8_58·a_1_22·b_5_24 + c_4_16·b_1_3·a_3_11·a_7_35
       + c_4_16·b_1_35·a_3_112 + c_4_16·a_6_28·b_1_32·a_3_11
       + c_8_58·a_1_22·b_1_32·a_3_11 + c_4_16·c_8_58·a_1_2·b_1_1·b_1_3
       + c_4_162·b_1_34·a_3_11 + c_4_162·b_1_12·b_1_32·a_3_11 + c_4_162·b_1_14·a_3_10
       + c_4_162·a_1_2·b_1_36 + c_4_162·a_6_28·b_1_1 + c_4_16·c_8_58·a_1_0·a_1_2·b_1_3
       + c_4_162·a_1_2·b_1_33·a_3_11 + c_4_162·a_1_2·b_1_1·b_1_32·a_3_11
       + c_4_162·a_1_22·b_5_24 + c_4_162·a_6_28·a_1_2 + c_4_162·a_6_28·a_1_0
       + c_4_163·a_1_22·b_1_3 + c_4_163·a_1_23
  72. a_7_35·b_9_76 + b_6_35·b_1_16·b_1_3·a_3_11 + b_6_35·b_1_17·a_3_11
       + b_6_35·b_1_17·a_3_10 + b_6_352·b_1_3·a_3_11 + b_6_352·b_1_1·a_3_11
       + b_6_352·b_1_1·a_3_10 + a_6_28·b_1_1·b_9_76 + a_6_28·b_1_13·b_1_32·b_5_24
       + a_6_28·b_1_15·b_5_24 + a_6_28·b_1_15·b_5_22 + a_6_28·b_6_35·b_1_13·b_1_3
       + a_6_28·b_6_35·b_1_14 + c_8_58·b_1_14·b_1_3·a_3_11 + c_8_58·b_1_15·a_3_11
       + c_8_58·b_1_15·a_3_10 + a_6_28·c_8_58·b_1_12 + c_4_16·b_1_35·a_7_35
       + c_4_16·b_1_1·b_1_34·a_7_35 + c_4_16·b_6_35·b_1_33·a_3_11
       + c_4_16·b_6_35·b_1_12·b_1_3·a_3_11 + c_4_16·b_6_35·b_1_13·a_3_11
       + c_4_16·a_6_28·b_1_36 + c_4_16·a_6_28·b_1_1·b_1_35
       + c_4_16·a_6_28·b_1_12·b_1_34 + c_4_16·a_6_28·b_1_13·b_1_33
       + c_4_16·a_6_28·b_1_14·b_1_32 + c_4_16·a_6_28·b_1_16
       + c_4_16·a_1_2·b_1_38·a_3_11 + c_4_16·b_6_35·a_3_112
       + c_4_16·a_6_28·b_1_33·a_3_11 + c_4_16·a_6_28·b_1_1·b_1_32·a_3_11
       + c_4_162·a_3_11·b_5_24 + c_4_162·b_1_3·a_7_35 + c_4_162·b_1_1·a_7_35
       + c_4_162·b_1_13·b_1_32·a_3_11 + c_4_162·b_1_15·a_3_11
       + c_4_162·b_6_35·a_1_2·b_1_3 + c_4_162·b_6_35·a_1_2·b_1_1
       + c_4_162·a_6_28·b_1_32 + c_4_162·a_6_28·b_1_1·b_1_3 + c_4_162·a_6_28·b_1_12
       + c_4_16·c_8_58·a_1_0·a_3_11 + c_4_162·a_1_2·a_7_35 + c_4_16·c_8_58·a_1_23·b_1_3
       + c_4_162·a_6_28·a_1_22 + c_4_163·b_1_1·a_3_11 + c_4_163·a_1_2·b_1_33
       + c_4_163·a_1_2·b_1_1·b_1_32 + c_4_163·a_1_0·b_1_33 + c_4_163·a_1_22·b_1_32
       + c_4_163·a_1_0·a_3_11 + c_4_163·a_1_23·b_1_3
  73. b_6_35·b_1_1·b_1_32·a_7_35 + b_6_35·b_1_17·a_3_11 + b_6_35·a_10_68
       + b_6_352·b_1_3·a_3_10 + b_6_352·b_1_1·a_3_11 + a_6_28·b_1_3·b_9_76
       + a_6_28·b_1_35·b_5_24 + a_6_28·b_1_1·b_1_34·b_5_24 + a_6_28·b_1_13·b_1_32·b_5_24
       + a_6_28·b_1_14·b_1_3·b_5_22 + a_6_28·b_1_15·b_5_24 + a_6_28·b_6_35·b_1_1·b_1_33
       + b_6_35·b_1_34·a_3_112 + c_8_58·b_1_14·b_1_3·a_3_11 + c_8_58·b_1_15·a_3_11
       + c_8_58·b_1_15·a_3_10 + b_6_35·c_8_58·a_1_2·b_1_3 + a_6_28·c_8_58·b_1_12
