Cohomology of group number 194 of order 128

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

General information on the group

  • The group has 3 minimal generators and exponent 8.
  • It is non-abelian.
  • It has p-Rank 5.
  • Its center has rank 2.
  • It has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 5.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 5 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t3  +  t2  −  t  +  1)
    (t  +  1) · (t  −  1)5 · (t2  +  1)2
  • The a-invariants are -∞,-∞,-6,-6,-5,-5. 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 21 minimal generators of maximal degree 7:

  1. a_1_0, a nilpotent 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. a_3_7, a nilpotent element of degree 3
  7. a_3_5, a nilpotent element of degree 3
  8. b_3_8, an element of degree 3
  9. b_3_9, an element of degree 3
  10. b_3_11, an element of degree 3
  11. b_4_19, an element of degree 4
  12. b_4_20, an element of degree 4
  13. b_4_21, an element of degree 4
  14. c_4_22, a Duflot regular element of degree 4
  15. c_4_23, a Duflot regular element of degree 4
  16. a_5_39, a nilpotent element of degree 5
  17. b_5_38, an element of degree 5
  18. b_5_40, an element of degree 5
  19. b_5_41, an element of degree 5
  20. b_6_65, an element of degree 6
  21. b_7_99, an element of degree 7

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

Ring relations

There are 148 minimal relations of maximal degree 14:

  1. a_1_02
  2. a_1_0·b_1_1
  3. a_1_0·b_1_22
  4. a_2_4·a_1_0
  5. a_2_4·b_1_1
  6. b_2_5·a_1_0
  7. a_2_42
  8. a_1_0·a_3_7
  9. b_1_1·a_3_7
  10. a_1_0·a_3_5
  11. b_1_1·a_3_5
  12. a_1_0·b_3_8
  13. a_1_0·b_3_9
  14. a_1_0·b_3_11
  15. a_2_4·a_3_7
  16. b_1_22·a_3_5 + b_2_5·a_3_7 + a_2_4·b_1_23
  17. a_2_4·a_3_5
  18. b_2_5·a_3_7 + a_2_4·b_3_8
  19. a_2_4·b_3_9
  20. b_2_5·a_3_5 + a_2_4·b_3_11 + a_2_4·b_2_5·b_1_2
  21. b_4_19·a_1_0
  22. b_1_22·b_3_9 + b_1_1·b_1_2·b_3_8 + b_4_19·b_1_1 + b_2_5·a_3_7
  23. b_4_20·a_1_0
  24. b_1_22·b_3_11 + b_4_20·b_1_1 + b_2_5·b_3_8
  25. b_4_21·a_1_0
  26. b_1_22·b_3_11 + b_4_21·b_1_1 + b_2_5·b_3_9 + b_2_5·b_3_8 + b_2_5·a_3_5
       + a_2_4·b_2_5·b_1_2
  27. a_3_72
  28. a_3_7·a_3_5
  29. a_3_52
  30. a_3_7·b_3_8 + a_2_4·b_1_24
  31. a_3_5·b_3_8 + a_2_4·b_1_2·b_3_8 + a_2_4·b_2_5·b_1_22
  32. a_3_7·b_3_9
  33. a_3_5·b_3_9
  34. b_3_92 + b_1_13·b_3_8 + b_2_5·b_1_12·b_1_22
  35. a_3_7·b_3_11 + a_2_4·b_2_5·b_1_22
  36. a_3_5·b_3_11 + a_2_4·b_1_2·b_3_11 + a_2_4·b_2_52
  37. b_3_82 + b_1_1·b_1_22·b_3_8 + b_2_5·b_1_24 + c_4_23·b_1_12
  38. a_2_4·b_4_19
  39. b_3_112 + b_1_12·b_1_2·b_3_11 + b_1_12·b_1_2·b_3_8 + b_4_20·b_1_12
       + b_2_5·b_1_1·b_3_11 + b_2_5·b_1_1·b_3_9 + b_2_53 + c_4_22·b_1_12
  40. b_4_21·b_1_22 + b_4_20·b_1_22 + b_2_5·b_1_2·b_3_8 + b_2_5·b_4_19 + a_2_4·b_1_24
       + a_2_4·b_4_20 + a_2_4·b_2_5·b_1_22
  41. a_3_5·b_3_11 + a_2_4·b_4_21 + a_2_4·b_4_20 + a_2_4·b_2_52
  42. a_1_0·a_5_39
  43. b_1_1·a_5_39
  44. a_1_0·b_5_38
  45. b_3_8·b_3_9 + b_1_1·b_5_38 + b_1_12·b_1_2·b_3_8 + b_2_5·b_1_1·b_1_23
       + a_2_4·b_2_5·b_1_22
  46. a_1_0·b_5_40 + c_4_22·a_1_0·b_1_2
  47. b_3_8·b_3_11 + b_3_8·b_3_9 + b_1_1·b_5_40 + b_1_12·b_1_2·b_3_8 + b_4_19·b_1_12
       + b_2_5·b_1_1·b_3_8 + b_2_5·b_1_1·b_1_23 + b_2_52·b_1_22 + a_2_4·b_2_5·b_1_22
       + c_4_22·b_1_1·b_1_2
  48. a_1_0·b_5_41 + c_4_22·a_1_0·b_1_2
  49. b_3_9·b_3_11 + b_3_8·b_3_11 + b_1_1·b_5_41 + b_1_13·b_3_8 + b_2_5·b_1_1·b_3_9
       + b_2_5·b_1_1·b_3_8 + b_2_5·b_1_12·b_1_22 + b_2_52·b_1_22 + a_2_4·b_2_52
       + c_4_22·b_1_1·b_1_2
  50. b_4_19·a_3_7
  51. b_4_19·a_3_5
  52. b_4_21·a_3_7 + b_4_20·a_3_7 + a_2_4·b_2_5·b_1_23
  53. b_4_21·a_3_5 + b_4_20·a_3_5 + a_2_4·b_2_5·b_3_8 + a_2_4·b_2_52·b_1_2
  54. b_4_21·b_3_9 + b_4_20·b_3_9 + b_2_5·b_1_12·b_3_8 + b_2_52·b_1_1·b_1_22
       + a_2_4·b_2_52·b_1_2
  55. b_4_20·a_3_5 + b_2_5·a_5_39 + a_2_4·b_4_20·b_1_2 + a_2_4·b_2_5·b_1_23
  56. b_1_22·a_5_39 + b_4_20·a_3_7 + a_2_4·b_1_25
  57. a_2_4·a_5_39
  58. b_4_21·b_3_8 + b_4_20·b_3_8 + b_2_5·b_5_38 + b_2_5·b_1_1·b_1_2·b_3_8 + b_2_52·b_1_23
       + b_4_20·a_3_5 + a_2_4·b_1_22·b_3_8 + a_2_4·b_4_20·b_1_2 + a_2_4·b_2_5·b_3_8
  59. b_1_22·b_5_38 + b_4_19·b_3_8 + c_4_23·b_1_12·b_1_2
  60. b_1_1·b_1_2·b_5_38 + b_4_19·b_3_9
  61. a_2_4·b_5_38
  62. b_1_1·b_1_23·b_3_8 + b_4_21·b_3_8 + b_4_20·b_3_11 + b_4_20·b_3_8
       + b_4_20·b_1_1·b_1_22 + b_4_20·b_1_12·b_1_2 + b_2_5·b_5_40 + b_2_5·b_1_1·b_1_2·b_3_8
       + b_2_5·b_4_20·b_1_1 + b_2_52·b_1_23 + a_2_4·b_1_22·b_3_8 + a_2_4·b_2_5·b_3_8
       + a_2_4·b_2_5·b_1_23 + c_4_22·b_1_1·b_1_22 + b_2_5·c_4_22·b_1_2
  63. b_1_22·b_5_40 + b_4_20·b_3_8 + b_4_19·b_3_8 + b_4_19·b_1_1·b_1_22 + b_4_20·a_3_7
       + a_2_4·b_1_25 + c_4_23·b_1_12·b_1_2 + c_4_22·b_1_23 + b_2_5·c_4_23·b_1_1
  64. b_1_1·b_1_2·b_5_40 + b_4_21·b_3_8 + b_4_20·b_3_9 + b_4_20·b_3_8 + b_4_19·b_3_11
       + b_4_19·b_3_9 + b_4_19·b_1_12·b_1_2 + b_2_5·b_1_1·b_1_2·b_3_8 + b_2_52·b_1_23
       + a_2_4·b_1_22·b_3_8 + a_2_4·b_2_5·b_3_8 + c_4_22·b_1_1·b_1_22
  65. b_4_20·a_3_5 + a_2_4·b_5_40 + a_2_4·b_4_20·b_1_2 + a_2_4·c_4_22·b_1_2
  66. b_1_1·b_1_23·b_3_8 + b_4_21·b_3_11 + b_4_20·b_1_1·b_1_22 + b_4_20·b_1_12·b_1_2
       + b_2_5·b_5_41 + b_2_5·b_1_12·b_3_8 + b_2_5·b_4_20·b_1_1 + b_2_5·b_4_19·b_1_1
       + b_2_52·b_3_9 + b_2_52·b_1_1·b_1_22 + b_4_20·a_3_5 + a_2_4·b_4_20·b_1_2
       + a_2_4·b_2_5·b_3_11 + a_2_4·b_2_5·b_1_23 + c_4_22·b_1_1·b_1_22
       + b_2_5·c_4_22·b_1_2
  67. b_1_22·b_5_41 + b_1_12·b_1_22·b_3_8 + b_4_21·b_3_8 + b_4_20·b_3_9
       + b_2_5·b_1_1·b_1_2·b_3_8 + b_2_5·b_1_1·b_1_24 + b_2_5·b_4_19·b_1_1 + b_4_20·a_3_5
       + b_4_20·a_3_7 + a_2_4·b_1_25 + a_2_4·b_4_20·b_1_2 + c_4_22·b_1_23
       + b_2_5·c_4_23·b_1_1
  68. b_4_20·a_3_5 + a_2_4·b_5_41 + a_2_4·b_4_20·b_1_2 + a_2_4·b_2_52·b_1_2
       + a_2_4·c_4_22·b_1_2
  69. b_6_65·a_1_0
  70. b_6_65·b_1_1 + b_4_21·b_3_8 + b_4_20·b_3_8 + b_4_19·b_3_11 + b_4_19·b_3_9
       + b_2_5·b_1_1·b_1_2·b_3_8 + b_2_52·b_1_23 + b_4_20·a_3_5 + a_2_4·b_1_22·b_3_8
       + a_2_4·b_4_20·b_1_2 + a_2_4·b_2_5·b_3_8
  71. b_4_192 + c_4_23·b_1_12·b_1_22
  72. b_1_25·b_3_8 + b_4_20·b_1_24 + b_4_20·b_1_1·b_1_23 + b_4_202
       + b_2_5·b_4_20·b_1_22 + b_2_5·b_4_19·b_1_22 + a_2_4·b_4_20·b_1_22
       + c_4_22·b_1_24 + b_2_52·c_4_23
  73. b_4_212 + b_4_202 + b_2_52·b_1_1·b_3_8 + b_2_53·b_1_22
  74. a_3_7·a_5_39
  75. b_3_11·a_5_39 + a_2_4·b_2_5·b_1_2·b_3_8 + a_2_4·b_2_5·b_4_20
  76. a_3_5·a_5_39
  77. b_1_25·b_3_8 + b_4_20·b_1_24 + b_4_20·b_1_1·b_1_23 + b_4_202
       + b_2_5·b_4_20·b_1_22 + b_2_5·b_4_19·b_1_22 + b_3_8·a_5_39 + a_2_4·b_1_23·b_3_8
       + c_4_22·b_1_24 + b_2_52·c_4_23
  78. b_3_9·a_5_39
  79. a_3_7·b_5_38
  80. b_4_19·b_4_21 + b_4_19·b_4_20 + b_2_5·b_1_2·b_5_38
  81. a_3_5·b_5_38
  82. b_3_8·b_5_38 + b_4_19·b_1_1·b_3_8 + b_2_5·b_4_19·b_1_22 + c_4_23·b_1_1·b_3_9
  83. b_3_9·b_5_38 + b_4_19·b_1_1·b_3_9 + b_2_5·b_4_19·b_1_1·b_1_2 + c_4_23·b_1_14
  84. b_1_25·b_3_8 + b_4_20·b_1_24 + b_4_20·b_1_1·b_1_23 + b_4_202
       + b_2_5·b_4_20·b_1_22 + b_2_5·b_4_19·b_1_22 + a_3_7·b_5_40 + c_4_22·b_1_24
       + b_2_52·c_4_23 + c_4_22·b_1_2·a_3_7
  85. b_3_11·b_5_40 + b_3_11·b_5_38 + b_4_20·b_1_1·b_3_11 + b_4_20·b_1_1·b_3_9
       + b_4_20·b_1_1·b_3_8 + b_4_20·b_1_12·b_1_22 + b_4_20·b_1_13·b_1_2
       + b_2_5·b_1_1·b_5_40 + b_2_5·b_1_1·b_5_38 + b_2_5·b_1_1·b_1_25
       + b_2_5·b_4_20·b_1_12 + b_2_52·b_4_20 + a_2_4·b_2_5·b_1_2·b_3_8 + a_2_4·b_2_5·b_4_20
       + c_4_23·b_1_13·b_1_2 + c_4_22·b_1_2·b_3_11 + c_4_22·b_1_1·b_3_8
       + c_4_22·b_1_12·b_1_22 + b_2_5·c_4_22·b_1_1·b_1_2
  86. a_3_5·b_5_40 + a_2_4·b_1_2·b_5_40 + a_2_4·b_2_5·b_4_20 + c_4_22·b_1_2·a_3_5
       + a_2_4·c_4_22·b_1_22
  87. b_3_8·b_5_40 + b_1_25·b_3_8 + b_4_20·b_1_24 + b_4_20·b_1_1·b_3_8
       + b_4_20·b_1_1·b_1_23 + b_4_202 + a_2_4·b_1_23·b_3_8 + c_4_23·b_1_1·b_3_11
       + c_4_23·b_1_1·b_3_9 + c_4_22·b_1_2·b_3_8 + c_4_22·b_1_24 + b_2_52·c_4_23
  88. b_3_11·b_5_38 + b_3_9·b_5_40 + b_4_20·b_1_1·b_3_9 + b_4_19·b_1_1·b_3_11
       + b_2_5·b_4_20·b_1_1·b_1_2 + b_2_5·b_4_19·b_1_1·b_1_2 + b_2_52·b_4_19
       + a_2_4·b_2_5·b_4_20 + c_4_23·b_1_14 + c_4_22·b_1_2·b_3_9