       + c_4_16·b_1_35·a_7_35 + c_4_16·b_1_1·b_1_34·a_7_35 + c_4_16·b_1_17·b_1_32·a_3_11
       + c_4_16·b_1_18·b_1_3·a_3_11 + c_4_16·b_1_18·b_1_3·a_3_10 + c_4_16·b_1_19·a_3_11
       + c_4_16·a_1_2·b_1_311 + c_4_16·a_10_68·b_1_32 + c_4_16·a_10_68·b_1_12
       + c_4_16·b_6_35·b_1_33·a_3_11 + c_4_16·b_6_35·b_1_1·b_1_32·a_3_11
       + c_4_16·b_6_35·b_1_12·b_1_3·a_3_11 + c_4_16·b_6_35·b_1_12·b_1_3·a_3_10
       + c_4_16·b_6_35·b_1_13·a_3_10 + c_4_16·a_6_28·b_1_3·b_5_22 + c_4_16·a_6_28·b_1_36
       + c_4_16·a_6_28·b_1_1·b_5_24 + c_4_16·a_6_28·b_1_1·b_1_35
       + a_6_28·c_8_58·a_1_2·b_1_1 + c_4_16·b_1_36·a_3_112 + c_4_16·a_1_2·b_1_38·a_3_11
       + c_4_16·a_6_28·b_1_33·a_3_11 + c_4_16·a_6_28·b_1_1·b_1_32·a_3_11
       + c_4_16·b_1_33·a_3_113 + c_4_16·c_8_58·a_1_2·b_1_33
       + c_4_16·c_8_58·a_1_0·b_1_33 + c_4_162·b_1_14·b_1_3·a_3_11
       + c_4_162·b_1_14·b_1_3·a_3_10 + c_4_162·a_1_2·b_1_37
       + c_4_162·b_6_35·a_1_2·b_1_1 + c_4_162·a_6_28·b_1_32
       + c_4_162·a_6_28·b_1_1·b_1_3 + c_4_162·a_6_28·b_1_12 + c_4_162·b_1_32·a_3_112
       + c_4_162·a_1_2·b_1_34·a_3_11 + c_4_162·a_1_2·b_1_1·b_1_33·a_3_11
       + c_4_163·a_1_2·b_1_1·b_1_32 + c_4_163·a_1_23·b_1_3
  74. a_6_28·a_10_68 + a_6_28·c_8_58·a_1_2·b_1_1 + c_4_16·a_6_28·b_1_1·b_1_32·a_3_11
       + c_4_162·a_6_28·a_1_2·b_1_1 + c_4_162·a_6_28·a_1_22
  75. a_10_68·a_7_35 + b_6_35·b_1_32·a_3_113 + c_8_58·a_1_2·b_1_1·a_7_35
       + a_6_28·c_8_58·a_3_11 + c_4_16·a_3_112·a_7_35 + c_4_16·c_8_58·a_1_2·b_1_3·a_3_11
       + c_4_16·c_8_58·a_1_2·b_1_1·a_3_11 + c_4_16·c_8_58·a_1_22·b_1_33
       + c_4_16·c_8_58·a_1_0·b_1_3·a_3_11 + c_4_163·a_1_2·b_1_1·a_3_11
       + c_4_163·a_1_0·b_1_3·a_3_11
  76. b_9_762 + b_6_352·b_1_36 + b_6_352·b_1_12·b_1_34 + b_6_352·b_1_14·b_1_32
       + c_4_16·b_1_12·b_1_312 + c_4_16·b_1_14·b_1_310 + c_4_16·b_1_18·b_1_36
       + c_4_16·b_1_112·b_1_32 + c_4_16·b_1_114 + c_4_16·b_6_352·b_1_12
       + c_4_16·b_1_38·a_3_112 + c_4_162·b_1_12·b_1_38 + c_4_162·b_1_34·a_3_112
       + c_4_163·b_1_16 + c_4_162·c_8_58·a_1_22 + c_4_163·a_1_22·b_1_3·a_3_11
       + c_4_164·b_1_32 + c_4_164·b_1_12
  77. a_10_68·b_9_76 + a_10_68·b_1_16·b_1_33 + a_10_68·b_1_17·b_1_32
       + a_10_68·b_1_18·b_1_3 + b_6_35·a_10_68·b_1_33 + b_6_352·b_1_13·b_1_3·a_3_11
       + b_6_352·b_1_13·b_1_3·a_3_10 + b_6_352·b_1_14·a_3_10 + a_6_28·b_1_38·b_5_24
       + a_6_28·b_1_1·b_1_37·b_5_24 + a_6_28·b_1_14·b_1_34·b_5_24
       + a_6_28·b_1_16·b_1_32·b_5_24 + a_6_28·b_1_16·b_1_37
       + a_6_28·b_1_17·b_1_3·b_5_22 + a_6_28·b_1_17·b_1_36 + a_6_28·b_1_18·b_5_24