  89. b_1_25·b_3_8 + b_4_20·b_1_24 + b_4_20·b_1_1·b_1_23 + b_4_202
       + b_2_5·b_4_20·b_1_22 + b_2_5·b_4_19·b_1_22 + a_3_7·b_5_41
       + a_2_4·b_2_5·b_1_2·b_3_8 + c_4_22·b_1_24 + b_2_52·c_4_23 + c_4_22·b_1_2·a_3_7
  90. b_3_11·b_5_41 + b_3_11·b_5_40 + b_3_11·b_5_38 + b_1_12·b_1_2·b_5_41 + b_1_13·b_5_40
       + b_1_13·b_5_38 + b_1_13·b_1_22·b_3_8 + b_1_14·b_1_2·b_3_8 + b_4_19·b_1_1·b_3_9
       + b_4_19·b_1_14 + b_2_5·b_1_1·b_5_38 + b_2_5·b_1_12·b_1_2·b_3_9
       + b_2_5·b_1_12·b_1_24 + b_2_5·b_1_13·b_1_23 + b_2_5·b_4_20·b_1_12
       + b_2_52·b_1_1·b_3_8 + b_2_52·b_4_21 + b_2_52·b_4_20 + c_4_22·b_1_1·b_3_9
       + c_4_22·b_1_12·b_1_22 + c_4_22·b_1_13·b_1_2
  91. a_3_5·b_5_41 + a_3_5·b_5_40 + a_2_4·b_2_5·b_4_21 + a_2_4·b_2_5·b_4_20
       + a_2_4·b_2_52·b_1_22
  92. b_3_11·b_5_38 + b_3_8·b_5_41 + b_1_25·b_3_8 + b_1_13·b_1_22·b_3_8 + b_4_20·b_1_24
       + b_4_20·b_1_1·b_3_9 + b_4_20·b_1_1·b_3_8 + b_4_20·b_1_1·b_1_23 + b_4_202
       + b_4_19·b_1_1·b_3_11 + b_2_5·b_1_1·b_1_22·b_3_8 + b_2_5·b_1_12·b_1_24
       + b_2_5·b_4_20·b_1_1·b_1_2 + b_2_5·b_4_19·b_1_22 + b_2_52·b_1_2·b_3_8
       + a_2_4·b_1_23·b_3_8 + a_2_4·b_2_5·b_1_24 + a_2_4·b_2_5·b_4_20
       + a_2_4·b_2_52·b_1_22 + c_4_23·b_1_1·b_3_11 + c_4_23·b_1_14 + c_4_22·b_1_2·b_3_8
       + c_4_22·b_1_24 + b_2_52·c_4_23
  93. b_3_11·b_5_38 + b_3_9·b_5_41 + b_1_13·b_5_40 + b_1_14·b_1_2·b_3_8 + b_4_20·b_1_1·b_3_9
       + b_4_19·b_1_1·b_3_11 + b_4_19·b_1_14 + b_2_5·b_1_12·b_1_2·b_3_8
       + b_2_5·b_1_13·b_1_23 + b_2_5·b_4_20·b_1_1·b_1_2 + b_2_5·b_4_20·b_1_12
       + b_2_5·b_4_19·b_1_12 + b_2_52·b_1_1·b_3_8 + b_2_52·b_4_19 + a_2_4·b_2_5·b_4_21
       + c_4_22·b_1_2·b_3_9 + c_4_22·b_1_13·b_1_2
  94. b_4_20·b_4_21 + b_4_202 + b_2_5·b_1_2·b_5_40 + b_2_5·b_6_65 + b_2_5·b_4_19·b_1_1·b_1_2
       + a_3_5·b_5_40 + a_2_4·b_1_23·b_3_8 + a_2_4·b_2_5·b_1_24 + a_2_4·b_2_5·b_4_20
       + b_2_5·c_4_22·b_1_22 + c_4_22·b_1_2·a_3_5 + a_2_4·c_4_22·b_1_22
  95. b_6_65·b_1_22 + b_4_19·b_1_2·b_3_8 + b_4_19·b_4_20 + c_4_23·b_1_12·b_1_22
       + b_2_5·c_4_23·b_1_1·b_1_2 + a_2_4·b_2_5·c_4_23
  96. a_2_4·b_6_65
  97. a_1_0·b_7_99
  98. b_3_11·b_5_40 + b_1_1·b_7_99 + b_4_20·b_1_1·b_3_11 + b_4_20·b_1_1·b_3_9
       + b_4_20·b_1_1·b_3_8 + b_4_20·b_1_12·b_1_22 + b_4_20·b_1_13·b_1_2
       + b_4_19·b_1_1·b_3_9 + b_2_5·b_1_1·b_5_41 + b_2_5·b_1_1·b_5_38 + b_2_5·b_1_1·b_1_25
       + b_2_5·b_4_19·b_1_1·b_1_2 + b_2_52·b_4_20 + b_2_52·b_4_19 + a_2_4·b_2_5·b_1_2·b_3_8
       + a_2_4·b_2_5·b_4_20 + c_4_23·b_1_1·b_3_9 + c_4_23·b_1_13·b_1_2 + c_4_23·b_1_14
       + c_4_22·b_1_2·b_3_11 + c_4_22·b_1_1·b_3_8 + c_4_22·b_1_12·b_1_22
       + b_2_5·c_4_22·b_1_1·b_1_2
  99. b_4_21·a_5_39 + b_4_20·b_1_22·a_3_7 + a_2_4·b_1_27 + a_2_4·b_4_20·b_3_8
       + a_2_4·b_4_20·b_1_23 + a_2_4·b_2_5·b_1_22·b_3_8 + a_2_4·b_2_5·b_4_20·b_1_2
       + c_4_22·b_1_22·a_3_7 + a_2_4·c_4_23·b_3_11
  100. b_4_20·a_5_39 + b_4_20·b_1_22·a_3_7 + a_2_4·b_1_27 + a_2_4·b_4_20·b_3_8
       + a_2_4·b_4_20·b_1_23 + c_4_22·b_1_22·a_3_7 + a_2_4·c_4_23·b_3_11
  101. b_4_19·a_5_39
  102. b_4_21·b_5_38 + b_4_20·b_5_38 + b_2_5·b_4_19·b_3_9 + b_2_52·b_4_19·b_1_2
       + b_2_5·c_4_23·b_1_13
  103. b_4_19·b_5_38 + c_4_23·b_1_1·b_1_2·b_3_9
  104. b_4_21·b_5_38 + b_4_20·b_5_40 + b_4_20·b_1_22·b_3_8 + b_4_20·b_1_1·b_1_2·b_3_8
       + b_4_20·b_1_1·b_1_24 + b_4_20·b_1_12·b_1_23 + b_4_202·b_1_1
       + b_4_19·b_4_20·b_1_1 + b_2_5·b_1_27 + b_2_5·b_4_20·b_3_8
       + b_2_5·b_4_20·b_1_1·b_1_22 + b_2_5·b_4_19·b_3_9 + b_2_5·b_4_19·b_3_8
       + b_2_5·b_4_19·b_1_1·b_1_22 + b_2_52·b_4_19·b_1_2 + b_4_20·b_1_22·a_3_7
       + a_2_4·b_1_27 + a_2_4·b_4_20·b_1_23 + c_4_23·b_1_12·b_1_23
       + c_4_22·b_1_22·b_3_8 + c_4_22·b_1_1·b_1_24 + b_4_20·c_4_22·b_1_2
       + b_2_5·c_4_23·b_3_11 + b_2_5·c_4_23·b_1_13 + b_2_52·c_4_23·b_1_1
       + c_4_22·b_1_22·a_3_7 + a_2_4·c_4_23·b_3_11
  105. b_4_21·b_5_38 + b_4_19·b_5_40 + b_2_5·b_4_19·b_3_9 + b_2_52·b_4_19·b_1_2
       + c_4_23·b_1_1·b_1_2·b_3_11 + c_4_23·b_1_1·b_1_2·b_3_9 + c_4_23·b_1_13·b_1_22
       + b_4_19·c_4_22·b_1_2 + b_2_5·c_4_23·b_3_9 + b_2_5·c_4_23·b_1_13
       + a_2_4·c_4_23·b_3_11
  106. b_4_21·b_5_41 + b_4_20·b_1_22·b_3_8 + b_4_20·b_1_1·b_1_2·b_3_11
       + b_4_20·b_1_1·b_1_24 + b_4_20·b_1_13·b_1_22 + b_4_202·b_1_1
       + b_4_19·b_1_1·b_1_2·b_3_11 + b_4_19·b_1_1·b_1_2·b_3_8 + b_4_19·b_4_20·b_1_1
       + b_2_5·b_1_27 + b_2_5·b_1_1·b_1_26 + b_2_5·b_1_12·b_5_40
       + b_2_5·b_1_13·b_1_2·b_3_8 + b_2_5·b_4_20·b_3_9 + b_2_5·b_4_20·b_3_8
       + b_2_5·b_4_20·b_1_12·b_1_2 + b_2_5·b_4_19·b_3_11 + b_2_5·b_4_19·b_3_8
       + b_2_5·b_4_19·b_1_1·b_1_22 + b_2_5·b_4_19·b_1_12·b_1_2 + b_2_5·b_4_19·b_1_13
       + b_2_52·b_5_38 + b_2_52·b_1_1·b_1_2·b_3_8 + b_2_52·b_1_12·b_1_23
       + b_2_52·b_4_20·b_1_1 + b_2_52·b_4_19·b_1_1 + b_2_53·b_3_8 + b_4_20·b_1_22·a_3_7
       + a_2_4·b_1_27 + a_2_4·b_4_20·b_1_23 + a_2_4·b_2_5·b_5_40
       + a_2_4·b_2_5·b_1_22·b_3_8 + a_2_4·b_2_5·b_4_20·b_1_2 + c_4_23·b_1_12·b_1_23
       + c_4_23·b_1_13·b_1_22 + c_4_22·b_1_22·b_3_8 + c_4_22·b_1_1·b_1_2·b_3_8
       + c_4_22·b_1_1·b_1_24 + c_4_22·b_1_12·b_1_23 + b_4_21·c_4_22·b_1_2
       + b_4_19·c_4_22·b_1_1 + b_2_5·c_4_23·b_3_11 + b_2_5·c_4_23·b_1_13
       + b_2_5·c_4_22·b_1_12·b_1_2 + b_2_52·c_4_23·b_1_1 + c_4_22·b_1_22·a_3_7
       + a_2_4·c_4_23·b_3_11 + a_2_4·b_2_5·c_4_22·b_1_2
  107. b_4_21·b_5_40 + b_4_21·b_5_38 + b_4_20·b_5_41 + b_4_20·b_1_1·b_1_2·b_3_11
       + b_4_20·b_1_1·b_1_2·b_3_8 + b_4_20·b_1_12·b_1_23 + b_4_20·b_1_13·b_1_22
       + b_4_19·b_1_1·b_1_2·b_3_11 + b_4_19·b_1_1·b_1_2·b_3_8 + b_2_5·b_1_1·b_1_26
       + b_2_5·b_4_20·b_3_9 + b_2_5·b_4_20·b_1_1·b_1_22 + b_2_5·b_4_20·b_1_12·b_1_2
       + b_2_5·b_4_19·b_3_11 + b_2_5·b_4_19·b_3_9 + b_2_5·b_4_19·b_1_12·b_1_2
       + b_2_52·b_5_38 + a_2_4·b_2_5·b_5_40 + a_2_4·b_2_5·b_1_22·b_3_8
       + a_2_4·b_2_5·b_4_20·b_1_2 + c_4_23·b_1_13·b_1_22 + c_4_22·b_1_1·b_1_2·b_3_8
       + c_4_22·b_1_12·b_1_23 + b_4_21·c_4_22·b_1_2 + b_4_20·c_4_22·b_1_2
       + b_4_19·c_4_22·b_1_1 + b_2_5·c_4_23·b_1_13 + a_2_4·b_2_5·c_4_22·b_1_2
  108. b_6_65·a_3_7
  109. b_6_65·b_3_11 + b_4_21·b_5_40 + b_4_20·b_1_22·b_3_8 + b_4_20·b_1_1·b_1_2·b_3_8
       + b_4_20·b_1_1·b_1_24 + b_4_20·b_1_12·b_1_23 + b_4_202·b_1_1 + b_4_19·b_5_41
       + b_4_19·b_1_1·b_1_2·b_3_11 + b_4_19·b_1_1·b_1_2·b_3_8 + b_4_19·b_1_12·b_3_8
       + b_2_5·b_1_27 + b_2_5·b_4_20·b_3_9 + b_2_5·b_4_20·b_3_8
       + b_2_5·b_4_20·b_1_1·b_1_22 + b_2_5·b_4_19·b_3_8 + b_2_52·b_4_20·b_1_2
       + b_2_52·b_4_19·b_1_2 + b_4_20·b_1_22·a_3_7 + a_2_4·b_1_27 + a_2_4·b_4_20·b_1_23
       + a_2_4·b_2_5·b_5_40 + a_2_4·b_2_5·b_1_22·b_3_8 + a_2_4·b_2_5·b_1_25
       + a_2_4·b_2_5·b_4_20·b_1_2 + c_4_23·b_1_1·b_1_2·b_3_11 + c_4_23·b_1_12·b_1_23
       + c_4_22·b_1_22·b_3_8 + c_4_22·b_1_1·b_1_24 + b_4_21·c_4_22·b_1_2
       + b_4_19·c_4_22·b_1_2 + b_4_19·c_4_22·b_1_1 + b_2_5·c_4_23·b_3_11 + b_2_5·c_4_23·b_3_9
       + b_2_5·c_4_23·b_1_13 + b_2_52·c_4_23·b_1_1 + c_4_22·b_1_22·a_3_7
       + a_2_4·c_4_22·b_3_8 + a_2_4·b_2_5·c_4_22·b_1_2
  110. b_6_65·a_3_5
  111. b_6_65·b_3_8 + b_4_21·b_5_38 + b_4_19·b_1_1·b_1_2·b_3_8 + b_2_5·b_4_19·b_3_9
       + b_2_5·b_4_19·b_1_23 + b_2_52·b_4_19·b_1_2 + c_4_23·b_1_1·b_1_2·b_3_11
       + c_4_23·b_1_1·b_1_2·b_3_9 + b_2_5·c_4_23·b_1_13 + a_2_4·c_4_23·b_3_11
  112. b_6_65·b_3_9 + b_4_21·b_5_38 + b_4_19·b_5_41 + b_2_5·b_4_19·b_3_9
       + c_4_23·b_1_1·b_1_2·b_3_11 + b_4_19·c_4_22·b_1_2 + b_2_5·c_4_23·b_3_9
       + a_2_4·c_4_23·b_3_11
  113. b_4_21·b_5_40 + b_4_21·b_5_38 + b_4_20·b_1_22·b_3_8 + b_4_20·b_1_1·b_1_2·b_3_8
       + b_4_20·b_1_1·b_1_24 + b_4_20·b_1_12·b_1_23 + b_4_202·b_1_1
       + b_4_19·b_4_20·b_1_1 + b_2_5·b_7_99 + b_2_5·b_1_27 + b_2_5·b_4_20·b_3_9
       + b_2_5·b_4_20·b_3_8 + b_2_5·b_4_20·b_1_1·b_1_22 + b_2_5·b_4_19·b_3_11
       + b_2_5·b_4_19·b_3_8 + b_2_5·b_4_19·b_1_1·b_1_22 + b_2_52·b_5_41 + b_2_52·b_5_40
       + b_2_52·b_4_20·b_1_2 + b_2_52·b_4_20·b_1_1 + b_2_52·b_4_19·b_1_2
       + b_4_20·b_1_22·a_3_7 + a_2_4·b_1_27 + a_2_4·b_4_20·b_1_23 + a_2_4·b_2_5·b_5_40
       + a_2_4·b_2_5·b_1_22·b_3_8 + a_2_4·b_2_5·b_1_25 + a_2_4·b_2_5·b_4_20·b_1_2
       + a_2_4·b_2_52·b_3_11 + c_4_23·b_1_12·b_1_23 + c_4_22·b_1_22·b_3_8
       + c_4_22·b_1_1·b_1_24 + b_4_21·c_4_22·b_1_2 + b_2_5·c_4_23·b_3_11
       + b_2_5·c_4_23·b_3_9 + b_2_5·c_4_23·b_1_13 + b_2_52·c_4_23·b_1_1
       + c_4_22·b_1_22·a_3_7 + a_2_4·c_4_23·b_3_11 + a_2_4·c_4_22·b_3_8
       + a_2_4·b_2_5·c_4_22·b_1_2
  114. b_1_22·b_7_99 + b_4_21·b_5_38 + b_4_19·b_1_1·b_1_2·b_3_8
       + b_2_5·b_1_12·b_1_22·b_3_8 + b_2_5·b_4_20·b_3_9 + b_2_5·b_4_20·b_1_1·b_1_22
       + b_2_5·b_4_19·b_3_9 + b_2_5·b_4_19·b_1_23 + b_2_5·b_4_19·b_1_1·b_1_22
       + b_2_52·b_5_38 + b_2_52·b_1_1·b_1_24 + b_2_52·b_4_19·b_1_2 + b_2_52·b_4_19·b_1_1
       + b_2_53·b_1_23 + a_2_4·b_2_5·b_1_22·b_3_8 + c_4_23·b_1_1·b_1_2·b_3_8
       + b_4_19·c_4_23·b_1_1 + b_2_5·c_4_23·b_3_9 + b_2_5·c_4_23·b_1_12·b_1_2
       + b_2_5·c_4_23·b_1_13 + a_2_4·c_4_23·b_3_8
  115. b_1_1·b_1_2·b_7_99 + b_4_21·b_5_38 + b_4_19·b_5_41 + b_2_5·b_1_1·b_1_2·b_5_41
       + b_2_5·b_4_20·b_3_9 + b_2_5·b_4_20·b_1_12·b_1_2 + b_2_5·b_4_19·b_3_11
       + b_2_5·b_4_19·b_3_9 + b_2_5·b_4_19·b_1_12·b_1_2 + b_2_52·b_5_38 + a_2_4·b_2_5·b_5_40
       + c_4_23·b_1_1·b_1_2·b_3_11 + c_4_23·b_1_1·b_1_2·b_3_9 + b_4_19·c_4_22·b_1_2
       + b_2_5·c_4_23·b_3_9 + b_2_5·c_4_23·b_1_13 + b_2_5·c_4_22·b_1_1·b_1_22
       + a_2_4·c_4_23·b_3_11 + a_2_4·b_2_5·c_4_22·b_1_2
  116. a_2_4·b_7_99 + a_2_4·b_2_53·b_1_2
  117. a_5_392
  118. a_5_39·b_5_38
  119. b_5_382 + c_4_23·b_1_13·b_3_8 + b_2_5·c_4_23·b_1_12·b_1_22
  120. a_5_39·b_5_40 + a_2_4·b_4_20·b_1_2·b_3_8 + a_2_4·b_4_202 + c_4_22·b_1_2·a_5_39
  121. b_5_402 + b_4_20·b_1_1·b_1_22·b_3_8 + b_4_20·b_1_12·b_1_2·b_3_8
       + b_4_20·b_1_12·b_1_24 + b_4_20·b_1_13·b_1_23 + b_4_202·b_1_12
       + b_2_5·b_1_1·b_1_27 + b_2_5·b_4_20·b_1_1·b_3_8 + b_2_5·b_4_20·b_1_12·b_1_22
       + b_2_5·b_4_202 + b_2_5·b_4_19·b_1_1·b_3_8 + b_2_5·b_4_19·b_1_12·b_1_22
       + c_4_23·b_1_12·b_1_2·b_3_11 + c_4_23·b_1_12·b_1_2·b_3_8 + c_4_23·b_1_13·b_3_8
       + c_4_23·b_1_13·b_1_23 + c_4_23·b_1_14·b_1_22 + c_4_22·b_1_1·b_1_22·b_3_8
       + c_4_22·b_1_12·b_1_24 + b_4_20·c_4_23·b_1_12 + b_2_5·c_4_23·b_1_1·b_3_11
       + b_2_5·c_4_23·b_1_1·b_3_9 + b_2_5·c_4_23·b_1_12·b_1_22 + b_2_52·c_4_23·b_1_12
       + c_4_22·c_4_23·b_1_12 + c_4_222·b_1_22
  122. a_5_39·b_5_41 + a_2_4·b_4_20·b_1_2·b_3_8 + a_2_4·b_4_202 + a_2_4·b_2_5·b_1_2·b_5_40
       + a_2_4·b_2_52·b_1_24 + c_4_22·b_1_2·a_5_39 + a_2_4·b_2_5·c_4_22·b_1_22
  123. b_5_412 + b_1_15·b_1_22·b_3_8 + b_4_20·b_1_1·b_1_22·b_3_8
       + b_4_20·b_1_12·b_1_2·b_3_8 + b_4_20·b_1_12·b_1_24 + b_4_20·b_1_13·b_3_11
       + b_4_20·b_1_13·b_3_9 + b_4_20·b_1_13·b_3_8 + b_4_20·b_1_13·b_1_23
       + b_4_20·b_1_14·b_1_22 + b_4_20·b_1_15·b_1_2 + b_4_202·b_1_12
       + b_4_19·b_1_13·b_3_11 + b_2_5·b_1_1·b_1_27 + b_2_5·b_1_13·b_1_25
       + b_2_5·b_1_14·b_1_24 + b_2_5·b_4_20·b_1_1·b_3_11 + b_2_5·b_4_20·b_1_1·b_3_8
       + b_2_5·b_4_20·b_1_12·b_1_22 + b_2_5·b_4_20·b_1_14 + b_2_5·b_4_202
       + b_2_5·b_4_19·b_1_1·b_3_8 + b_2_5·b_4_19·b_1_12·b_1_22 + b_2_5·b_4_19·b_1_14
       + b_2_52·b_1_1·b_5_40 + b_2_52·b_1_1·b_5_38 + b_2_52·b_1_12·b_1_24
       + b_2_52·b_4_19·b_1_12 + b_2_54·b_1_22 + c_4_23·b_1_12·b_1_2·b_3_11
       + c_4_23·b_1_12·b_1_2·b_3_8 + c_4_23·b_1_13·b_1_23 + c_4_23·b_1_15·b_1_2
       + c_4_23·b_1_16 + c_4_22·b_1_1·b_1_22·b_3_8 + c_4_22·b_1_12·b_1_24
       + c_4_22·b_1_13·b_3_8 + c_4_22·b_1_14·b_1_22 + b_4_20·c_4_23·b_1_12
       + b_2_5·c_4_23·b_1_1·b_3_11 + b_2_5·c_4_23·b_1_1·b_3_9 + b_2_52·c_4_23·b_1_12
       + b_2_52·c_4_22·b_1_1·b_1_2 + c_4_22·c_4_23·b_1_12 + c_4_222·b_1_22
  124. b_5_38·b_5_40 + b_4_19·b_1_1·b_5_40 + b_2_5·b_4_19·b_4_20 + c_4_23·b_1_1·b_5_41
       + c_4_23·b_1_1·b_5_40 + c_4_23·b_1_1·b_5_38 + c_4_23·b_1_14·b_1_22
       + c_4_22·b_1_2·b_5_38 + b_4_19·c_4_23·b_1_12 + b_4_19·c_4_22·b_1_1·b_1_2
       + b_2_52·c_4_23·b_1_1·b_1_2
  125. b_5_38·b_5_41 + b_5_38·b_5_40 + b_4_19·b_1_1·b_5_41 + b_4_19·b_1_1·b_5_40
       + b_2_5·b_4_19·b_1_2·b_3_11 + b_2_5·b_4_19·b_1_1·b_3_8 + b_2_52·b_4_19·b_1_1·b_1_2
       + c_4_23·b_1_13·b_3_11 + c_4_23·b_1_13·b_3_9 + c_4_23·b_1_13·b_3_8
       + c_4_23·b_1_14·b_1_22 + b_2_5·c_4_23·b_1_12·b_1_22
       + b_2_5·c_4_23·b_1_13·b_1_2 + b_2_5·c_4_23·b_1_14
  126. b_4_20·b_6_65 + b_4_19·b_1_2·b_5_40 + b_4_19·b_1_23·b_3_8 + b_4_19·b_4_20·b_1_22
       + b_4_19·b_4_20·b_1_1·b_1_2 + b_2_5·b_4_19·b_4_20 + c_4_23·b_1_12·b_1_2·b_3_8
       + c_4_23·b_1_13·b_1_23 + b_4_20·c_4_23·b_1_12 + b_4_19·c_4_23·b_1_12
       + b_2_5·c_4_23·b_1_2·b_3_11 + b_2_5·c_4_23·b_1_2·b_3_9 + b_2_5·c_4_23·b_1_1·b_3_8
       + b_2_5·c_4_23·b_1_12·b_1_22 + b_2_5·b_4_21·c_4_23 + b_2_5·b_4_20·c_4_23
       + a_2_4·b_4_21·c_4_23 + a_2_4·b_4_20·c_4_23 + a_2_4·b_2_5·c_4_23·b_1_22
       + a_2_4·b_2_52·c_4_23
  127. b_4_19·b_6_65 + c_4_23·b_1_12·b_1_2·b_3_8 + b_4_20·c_4_23·b_1_12
       + b_4_19·c_4_23·b_1_12 + b_2_5·c_4_23·b_1_2·b_3_9 + b_2_5·c_4_23·b_1_1·b_3_8
       + a_2_4·b_4_21·c_4_23 + a_2_4·b_4_20·c_4_23
  128. a_3_7·b_7_99 + a_2_4·b_2_52·b_1_2·b_3_8
  129. b_5_38·b_5_40 + b_3_11·b_7_99 + b_4_19·b_1_12·b_1_2·b_3_8
       + b_2_5·b_1_12·b_1_2·b_5_41 + b_2_5·b_1_13·b_5_40 + b_2_5·b_1_13·b_5_38
       + b_2_5·b_1_13·b_1_22·b_3_8 + b_2_5·b_1_14·b_1_2·b_3_8 + b_2_5·b_4_20·b_1_1·b_3_11