       + a_6_28·b_1_18·b_1_35 + a_6_28·b_1_110·b_1_33 + a_6_28·b_1_111·b_1_32
       + a_6_28·b_1_113 + a_6_28·b_6_35·b_1_32·b_5_24 + a_6_28·b_6_35·b_1_1·b_1_3·b_5_22
       + a_6_28·b_6_35·b_1_1·b_1_36 + a_6_28·b_6_35·b_1_12·b_5_22
       + a_6_28·b_6_35·b_1_12·b_1_35 + a_6_28·b_6_35·b_1_13·b_1_34
       + a_6_28·b_6_35·b_1_15·b_1_32 + a_6_28·b_6_352·b_1_1
       + c_8_58·b_1_15·b_1_33·a_3_11 + c_8_58·b_1_16·b_1_32·a_3_11
       + c_8_58·b_1_17·b_1_3·a_3_11 + c_8_58·b_1_17·b_1_3·a_3_10 + c_8_58·b_1_18·a_3_10
       + a_6_28·c_8_58·b_1_13·b_1_32 + c_4_16·a_10_68·b_1_35
       + c_4_16·a_10_68·b_1_12·b_1_33 + c_4_16·a_10_68·b_1_15
       + c_4_16·b_6_35·b_1_32·a_7_35 + c_4_16·b_6_35·b_1_13·b_1_33·a_3_11
       + c_4_16·b_6_35·b_1_14·b_1_32·a_3_11 + c_4_16·b_6_35·b_1_15·b_1_3·a_3_11
       + c_4_16·b_6_35·b_1_16·a_3_10 + c_4_16·b_6_35·a_1_2·b_1_38
       + c_4_16·b_6_352·a_3_10 + c_4_16·a_6_28·b_1_34·b_5_24 + c_4_16·a_6_28·b_1_39
       + c_4_16·a_6_28·b_1_1·b_1_33·b_5_24 + c_4_16·a_6_28·b_1_14·b_1_35
       + c_4_16·a_6_28·b_1_15·b_1_34 + c_4_16·a_6_28·b_1_16·b_1_33
       + c_4_16·a_6_28·b_1_18·b_1_3 + c_4_16·a_6_28·b_6_35·b_1_33
       + c_4_16·a_6_28·b_6_35·b_1_1·b_1_32 + a_6_28·c_8_58·b_1_32·a_3_11
       + a_6_28·c_8_58·b_1_1·b_1_3·a_3_11 + c_4_16·b_1_39·a_3_112
       + c_4_16·a_6_28·b_1_36·a_3_11 + c_4_16·b_6_35·a_3_113
       + c_4_16·c_8_58·b_1_14·a_3_11 + c_4_16·c_8_58·b_1_14·a_3_10
       + c_4_16·c_8_58·a_1_2·b_1_3·b_5_24 + c_4_16·c_8_58·a_1_2·b_1_36
       + c_4_162·b_1_34·a_7_35 + c_4_162·b_1_38·a_3_11 + c_4_162·b_1_15·b_1_33·a_3_11
       + c_4_162·a_10_68·b_1_3 + c_4_162·a_10_68·b_1_1 + c_4_162·b_6_35·b_1_32·a_3_11
       + c_4_162·b_6_35·b_1_12·a_3_11 + c_4_162·b_6_35·b_1_12·a_3_10
       + c_4_162·b_6_35·a_1_2·b_1_34 + c_4_162·a_6_28·b_5_24 + c_4_162·a_6_28·b_1_35
       + c_4_162·a_6_28·b_1_1·b_1_34 + c_4_162·a_6_28·b_1_13·b_1_32
       + c_4_162·a_6_28·b_1_15 + c_4_16·c_8_58·b_1_3·a_3_112
       + c_4_16·c_8_58·a_1_2·b_1_33·a_3_11 + c_4_16·c_8_58·a_1_22·b_5_24
       + c_4_16·a_6_28·c_8_58·a_1_0 + c_4_162·b_1_3·a_3_11·a_7_35
       + c_4_162·b_1_35·a_3_112 + c_4_162·a_1_2·b_1_37·a_3_11
       + c_4_162·a_6_28·b_1_32·a_3_11 + c_4_162·a_6_28·b_1_1·b_1_3·a_3_11
       + c_4_162·c_8_58·a_1_2·b_1_1·b_1_3 + c_4_163·b_1_34·a_3_11
       + c_4_163·b_1_14·a_3_11 + c_4_163·a_1_2·b_1_36 + c_4_163·a_6_28·b_1_1
       + c_4_162·c_8_58·a_1_0·a_1_2·b_1_3 + c_4_163·b_1_3·a_3_112
       + c_4_163·a_1_2·b_1_33·a_3_11 + c_4_163·a_1_2·b_1_1·b_1_32·a_3_11
       + c_4_163·a_6_28·a_1_2 + c_4_163·a_6_28·a_1_0 + c_4_162·c_8_58·a_1_23
       + c_4_164·a_1_0·a_1_2·b_1_3
  78. a_10_682 + c_8_582·a_1_22·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_16, a Duflot regular element of degree 4
    2. c_8_58, 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_10 → 0, an element of degree 3
  6. a_3_11 → 0, an element of degree 3
  7. c_4_16 → c_1_04, an element of degree 4
  8. a_5_23 → 0, an element of degree 5
  9. b_5_22 → 0, an element of degree 5
  10. b_5_24 → 0, an element of degree 5
  11. a_6_28 → 0, an element of degree 6
  12. b_6_35 → 0, an element of degree 6
  13. a_7_35 → 0, an element of degree 7
  14. c_8_58 → c_1_18 + c_1_08, an element of degree 8
  15. b_9_76 → 0, an element of degree 9
  16. a_10_68 → 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_10 → 0, an element of degree 3
  6. a_3_11 → 0, an element of degree 3
  7. c_4_16 → c_1_02·c_1_22 + c_1_04, an element of degree 4
  8. a_5_23 → 0, an element of degree 5
  9. b_5_22 → c_1_0·c_1_24 + c_1_02·c_1_23, an element of degree 5
  10. b_5_24 → c_1_0·c_1_22·c_1_32 + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  11. a_6_28 → 0, an element of degree 6
  12. b_6_35 → c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_0·c_1_22·c_1_33 + c_1_0·c_1_24·c_1_3
       + c_1_0·c_1_25 + c_1_02·c_1_34 + c_1_02·c_1_2·c_1_33 + c_1_02·c_1_23·c_1_3
       + c_1_02·c_1_24 + c_1_04·c_1_32, an element of degree 6
  13. a_7_35 → 0, an element of degree 7
  14. c_8_58 → c_1_12·c_1_22·c_1_34 + c_1_12·c_1_24·c_1_32 + c_1_14·c_1_34
       + c_1_14·c_1_22·c_1_32 + c_1_14·c_1_24 + c_1_18 + c_1_0·c_1_24·c_1_33
       + c_1_0·c_1_26·c_1_3 + c_1_02·c_1_23·c_1_33 + c_1_02·c_1_24·c_1_32
       + c_1_02·c_1_25·c_1_3 + c_1_04·c_1_22·c_1_32 + c_1_04·c_1_24 + c_1_08, an element of degree 8
  15. b_9_76 → c_1_12·c_1_24·c_1_33 + c_1_12·c_1_25·c_1_32 + c_1_12·c_1_26·c_1_3
       + c_1_14·c_1_22·c_1_33 + c_1_14·c_1_23·c_1_32 + c_1_14·c_1_24·c_1_3
       + c_1_0·c_1_25·c_1_33 + c_1_0·c_1_28 + c_1_0·c_1_12·c_1_26
       + c_1_0·c_1_14·c_1_24 + c_1_02·c_1_37 + c_1_02·c_1_2·c_1_36
       + c_1_02·c_1_22·c_1_35 + c_1_02·c_1_23·c_1_34 + c_1_02·c_1_26·c_1_3
       + c_1_02·c_1_12·c_1_25 + c_1_02·c_1_14·c_1_23 + c_1_03·c_1_22·c_1_34
       + c_1_03·c_1_26 + c_1_04·c_1_35 + c_1_04·c_1_2·c_1_34 + c_1_04·c_1_25
       + c_1_05·c_1_22·c_1_32 + c_1_05·c_1_24 + c_1_06·c_1_2·c_1_32
       + c_1_06·c_1_23 + c_1_08·c_1_3 + c_1_08·c_1_2, an element of degree 9
  16. a_10_68 → 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