       + b_2_5·b_4_19·b_1_2·b_3_11 + b_2_5·b_4_19·b_1_1·b_1_23 + b_2_5·b_4_19·b_1_14
       + b_2_5·b_4_19·b_4_20 + b_2_52·b_1_2·b_5_38 + b_2_52·b_1_1·b_5_38
       + b_2_52·b_1_12·b_1_2·b_3_9 + b_2_52·b_1_12·b_1_24 + b_2_52·b_1_13·b_1_23
       + b_2_52·b_6_65 + b_2_52·b_4_20·b_1_12 + b_2_52·b_4_19·b_1_1·b_1_2
       + b_2_53·b_1_1·b_3_8 + b_2_53·b_4_21 + b_2_53·b_4_20 + a_2_4·b_2_54
       + c_4_23·b_1_12·b_1_2·b_3_11 + c_4_23·b_1_13·b_3_11 + c_4_23·b_1_13·b_3_8
       + c_4_22·b_1_2·b_5_38 + c_4_22·b_1_1·b_5_38 + b_2_5·c_4_23·b_1_12·b_1_22
       + b_2_5·c_4_23·b_1_14 + b_2_5·c_4_22·b_1_1·b_3_9 + b_2_5·c_4_22·b_1_12·b_1_22
       + b_2_5·c_4_22·b_1_13·b_1_2 + b_2_52·c_4_23·b_1_1·b_1_2 + a_2_4·b_2_52·c_4_23
  130. b_4_21·b_6_65 + b_4_19·b_1_2·b_5_40 + b_4_19·b_1_23·b_3_8 + b_4_19·b_4_20·b_1_22
       + b_4_19·b_4_20·b_1_1·b_1_2 + b_2_5·b_1_2·b_7_99 + b_2_5·b_4_19·b_4_20
       + b_2_52·b_1_2·b_5_41 + b_2_52·b_1_2·b_5_40 + b_2_52·b_1_2·b_5_38
       + b_2_52·b_4_20·b_1_1·b_1_2 + a_2_4·b_2_52·b_4_21 + a_2_4·b_2_52·b_4_20
       + c_4_23·b_1_12·b_1_2·b_3_8 + c_4_23·b_1_13·b_1_23 + b_4_20·c_4_23·b_1_12
       + b_4_19·c_4_23·b_1_12 + b_2_5·c_4_23·b_1_2·b_3_11 + b_2_5·c_4_23·b_1_1·b_3_8
       + b_2_5·c_4_23·b_1_12·b_1_22 + b_2_5·b_4_21·c_4_23 + b_2_5·b_4_20·c_4_23
       + b_2_52·c_4_23·b_1_12 + a_2_4·b_4_21·c_4_23 + a_2_4·b_4_20·c_4_23
       + a_2_4·b_2_5·c_4_23·b_1_22 + a_2_4·b_2_52·c_4_23
  131. b_5_40·b_5_41 + b_5_38·b_5_41 + b_4_20·b_1_1·b_1_22·b_3_8
       + b_4_20·b_1_12·b_1_2·b_3_11 + b_4_20·b_1_12·b_1_24 + b_4_20·b_1_14·b_1_22
       + b_4_202·b_1_12 + b_4_19·b_1_12·b_1_2·b_3_8 + b_4_19·b_1_13·b_3_8
       + b_2_5·b_1_1·b_7_99 + b_2_5·b_1_1·b_1_27 + b_2_5·b_1_12·b_1_26
       + b_2_5·b_4_20·b_1_2·b_3_11 + b_2_5·b_4_20·b_1_13·b_1_2 + b_2_5·b_4_202
       + b_2_5·b_4_19·b_1_1·b_3_8 + b_2_5·b_4_19·b_1_1·b_1_23 + b_2_5·b_4_19·b_1_13·b_1_2
       + b_2_52·b_1_2·b_5_38 + b_2_52·b_1_1·b_5_41 + b_2_52·b_1_1·b_5_40
       + b_2_52·b_1_1·b_5_38 + b_2_52·b_6_65 + b_2_52·b_4_20·b_1_12
       + a_2_4·b_2_5·b_1_2·b_5_40 + a_2_4·b_2_5·b_1_23·b_3_8 + a_2_4·b_2_52·b_1_24
       + c_4_23·b_1_12·b_1_2·b_3_9 + c_4_23·b_1_12·b_1_2·b_3_8 + c_4_23·b_1_13·b_3_11
       + c_4_23·b_1_13·b_1_23 + c_4_23·b_1_14·b_1_22 + c_4_22·b_1_2·b_5_41
       + c_4_22·b_1_2·b_5_40 + c_4_22·b_1_2·b_5_38 + c_4_22·b_1_1·b_5_38
       + c_4_22·b_1_1·b_1_22·b_3_8 + c_4_22·b_1_12·b_1_2·b_3_8 + c_4_22·b_1_12·b_1_24
       + c_4_22·b_1_13·b_1_23 + b_4_20·c_4_23·b_1_12 + b_2_5·c_4_23·b_1_1·b_3_11
       + b_2_5·c_4_23·b_1_1·b_3_9 + b_2_5·c_4_23·b_1_14 + c_4_22·c_4_23·b_1_12
       + c_4_222·b_1_22
  132. a_3_5·b_7_99 + a_2_4·b_2_52·b_4_21 + a_2_4·b_2_52·b_4_20 + a_2_4·b_2_53·b_1_22
  133. b_5_40·b_5_41 + b_5_38·b_5_41 + b_5_38·b_5_40 + b_3_8·b_7_99
       + b_4_20·b_1_1·b_1_22·b_3_8 + b_4_20·b_1_12·b_1_2·b_3_11 + b_4_20·b_1_12·b_1_24
       + b_4_20·b_1_14·b_1_22 + b_4_202·b_1_12 + b_4_19·b_1_13·b_3_8
       + b_2_5·b_1_1·b_1_27 + b_2_5·b_1_12·b_1_26 + b_2_5·b_1_13·b_1_22·b_3_8
       + b_2_5·b_4_20·b_1_2·b_3_11 + b_2_5·b_4_20·b_1_1·b_3_9 + b_2_5·b_4_20·b_1_1·b_3_8
       + b_2_5·b_4_20·b_1_13·b_1_2 + b_2_5·b_4_202 + b_2_5·b_4_19·b_1_2·b_3_8
       + b_2_5·b_4_19·b_1_1·b_3_11 + b_2_5·b_4_19·b_1_1·b_3_9 + b_2_5·b_4_19·b_1_13·b_1_2
       + b_2_52·b_1_2·b_5_38 + b_2_52·b_1_1·b_5_38 + b_2_52·b_1_1·b_1_22·b_3_8
       + b_2_52·b_1_12·b_1_24 + b_2_52·b_6_65 + b_2_52·b_4_20·b_1_1·b_1_2
       + b_2_52·b_4_19·b_1_1·b_1_2 + b_2_53·b_1_2·b_3_8 + b_2_53·b_4_19
       + a_2_4·b_2_5·b_1_2·b_5_40 + a_2_4·b_2_5·b_1_23·b_3_8 + a_2_4·b_2_52·b_4_20
       + c_4_23·b_1_1·b_5_38 + c_4_23·b_1_12·b_1_2·b_3_9 + c_4_23·b_1_13·b_3_11
       + c_4_23·b_1_13·b_1_23 + c_4_23·b_1_14·b_1_22 + c_4_22·b_1_2·b_5_41
       + c_4_22·b_1_2·b_5_40 + c_4_22·b_1_1·b_5_38 + c_4_22·b_1_1·b_1_22·b_3_8
       + c_4_22·b_1_12·b_1_2·b_3_8 + c_4_22·b_1_12·b_1_24 + c_4_22·b_1_13·b_1_23
       + b_4_20·c_4_23·b_1_12 + b_2_5·c_4_23·b_1_1·b_3_11 + b_2_5·c_4_23·b_1_1·b_1_23
       + b_2_5·c_4_23·b_1_12·b_1_22 + b_2_5·c_4_23·b_1_14 + b_2_52·c_4_23·b_1_1·b_1_2
       + a_2_4·b_2_5·c_4_23·b_1_22 + a_2_4·b_2_52·c_4_23 + c_4_22·c_4_23·b_1_12
       + c_4_222·b_1_22
  134. b_5_38·b_5_41 + b_5_38·b_5_40 + b_3_9·b_7_99 + b_2_5·b_1_13·b_5_40
       + b_2_5·b_1_14·b_1_2·b_3_8 + b_2_5·b_4_20·b_1_1·b_3_9 + b_2_5·b_4_19·b_1_1·b_3_9
       + b_2_5·b_4_19·b_1_14 + b_2_52·b_1_2·b_5_38 + b_2_52·b_1_12·b_1_2·b_3_8
       + b_2_52·b_1_13·b_1_23 + b_2_52·b_4_20·b_1_12 + b_2_52·b_4_19·b_1_12
       + b_2_53·b_1_1·b_3_8 + a_2_4·b_2_52·b_4_21 + a_2_4·b_2_52·b_4_20
       + c_4_23·b_1_12·b_1_2·b_3_9 + b_2_5·c_4_22·b_1_13·b_1_2
  135. b_6_65·a_5_39
  136. b_6_65·b_5_38 + c_4_23·b_1_1·b_1_2·b_5_41 + b_4_20·c_4_23·b_3_9 + b_4_19·c_4_23·b_3_11
       + b_2_5·c_4_23·b_5_38 + b_2_5·c_4_23·b_1_1·b_1_2·b_3_9 + b_2_5·c_4_23·b_1_12·b_3_8
       + b_2_52·c_4_23·b_1_1·b_1_22 + a_2_4·c_4_23·b_5_40 + c_4_22·c_4_23·b_1_1·b_1_22
       + a_2_4·c_4_22·c_4_23·b_1_2
  137. b_6_65·b_5_41 + b_4_19·b_1_12·b_5_40 + b_4_19·b_1_12·b_1_22·b_3_8
       + b_4_19·b_1_13·b_1_2·b_3_8 + b_4_19·b_4_20·b_3_11 + b_4_19·b_4_20·b_3_9
       + b_4_19·b_4_20·b_3_8 + b_4_19·b_4_20·b_1_1·b_1_22 + b_4_19·b_4_20·b_1_12·b_1_2
       + b_2_5·b_4_19·b_5_41 + b_2_5·b_4_19·b_5_40 + b_2_5·b_4_19·b_1_25
       + b_2_5·b_4_19·b_1_1·b_1_2·b_3_8 + b_2_5·b_4_19·b_1_1·b_1_24
       + b_2_5·b_4_19·b_1_12·b_3_8 + b_2_5·b_4_19·b_1_12·b_1_23
       + b_2_5·b_4_19·b_4_20·b_1_2 + b_2_5·b_4_19·b_4_20·b_1_1 + b_2_52·b_6_65·b_1_2
       + b_2_52·b_4_19·b_1_1·b_1_22 + b_2_53·b_4_19·b_1_2 + c_4_23·b_1_1·b_1_2·b_5_41
       + c_4_23·b_1_13·b_1_2·b_3_11 + c_4_23·b_1_15·b_1_22 + c_4_22·b_6_65·b_1_2
       + b_4_20·c_4_23·b_3_9 + b_4_19·c_4_23·b_3_11 + b_4_19·c_4_23·b_1_12·b_1_2
       + b_4_19·c_4_23·b_1_13 + b_4_19·c_4_22·b_3_9 + b_4_19·c_4_22·b_3_8
       + b_4_19·c_4_22·b_1_1·b_1_22 + b_4_19·c_4_22·b_1_12·b_1_2 + b_2_5·c_4_23·b_5_41
       + b_2_5·c_4_23·b_5_40 + b_2_5·c_4_23·b_1_12·b_3_11 + b_2_5·c_4_23·b_1_12·b_3_9
       + b_2_5·c_4_23·b_1_12·b_3_8 + b_2_5·c_4_23·b_1_12·b_1_23
       + b_2_5·c_4_23·b_1_13·b_1_22 + b_2_5·b_4_19·c_4_23·b_1_1 + b_2_52·c_4_23·b_1_13
       + b_2_53·c_4_23·b_1_2 + a_2_4·c_4_23·b_5_40 + a_2_4·b_2_5·c_4_23·b_3_11
       + a_2_4·b_2_5·c_4_23·b_3_8 + c_4_22·c_4_23·b_1_1·b_1_22 + a_2_4·c_4_22·c_4_23·b_1_2
  138. b_6_65·b_5_41 + b_6_65·b_5_40 + b_4_19·b_1_12·b_5_40 + b_4_19·b_1_12·b_1_22·b_3_8
       + b_4_19·b_1_13·b_1_2·b_3_8 + b_4_19·b_4_20·b_3_9 + b_2_5·b_4_19·b_5_41
       + b_2_5·b_4_19·b_5_40 + b_2_5·b_4_19·b_1_1·b_1_2·b_3_8 + b_2_5·b_4_19·b_1_1·b_1_24
       + b_2_5·b_4_19·b_1_12·b_3_8 + b_2_5·b_4_19·b_1_12·b_1_23 + b_2_52·b_6_65·b_1_2
       + b_2_52·b_4_19·b_1_1·b_1_22 + b_2_53·b_4_19·b_1_2 + c_4_23·b_1_1·b_1_2·b_5_41
       + c_4_23·b_1_13·b_1_2·b_3_11 + c_4_23·b_1_15·b_1_22 + b_4_20·c_4_23·b_3_9
       + b_4_20·c_4_23·b_1_13 + b_4_19·c_4_23·b_3_11 + b_4_19·c_4_22·b_3_9
       + b_4_19·c_4_22·b_1_12·b_1_2 + b_2_5·c_4_23·b_5_38 + b_2_5·c_4_23·b_1_1·b_1_2·b_3_9
       + b_2_5·c_4_23·b_1_12·b_3_11 + b_2_5·c_4_23·b_1_12·b_3_9
       + b_2_52·c_4_23·b_1_1·b_1_22 + b_2_52·c_4_23·b_1_13 + a_2_4·c_4_23·b_5_40
       + c_4_22·c_4_23·b_1_1·b_1_22 + a_2_4·c_4_22·c_4_23·b_1_2
  139. b_4_21·b_7_99 + b_4_20·b_7_99 + b_2_5·b_4_19·b_5_41 + b_2_5·b_4_19·b_5_40
       + b_2_52·b_1_12·b_5_40 + b_2_52·b_1_13·b_1_2·b_3_8 + b_2_52·b_6_65·b_1_2
       + b_2_52·b_4_20·b_3_9 + b_2_52·b_4_19·b_3_9 + b_2_52·b_4_19·b_1_13
       + b_2_53·b_1_1·b_1_2·b_3_8 + b_2_53·b_1_12·b_1_23 + b_2_53·b_4_20·b_1_1
       + b_2_53·b_4_19·b_1_2 + b_2_53·b_4_19·b_1_1 + b_2_54·b_3_8 + a_2_4·b_2_52·b_5_40
       + a_2_4·b_2_54·b_1_2 + b_2_5·c_4_23·b_1_1·b_1_2·b_3_9 + b_2_5·c_4_23·b_1_12·b_3_11
       + b_2_5·c_4_23·b_1_12·b_3_9 + b_2_5·c_4_23·b_1_12·b_3_8
       + b_2_5·c_4_23·b_1_13·b_1_22 + b_2_52·c_4_23·b_1_1·b_1_22
       + b_2_52·c_4_23·b_1_13 + b_2_52·c_4_22·b_1_12·b_1_2 + a_2_4·b_2_52·c_4_23·b_1_2
       + a_2_4·b_2_52·c_4_22·b_1_2
  140. b_4_21·b_7_99 + b_4_19·b_4_20·b_3_11 + b_4_19·b_4_20·b_3_8
       + b_4_19·b_4_20·b_1_1·b_1_22 + b_4_19·b_4_20·b_1_12·b_1_2
       + b_2_5·b_4_20·b_1_1·b_1_2·b_3_11 + b_2_5·b_4_20·b_1_1·b_1_2·b_3_8
       + b_2_5·b_4_20·b_1_12·b_1_23 + b_2_5·b_4_20·b_1_13·b_1_22
       + b_2_5·b_4_202·b_1_1 + b_2_5·b_4_19·b_5_41 + b_2_5·b_4_19·b_5_40
       + b_2_5·b_4_19·b_1_25 + b_2_5·b_4_19·b_1_1·b_1_2·b_3_11
       + b_2_5·b_4_19·b_1_1·b_1_2·b_3_8 + b_2_5·b_4_19·b_4_20·b_1_2
       + b_2_5·b_4_19·b_4_20·b_1_1 + b_2_52·b_7_99 + b_2_52·b_1_1·b_1_26
       + b_2_52·b_1_12·b_5_40 + b_2_52·b_1_13·b_1_2·b_3_8 + b_2_52·b_6_65·b_1_2
       + b_2_52·b_4_20·b_3_9 + b_2_52·b_4_20·b_1_1·b_1_22 + b_2_52·b_4_20·b_1_12·b_1_2
       + b_2_52·b_4_19·b_1_12·b_1_2 + b_2_52·b_4_19·b_1_13 + b_2_53·b_5_41
       + b_2_53·b_5_40 + b_2_53·b_5_38 + b_2_53·b_1_1·b_1_2·b_3_8
       + b_2_53·b_1_12·b_1_23 + b_2_53·b_4_20·b_1_2 + b_2_53·b_4_19·b_1_1
       + b_2_54·b_3_8 + a_2_4·b_2_52·b_1_25 + a_2_4·b_2_53·b_3_11 + a_2_4·b_2_54·b_1_2
       + c_4_23·b_1_12·b_1_22·b_3_8 + b_4_20·c_4_23·b_3_9 + b_4_20·c_4_23·b_1_12·b_1_2
       + b_4_20·c_4_23·b_1_13 + b_4_19·c_4_23·b_1_12·b_1_2 + b_4_19·c_4_22·b_3_8
       + b_4_19·c_4_22·b_1_1·b_1_22 + b_2_5·c_4_23·b_5_41 + b_2_5·c_4_23·b_5_40
       + b_2_5·c_4_23·b_5_38 + b_2_5·c_4_23·b_1_12·b_3_11 + b_2_5·c_4_23·b_1_12·b_3_9
       + b_2_5·c_4_23·b_1_13·b_1_22 + b_2_5·c_4_22·b_1_1·b_1_2·b_3_8
       + b_2_5·c_4_22·b_1_12·b_1_23 + b_2_5·b_4_19·c_4_23·b_1_1
       + b_2_5·b_4_19·c_4_22·b_1_1 + b_2_52·c_4_23·b_3_9 + b_2_52·c_4_23·b_1_13
       + b_2_52·c_4_22·b_1_12·b_1_2 + b_2_53·c_4_23·b_1_2 + a_2_4·b_2_5·c_4_23·b_3_11
       + a_2_4·b_2_5·c_4_23·b_3_8 + a_2_4·b_2_5·c_4_22·b_3_8 + a_2_4·b_2_52·c_4_23·b_1_2
       + c_4_22·c_4_23·b_1_12·b_1_2
  141. b_4_19·b_7_99 + b_2_5·b_4_19·b_5_41 + b_2_5·b_4_19·b_5_40 + b_2_5·b_4_19·b_4_20·b_1_1
       + c_4_23·b_1_1·b_1_2·b_5_41 + b_4_20·c_4_23·b_3_9 + b_4_19·c_4_23·b_3_11
       + b_4_19·c_4_23·b_3_9 + b_2_5·c_4_23·b_5_38 + b_2_5·c_4_23·b_1_1·b_1_2·b_3_9
       + b_2_52·c_4_23·b_1_1·b_1_22 + a_2_4·c_4_23·b_5_40 + c_4_22·c_4_23·b_1_1·b_1_22
       + a_2_4·c_4_22·c_4_23·b_1_2
  142. b_6_652 + c_4_23·b_1_13·b_1_22·b_3_8 + b_4_20·c_4_23·b_1_1·b_3_11
       + b_2_5·c_4_23·b_1_1·b_5_40 + b_2_5·c_4_23·b_1_1·b_5_38
       + b_2_5·c_4_23·b_1_12·b_1_24 + b_2_5·b_4_19·c_4_23·b_1_12
       + b_2_5·c_4_22·c_4_23·b_1_1·b_1_2
  143. a_5_39·b_7_99 + a_2_4·b_2_52·b_1_2·b_5_40 + a_2_4·b_2_53·b_1_24
       + a_2_4·b_2_52·c_4_22·b_1_22
  144. b_5_38·b_7_99 + b_2_5·b_4_19·b_1_1·b_5_41 + b_2_52·b_4_19·b_1_2·b_3_11
       + b_2_52·b_4_19·b_1_1·b_3_8 + b_2_53·b_4_19·b_1_1·b_1_2 + c_4_23·b_1_13·b_5_40
       + c_4_23·b_1_14·b_1_2·b_3_8 + b_4_19·c_4_23·b_1_1·b_3_9 + b_4_19·c_4_23·b_1_14
       + b_2_5·c_4_23·b_1_12·b_1_2·b_3_11 + b_2_5·c_4_23·b_1_12·b_1_2·b_3_9
       + b_2_5·c_4_23·b_1_12·b_1_2·b_3_8 + b_2_5·c_4_23·b_1_13·b_3_11
       + b_2_5·c_4_23·b_1_13·b_3_9 + b_2_5·c_4_23·b_1_13·b_1_23
       + b_2_5·b_4_20·c_4_23·b_1_12 + b_2_5·b_4_19·c_4_23·b_1_1·b_1_2
       + b_2_5·b_4_19·c_4_23·b_1_12 + b_2_5·b_4_19·c_4_22·b_1_1·b_1_2
       + b_2_52·c_4_23·b_1_2·b_3_9 + b_2_52·c_4_23·b_1_1·b_3_9
       + b_2_52·c_4_23·b_1_1·b_3_8 + b_2_52·c_4_23·b_1_13·b_1_2 + b_2_52·c_4_23·b_1_14
       + a_2_4·b_2_5·b_4_21·c_4_23 + a_2_4·b_2_5·b_4_20·c_4_23 + c_4_232·b_1_14
       + c_4_22·c_4_23·b_1_13·b_1_2
  145. b_5_41·b_7_99 + b_4_19·b_1_13·b_5_40 + b_4_19·b_1_13·b_1_22·b_3_8
       + b_4_19·b_1_14·b_1_2·b_3_8 + b_4_19·b_4_20·b_1_1·b_3_11 + b_4_19·b_4_20·b_1_1·b_3_9
       + b_4_19·b_4_20·b_1_1·b_3_8 + b_4_19·b_4_20·b_1_12·b_1_22
       + b_4_19·b_4_20·b_1_13·b_1_2 + b_2_5·b_1_15·b_1_22·b_3_8
       + b_2_5·b_4_20·b_1_1·b_1_22·b_3_8 + b_2_5·b_4_20·b_1_12·b_1_2·b_3_8
       + b_2_5·b_4_20·b_1_12·b_1_24 + b_2_5·b_4_20·b_1_13·b_3_11
       + b_2_5·b_4_20·b_1_13·b_3_9 + b_2_5·b_4_20·b_1_13·b_3_8
       + b_2_5·b_4_20·b_1_13·b_1_23 + b_2_5·b_4_20·b_1_14·b_1_22
       + b_2_5·b_4_20·b_1_15·b_1_2 + b_2_5·b_4_202·b_1_12 + b_2_5·b_4_19·b_1_2·b_5_40
       + b_2_5·b_4_19·b_1_23·b_3_8 + b_2_5·b_4_19·b_1_1·b_5_41 + b_2_5·b_4_19·b_1_1·b_5_40
       + b_2_5·b_4_19·b_1_1·b_1_22·b_3_8 + b_2_5·b_4_19·b_1_1·b_1_25
       + b_2_5·b_4_19·b_1_12·b_1_2·b_3_11 + b_2_5·b_4_19·b_1_12·b_1_24
       + b_2_5·b_4_19·b_1_13·b_3_11 + b_2_5·b_4_19·b_1_13·b_1_23
       + b_2_5·b_4_19·b_4_20·b_1_22 + b_2_5·b_4_19·b_4_20·b_1_1·b_1_2
       + b_2_5·b_4_19·b_4_20·b_1_12 + b_2_52·b_1_2·b_7_99 + b_2_52·b_1_1·b_1_27
       + b_2_52·b_1_13·b_1_25 + b_2_52·b_1_14·b_1_24 + b_2_52·b_4_20·b_1_2·b_3_11
       + b_2_52·b_4_20·b_1_1·b_3_11 + b_2_52·b_4_20·b_1_12·b_1_22
       + b_2_52·b_4_20·b_1_14 + b_2_52·b_4_19·b_1_2·b_3_11 + b_2_52·b_4_19·b_1_1·b_3_9
       + b_2_52·b_4_19·b_1_1·b_3_8 + b_2_52·b_4_19·b_1_12·b_1_22
       + b_2_52·b_4_19·b_1_14 + b_2_52·b_4_19·b_4_20 + b_2_53·b_1_2·b_5_41
       + b_2_53·b_1_2·b_5_40 + b_2_53·b_1_2·b_5_38 + b_2_53·b_1_1·b_5_40
       + b_2_53·b_1_1·b_5_38 + b_2_53·b_1_12·b_1_24 + b_2_53·b_6_65
       + b_2_53·b_4_19·b_1_12 + b_2_55·b_1_22 + a_2_4·b_2_52·b_1_2·b_5_40
       + a_2_4·b_2_52·b_1_23·b_3_8 + a_2_4·b_2_53·b_1_24 + a_2_4·b_2_53·b_4_20
       + c_4_23·b_1_1·b_7_99 + c_4_23·b_1_13·b_5_38 + c_4_23·b_1_13·b_1_22·b_3_8
       + c_4_23·b_1_14·b_1_2·b_3_8 + c_4_23·b_1_15·b_3_8 + c_4_23·b_1_16·b_1_22
       + c_4_22·b_1_2·b_7_99 + b_4_20·c_4_23·b_1_14 + b_4_19·c_4_23·b_1_1·b_3_11
       + b_4_19·c_4_23·b_1_13·b_1_2 + b_4_19·c_4_23·b_1_14 + b_4_19·c_4_22·b_1_1·b_3_9
       + b_4_19·c_4_22·b_1_1·b_3_8 + b_4_19·c_4_22·b_1_12·b_1_22
       + b_4_19·c_4_22·b_1_13·b_1_2 + b_2_5·c_4_23·b_1_1·b_5_38
       + b_2_5·c_4_23·b_1_12·b_1_2·b_3_11 + b_2_5·c_4_23·b_1_12·b_1_24
       + b_2_5·c_4_23·b_1_13·b_3_9 + b_2_5·c_4_23·b_1_13·b_1_23
       + b_2_5·c_4_23·b_1_15·b_1_2 + b_2_5·c_4_23·b_1_16 + b_2_5·c_4_22·b_1_1·b_5_38
       + b_2_5·c_4_22·b_1_1·b_1_22·b_3_8 + b_2_5·c_4_22·b_1_12·b_1_24
       + b_2_5·c_4_22·b_1_13·b_3_8 + b_2_5·c_4_22·b_1_14·b_1_22
       + b_2_5·b_4_20·c_4_23·b_1_1·b_1_2 + b_2_5·b_4_19·c_4_23·b_1_1·b_1_2
       + b_2_5·b_4_19·c_4_23·b_1_12 + b_2_5·b_4_19·c_4_22·b_1_1·b_1_2
       + b_2_5·b_4_19·c_4_22·b_1_12 + b_2_52·c_4_23·b_1_2·b_3_11
       + b_2_52·c_4_23·b_1_2·b_3_9 + b_2_52·c_4_23·b_1_1·b_3_11
       + b_2_52·c_4_23·b_1_1·b_3_9 + b_2_52·c_4_23·b_1_1·b_3_8
       + b_2_52·c_4_23·b_1_13·b_1_2 + b_2_52·b_4_21·c_4_23 + b_2_52·b_4_20·c_4_23
       + b_2_53·c_4_23·b_1_1·b_1_2 + b_2_53·c_4_23·b_1_12 + b_2_53·c_4_22·b_1_1·b_1_2
       + a_2_4·b_2_5·b_4_21·c_4_23 + a_2_4·b_2_52·c_4_23·b_1_22 + a_2_4·b_2_53·c_4_23
       + c_4_232·b_1_1·b_3_9 + c_4_232·b_1_14 + c_4_22·c_4_23·b_1_1·b_3_9
       + c_4_22·c_4_23·b_1_14
  146. b_5_41·b_7_99 + b_5_40·b_7_99 + b_4_19·b_1_13·b_5_40 + b_4_19·b_1_13·b_1_22·b_3_8
       + b_4_19·b_1_14·b_1_2·b_3_8 + b_4_19·b_4_20·b_1_1·b_3_9
       + b_2_5·b_1_15·b_1_22·b_3_8 + b_2_5·b_4_20·b_1_12·b_1_2·b_3_11
       + b_2_5·b_4_20·b_1_12·b_1_2·b_3_8 + b_2_5·b_4_20·b_1_13·b_3_11
       + b_2_5·b_4_20·b_1_13·b_3_9 + b_2_5·b_4_20·b_1_13·b_3_8
       + b_2_5·b_4_20·b_1_13·b_1_23 + b_2_5·b_4_20·b_1_15·b_1_2
       + b_2_5·b_4_19·b_1_1·b_5_40 + b_2_5·b_4_19·b_1_1·b_1_22·b_3_8
       + b_2_5·b_4_19·b_1_12·b_1_2·b_3_11 + b_2_5·b_4_19·b_1_12·b_1_2·b_3_8
       + b_2_5·b_4_19·b_1_12·b_1_24 + b_2_5·b_4_19·b_1_13·b_3_11
       + b_2_5·b_4_19·b_1_13·b_3_8 + b_2_5·b_4_19·b_1_13·b_1_23
       + b_2_5·b_4_19·b_4_20·b_1_1·b_1_2 + b_2_5·b_4_19·b_4_20·b_1_12
       + b_2_52·b_1_2·b_7_99 + b_2_52·b_1_1·b_7_99 + b_2_52·b_1_12·b_1_26
       + b_2_52·b_1_13·b_1_25 + b_2_52·b_1_14·b_1_24 + b_2_52·b_4_20·b_1_1·b_3_11
       + b_2_52·b_4_20·b_1_12·b_1_22 + b_2_52·b_4_20·b_1_13·b_1_2
       + b_2_52·b_4_20·b_1_14 + b_2_52·b_4_19·b_1_1·b_3_9 + b_2_52·b_4_19·b_1_1·b_3_8
       + b_2_52·b_4_19·b_1_1·b_1_23 + b_2_52·b_4_19·b_1_12·b_1_22
       + b_2_52·b_4_19·b_1_13·b_1_2 + b_2_52·b_4_19·b_1_14 + b_2_53·b_1_2·b_5_41
       + b_2_53·b_1_2·b_5_40 + b_2_53·b_1_1·b_5_41 + b_2_53·b_1_12·b_1_24
       + b_2_53·b_4_20·b_1_12 + b_2_53·b_4_19·b_1_1·b_1_2 + b_2_53·b_4_19·b_1_12
       + b_2_55·b_1_22 + c_4_23·b_1_12·b_1_2·b_5_41 + c_4_23·b_1_15·b_3_8
       + c_4_23·b_1_16·b_1_22 + b_4_20·c_4_23·b_1_1·b_3_9 + b_4_20·c_4_23·b_1_14
       + b_4_19·c_4_23·b_1_1·b_3_11 + b_4_19·c_4_23·b_1_14 + b_4_19·c_4_22·b_1_1·b_3_9
       + b_4_19·c_4_22·b_1_13·b_1_2 + b_2_5·c_4_23·b_1_1·b_5_38
       + b_2_5·c_4_23·b_1_12·b_1_2·b_3_11 + b_2_5·c_4_23·b_1_14·b_1_22
       + b_2_5·c_4_23·b_1_15·b_1_2 + b_2_5·c_4_23·b_1_16
       + b_2_5·c_4_22·b_1_12·b_1_2·b_3_8 + b_2_5·c_4_22·b_1_13·b_3_8
       + b_2_5·c_4_22·b_1_13·b_1_23 + b_2_5·c_4_22·b_1_14·b_1_22
       + b_2_5·b_4_19·c_4_23·b_1_1·b_1_2 + b_2_5·b_4_19·c_4_22·b_1_12
       + b_2_52·c_4_23·b_1_12·b_1_22 + b_2_53·c_4_23·b_1_12
       + b_2_53·c_4_22·b_1_1·b_1_2 + c_4_232·b_1_14 + c_4_22·c_4_23·b_1_12·b_1_22
       + c_4_22·c_4_23·b_1_14
  147. b_6_65·b_7_99 + b_2_5·b_4_19·b_1_12·b_5_40 + b_2_5·b_4_19·b_1_12·b_1_22·b_3_8
       + b_2_5·b_4_19·b_1_13·b_1_2·b_3_8 + b_2_5·b_4_19·b_4_20·b_3_11
       + b_2_52·b_4_19·b_5_41 + b_2_52·b_4_19·b_1_1·b_1_2·b_3_8
       + b_2_52·b_4_19·b_1_1·b_1_24 + b_2_52·b_4_19·b_1_12·b_3_8
       + b_2_52·b_4_19·b_1_12·b_1_23 + b_2_53·b_6_65·b_1_2
       + b_2_53·b_4_19·b_1_1·b_1_22 + b_2_54·b_4_19·b_1_2 + c_4_23·b_1_14·b_1_22·b_3_8
       + b_4_20·c_4_23·b_1_12·b_3_11 + b_4_20·c_4_23·b_1_12·b_3_9
       + b_4_20·c_4_23·b_1_12·b_3_8 + b_4_20·c_4_23·b_1_13·b_1_22
       + b_4_20·c_4_23·b_1_14·b_1_2 + b_4_19·c_4_23·b_5_41 + b_4_19·c_4_23·b_5_40
       + b_4_19·c_4_23·b_1_1·b_1_2·b_3_11 + b_4_19·c_4_23·b_1_12·b_3_9
       + b_4_19·c_4_23·b_1_12·b_3_8 + b_2_5·c_4_23·b_1_12·b_1_22·b_3_8
       + b_2_5·c_4_23·b_1_12·b_1_25 + b_2_5·c_4_23·b_1_13·b_1_2·b_3_11
       + b_2_5·c_4_23·b_1_13·b_1_24 + b_2_5·c_4_23·b_1_15·b_1_22
       + b_2_5·b_4_19·c_4_23·b_3_9 + b_2_5·b_4_19·c_4_23·b_1_12·b_1_2
       + b_2_5·b_4_19·c_4_23·b_1_13 + b_2_5·b_4_19·c_4_22·b_3_9
       + b_2_5·b_4_19·c_4_22·b_1_12·b_1_2 + b_2_52·c_4_23·b_1_1·b_1_2·b_3_11
       + b_2_52·c_4_23·b_1_1·b_1_2·b_3_9 + b_2_52·c_4_23·b_1_12·b_3_11
       + b_2_52·c_4_23·b_1_12·b_3_9 + b_2_52·c_4_23·b_1_12·b_3_8
       + b_2_52·c_4_23·b_1_13·b_1_22 + b_2_52·b_4_19·c_4_23·b_1_2
       + b_2_52·b_4_19·c_4_22·b_1_2 + b_2_53·c_4_23·b_3_9 + b_2_53·c_4_23·b_1_13
       + a_2_4·b_2_52·c_4_23·b_3_11 + c_4_232·b_1_1·b_1_2·b_3_9
       + c_4_232·b_1_13·b_1_22 + c_4_232·b_1_14·b_1_2
       + c_4_22·c_4_23·b_1_1·b_1_2·b_3_9 + c_4_22·c_4_23·b_1_13·b_1_22
  148. b_7_992 + b_2_52·b_1_15·b_1_22·b_3_8 + b_2_52·b_4_20·b_1_13·b_3_11
       + b_2_52·b_4_20·b_1_13·b_3_9 + b_2_52·b_4_20·b_1_13·b_3_8
       + b_2_52·b_4_20·b_1_14·b_1_22 + b_2_52·b_4_20·b_1_15·b_1_2
       + b_2_52·b_4_202·b_1_12 + b_2_52·b_4_19·b_1_13·b_3_11
       + b_2_53·b_1_13·b_1_25 + b_2_53·b_1_14·b_1_24 + b_2_53·b_4_20·b_1_1·b_3_11
       + b_2_53·b_4_20·b_1_14 + b_2_53·b_4_19·b_1_14 + b_2_54·b_1_1·b_5_40
       + b_2_54·b_1_1·b_5_38 + b_2_54·b_1_12·b_1_24 + b_2_54·b_4_19·b_1_12
       + b_2_56·b_1_22 + c_4_23·b_1_15·b_1_22·b_3_8 + b_4_20·c_4_23·b_1_13·b_3_11
       + b_4_20·c_4_23·b_1_13·b_3_9 + b_4_20·c_4_23·b_1_13·b_3_8
       + b_4_20·c_4_23·b_1_14·b_1_22 + b_4_20·c_4_23·b_1_15·b_1_2
       + b_4_19·c_4_23·b_1_13·b_3_11 + b_2_5·c_4_23·b_1_13·b_1_25
       + b_2_5·c_4_23·b_1_14·b_1_24 + b_2_5·b_4_20·c_4_23·b_1_1·b_3_11
       + b_2_5·b_4_20·c_4_23·b_1_14 + b_2_5·b_4_19·c_4_23·b_1_14
       + b_2_52·c_4_23·b_1_1·b_5_40 + b_2_52·c_4_23·b_1_1·b_5_38
       + b_2_52·c_4_23·b_1_12·b_1_24 + b_2_52·c_4_23·b_1_14·b_1_22
       + b_2_52·c_4_23·b_1_15·b_1_2 + b_2_52·c_4_23·b_1_16
       + b_2_52·c_4_22·b_1_13·b_3_8 + b_2_52·c_4_22·b_1_14·b_1_22
       + b_2_52·b_4_19·c_4_23·b_1_12 + b_2_54·c_4_22·b_1_1·b_1_2
       + c_4_232·b_1_13·b_3_8 + c_4_232·b_1_15·b_1_2 + c_4_232·b_1_16
       + c_4_22·c_4_23·b_1_13·b_3_8 + c_4_22·c_4_23·b_1_14·b_1_22
       + b_2_5·c_4_232·b_1_12·b_1_22 + b_2_52·c_4_22·c_4_23·b_1_1·b_1_2

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

Data used for Benson′s test

  • Benson′s completion test succeeded in degree 15.
  • However, the last relation was already found in degree 14 and the last generator in degree 7.
  • The following is a filter regular homogeneous system of parameters:
    1. c_4_22, a Duflot regular element of degree 4
    2. c_4_23, a Duflot regular element of degree 4
    3. b_1_24 + b_1_12·b_1_22 + b_1_14 + b_2_5·b_1_22 + b_2_5·b_1_1·b_1_2 + b_2_52, an element of degree 4
    4. b_1_12·b_1_24 + b_1_14·b_1_22 + b_2_5·b_1_24 + b_2_5·b_1_13·b_1_2
         + b_2_52·b_1_22 + b_2_52·b_1_1·b_1_2 + b_2_52·b_1_12, an element of degree 6
    5. b_1_22, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 2, 6, 13, 15].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -5, -5].

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. 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. a_3_7 → 0, an element of degree 3
  7. a_3_5 → 0, an element of degree 3
  8. b_3_8 → 0, an element of degree 3
  9. b_3_9 → 0, an element of degree 3
  10. b_3_11 → 0, an element of degree 3
  11. b_4_19 → 0, an element of degree 4
  12. b_4_20 → 0, an element of degree 4
  13. b_4_21 → 0, an element of degree 4
  14. c_4_22 → c_1_04, an element of degree 4
  15. c_4_23 → c_1_14, an element of degree 4
  16. a_5_39 → 0, an element of degree 5
  17. b_5_38 → 0, an element of degree 5
  18. b_5_40 → 0, an element of degree 5
  19. b_5_41 → 0, an element of degree 5
  20. b_6_65 → 0, an element of degree 6
  21. b_7_99 → 0, an element of degree 7

Restriction map to a maximal el. ab. subgp. of rank 5

  1. a_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_3, an element of degree 1
  4. a_2_4 → 0, an element of degree 2
  5. b_2_5 → c_1_42 + c_1_2·c_1_4, an element of degree 2
  6. a_3_7 → 0, an element of degree 3
  7. a_3_5 → 0, an element of degree 3
  8. b_3_8 → c_1_32·c_1_4 + c_1_12·c_1_2, an element of degree 3
  9. b_3_9 → c_1_2·c_1_3·c_1_4 + c_1_1·c_1_22, an element of degree 3
  10. b_3_11 → c_1_43 + c_1_2·c_1_3·c_1_4 + c_1_22·c_1_4 + c_1_1·c_1_22 + c_1_0·c_1_22
       + c_1_02·c_1_2, an element of degree 3
  11. b_4_19 → c_1_1·c_1_2·c_1_32 + c_1_12·c_1_2·c_1_3, an element of degree 4
  12. b_4_20 → c_1_32·c_1_42 + c_1_33·c_1_4 + c_1_2·c_1_32·c_1_4 + c_1_1·c_1_2·c_1_32
       + c_1_12·c_1_42 + c_1_12·c_1_2·c_1_4 + c_1_0·c_1_2·c_1_32 + c_1_02·c_1_32, an element of degree 4
  13. b_4_21 → c_1_3·c_1_43 + c_1_32·c_1_42 + c_1_33·c_1_4 + c_1_2·c_1_3·c_1_42
       + c_1_2·c_1_32·c_1_4 + c_1_1·c_1_2·c_1_42 + c_1_1·c_1_2·c_1_32
       + c_1_1·c_1_22·c_1_4 + c_1_12·c_1_42 + c_1_12·c_1_2·c_1_4 + c_1_0·c_1_2·c_1_32
       + c_1_02·c_1_32, an element of degree 4
  14. c_4_22 → c_1_3·c_1_43 + c_1_22·c_1_3·c_1_4 + c_1_1·c_1_2·c_1_32 + c_1_1·c_1_22·c_1_3
       + c_1_12·c_1_42 + c_1_12·c_1_2·c_1_4 + c_1_12·c_1_2·c_1_3 + c_1_12·c_1_22
       + c_1_0·c_1_2·c_1_42 + c_1_0·c_1_2·c_1_32 + c_1_0·c_1_22·c_1_4
       + c_1_0·c_1_22·c_1_3 + c_1_02·c_1_42 + c_1_02·c_1_32 + c_1_02·c_1_2·c_1_4
       + c_1_02·c_1_2·c_1_3 + c_1_02·c_1_22 + c_1_04, an element of degree 4
  15. c_4_23 → c_1_12·c_1_32 + c_1_14, an element of degree 4
  16. a_5_39 → 0, an element of degree 5
  17. b_5_38 → c_1_1·c_1_2·c_1_32·c_1_4 + c_1_12·c_1_2·c_1_3·c_1_4 + c_1_12·c_1_22·c_1_3
       + c_1_13·c_1_22, an element of degree 5
  18. b_5_40 → c_1_33·c_1_42 + c_1_2·c_1_32·c_1_42 + c_1_22·c_1_32·c_1_4
       + c_1_1·c_1_2·c_1_33 + c_1_12·c_1_43 + c_1_12·c_1_3·c_1_42
       + c_1_12·c_1_2·c_1_42 + c_1_12·c_1_2·c_1_3·c_1_4 + c_1_12·c_1_2·c_1_32
       + c_1_12·c_1_22·c_1_3 + c_1_0·c_1_2·c_1_3·c_1_42 + c_1_0·c_1_2·c_1_32·c_1_4
       + c_1_0·c_1_2·c_1_33 + c_1_0·c_1_22·c_1_3·c_1_4 + c_1_0·c_1_22·c_1_32
       + c_1_0·c_1_12·c_1_22 + c_1_02·c_1_3·c_1_42 + c_1_02·c_1_32·c_1_4
       + c_1_02·c_1_33 + c_1_02·c_1_2·c_1_3·c_1_4 + c_1_02·c_1_2·c_1_32
       + c_1_02·c_1_22·c_1_3 + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_3, an element of degree 5
  19. b_5_41 → c_1_3·c_1_44 + c_1_33·c_1_42 + c_1_2·c_1_3·c_1_43 + c_1_2·c_1_32·c_1_42
       + c_1_22·c_1_32·c_1_4 + c_1_1·c_1_2·c_1_43 + c_1_1·c_1_2·c_1_32·c_1_4
       + c_1_1·c_1_2·c_1_33 + c_1_1·c_1_22·c_1_42 + c_1_1·c_1_22·c_1_32
       + c_1_12·c_1_43 + c_1_12·c_1_3·c_1_42 + c_1_12·c_1_2·c_1_42
       + c_1_12·c_1_2·c_1_32 + c_1_12·c_1_22·c_1_3 + c_1_13·c_1_22
       + c_1_0·c_1_2·c_1_3·c_1_42 + c_1_0·c_1_2·c_1_32·c_1_4 + c_1_0·c_1_2·c_1_33
       + c_1_0·c_1_22·c_1_32 + c_1_0·c_1_1·c_1_23 + c_1_0·c_1_12·c_1_22
       + c_1_02·c_1_3·c_1_42 + c_1_02·c_1_32·c_1_4 + c_1_02·c_1_33
       + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3 + c_1_02·c_1_1·c_1_22
       + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_3, an element of degree 5
  20. b_6_65 → c_1_1·c_1_2·c_1_32·c_1_42 + c_1_1·c_1_22·c_1_32·c_1_4 + c_1_13·c_1_2·c_1_42
       + c_1_13·c_1_22·c_1_4 + c_1_0·c_1_1·c_1_22·c_1_32 + c_1_0·c_1_12·c_1_22·c_1_3
       + c_1_02·c_1_1·c_1_2·c_1_32 + c_1_02·c_1_12·c_1_2·c_1_3, an element of degree 6
  21. b_7_99 → c_1_3·c_1_46 + c_1_2·c_1_32·c_1_44 + c_1_2·c_1_33·c_1_43
       + c_1_22·c_1_3·c_1_44 + c_1_22·c_1_33·c_1_42 + c_1_23·c_1_32·c_1_42
       + c_1_1·c_1_2·c_1_45 + c_1_1·c_1_2·c_1_32·c_1_43
       + c_1_1·c_1_22·c_1_32·c_1_42 + c_1_1·c_1_23·c_1_43 + c_1_12·c_1_2·c_1_44
       + c_1_12·c_1_2·c_1_33·c_1_4 + c_1_12·c_1_22·c_1_3·c_1_42
       + c_1_12·c_1_23·c_1_42 + c_1_12·c_1_23·c_1_3·c_1_4 + c_1_13·c_1_2·c_1_43
       + c_1_13·c_1_22·c_1_42 + c_1_13·c_1_22·c_1_32 + c_1_14·c_1_2·c_1_3·c_1_4
       + c_1_15·c_1_22 + c_1_0·c_1_22·c_1_3·c_1_43 + c_1_0·c_1_22·c_1_32·c_1_42
       + c_1_0·c_1_23·c_1_3·c_1_42 + c_1_0·c_1_23·c_1_32·c_1_4
       + c_1_0·c_1_1·c_1_22·c_1_32·c_1_4 + c_1_0·c_1_1·c_1_23·c_1_42
       + c_1_0·c_1_1·c_1_24·c_1_4 + c_1_0·c_1_12·c_1_22·c_1_3·c_1_4
       + c_1_0·c_1_12·c_1_23·c_1_3 + c_1_0·c_1_13·c_1_23 + c_1_02·c_1_2·c_1_3·c_1_43
       + c_1_02·c_1_2·c_1_32·c_1_42 + c_1_02·c_1_22·c_1_3·c_1_42
       + c_1_02·c_1_22·c_1_32·c_1_4 + c_1_02·c_1_1·c_1_2·c_1_32·c_1_4
       + c_1_02·c_1_1·c_1_22·c_1_42 + c_1_02·c_1_1·c_1_23·c_1_4
       + c_1_02·c_1_12·c_1_2·c_1_3·c_1_4 + c_1_02·c_1_12·c_1_22·c_1_3
       + c_1_02·c_1_13·c_1_22, an element of degree 7

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