Cohomology of group number 85 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 2 minimal generators and exponent 8.
  • It is non-abelian.
  • It has p-Rank 3.
  • Its center has rank 2.
  • It has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 3.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 3 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t7  +  t6  +  t5  +  t4  +  t3  +  t  +  1)
    (t  +  1)2 · (t  −  1)3 · (t2  +  1) · (t4  +  1)
  • The a-invariants are -∞,-∞,-3,-3. 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 22 minimal generators of maximal degree 9:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_1, a nilpotent element of degree 1
  3. a_2_1, a nilpotent element of degree 2
  4. c_2_2, a Duflot regular element of degree 2
  5. a_3_2, a nilpotent element of degree 3
  6. a_3_3, a nilpotent element of degree 3
  7. a_3_4, a nilpotent element of degree 3
  8. a_4_3, a nilpotent element of degree 4
  9. b_4_5, an element of degree 4
  10. a_5_5, a nilpotent element of degree 5
  11. a_5_6, a nilpotent element of degree 5
  12. a_5_8, a nilpotent element of degree 5
  13. a_5_9, a nilpotent element of degree 5
  14. a_6_9, a nilpotent element of degree 6
  15. b_6_10, an element of degree 6
  16. a_7_10, a nilpotent element of degree 7
  17. a_7_15, a nilpotent element of degree 7
  18. a_7_16, a nilpotent element of degree 7
  19. a_8_15, a nilpotent element of degree 8
  20. c_8_20, a Duflot regular element of degree 8
  21. a_9_22, a nilpotent element of degree 9
  22. a_9_25, a nilpotent element of degree 9

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

Ring relations

There are 189 minimal relations of maximal degree 18:

  1. a_1_02
  2. a_1_0·a_1_1
  3. a_1_13
  4. a_2_1·a_1_1
  5. a_2_1·a_1_0
  6. a_2_12
  7. a_1_0·a_3_2
  8. a_1_1·a_3_3
  9. a_1_0·a_3_3
  10. a_1_0·a_3_4
  11. a_2_1·a_3_2
  12. a_1_12·a_3_2
  13. a_2_1·a_3_3
  14. a_2_1·a_3_4
  15. a_1_12·a_3_4
  16. a_4_3·a_1_1
  17. a_4_3·a_1_0
  18. b_4_5·a_1_0
  19. a_3_2·a_3_3
  20. a_3_3·a_3_4 + a_3_32 + a_3_22
  21. a_2_1·a_4_3
  22. a_2_1·b_4_5 + a_3_32 + a_3_22
  23. a_3_22 + b_4_5·a_1_12
  24. a_1_1·a_5_5
  25. a_1_0·a_5_5
  26. a_3_42 + a_1_1·a_5_6 + c_2_2·a_1_1·a_3_2 + c_2_22·a_1_12
  27. a_1_0·a_5_6
  28. a_3_42 + a_1_1·a_5_8 + c_2_2·a_1_1·a_3_4 + c_2_2·a_1_1·a_3_2 + c_2_22·a_1_12
  29. a_1_0·a_5_8
  30. a_3_2·a_3_4 + a_3_22 + a_1_1·a_5_9 + c_2_2·a_1_1·a_3_4 + c_2_2·a_1_1·a_3_2
  31. a_1_0·a_5_9
  32. a_4_3·a_3_2
  33. a_4_3·a_3_4 + a_4_3·a_3_3
  34. a_4_3·a_3_3 + a_2_1·a_5_5
  35. a_2_1·a_5_6
  36. a_1_12·a_5_6
  37. a_4_3·a_3_3 + a_2_1·a_5_8
  38. a_4_3·a_3_3 + a_2_1·a_5_9
  39. a_4_3·a_3_3 + a_1_12·a_5_9
  40. a_6_9·a_1_1 + a_4_3·a_3_3
  41. a_6_9·a_1_0 + a_4_3·a_3_3
  42. b_6_10·a_1_1 + b_4_5·a_3_2
  43. b_6_10·a_1_0
  44. a_4_32
  45. a_4_3·b_4_5 + a_3_3·a_5_5 + c_2_2·b_4_5·a_1_12
  46. a_3_2·a_5_5
  47. a_4_3·b_4_5 + a_3_4·a_5_5 + b_4_5·a_1_1·a_3_2 + c_2_2·b_4_5·a_1_12
  48. a_4_3·b_4_5 + a_3_3·a_5_6 + b_4_5·a_1_1·a_3_2 + c_2_2·b_4_5·a_1_12
  49. a_4_3·b_4_5 + a_3_3·a_5_8 + b_4_5·a_1_1·a_3_2 + c_2_2·a_3_32
  50. a_3_4·a_5_8 + a_3_4·a_5_6 + c_2_2·a_1_1·a_5_6 + c_2_22·a_1_1·a_3_2 + c_2_23·a_1_12
  51. a_4_3·b_4_5 + a_3_3·a_5_9 + b_4_5·a_1_1·a_3_2
  52. a_3_2·a_5_9 + a_3_2·a_5_8 + a_3_2·a_5_6 + b_4_5·a_1_1·a_3_4 + b_4_5·a_1_1·a_3_2
       + c_2_2·b_4_5·a_1_12
  53. a_3_4·a_5_9 + a_3_2·a_5_8 + b_4_5·a_1_1·a_3_4 + c_2_2·a_3_32 + c_2_2·a_1_1·a_5_6
       + c_2_23·a_1_12
  54. a_3_2·a_5_8 + a_3_2·a_5_6 + c_2_2·a_1_1·a_5_9 + c_2_2·b_4_5·a_1_12
       + c_2_22·a_1_1·a_3_4 + c_2_22·a_1_1·a_3_2
  55. a_2_1·a_6_9
  56. a_4_3·b_4_5 + a_2_1·b_6_10 + b_4_5·a_1_1·a_3_2 + c_2_2·b_4_5·a_1_12
  57. a_3_2·a_5_6 + a_1_1·a_7_10 + c_2_2·a_1_1·a_5_6 + c_2_22·a_1_1·a_3_2
  58. a_1_0·a_7_10
  59. a_3_2·a_5_8 + a_1_1·a_7_15 + b_4_5·a_1_1·a_3_4 + c_2_22·a_1_1·a_3_4
  60. a_1_0·a_7_15
  61. a_3_4·a_5_6 + a_3_2·a_5_8 + a_3_2·a_5_6 + a_1_1·a_7_16 + b_4_5·a_1_1·a_3_4
       + b_4_5·a_1_1·a_3_2 + c_2_2·a_1_1·a_5_6 + c_2_2·b_4_5·a_1_12 + c_2_22·a_1_1·a_3_4
       + c_2_22·a_1_1·a_3_2
  62. a_1_0·a_7_16
  63. a_4_3·a_5_5
  64. a_4_3·a_5_6
  65. a_4_3·a_5_9 + a_4_3·a_5_8
  66. a_4_3·a_5_8 + c_2_2·a_1_12·a_5_9
  67. b_4_5·a_5_8 + b_4_5·a_5_6 + a_6_9·a_3_3 + c_2_2·b_4_5·a_3_4
  68. a_6_9·a_3_2
  69. b_4_5·a_5_8 + b_4_5·a_5_6 + a_6_9·a_3_4 + c_2_2·b_4_5·a_3_4
  70. b_6_10·a_3_3 + b_4_5·a_5_8 + b_4_5·a_5_6 + b_4_5·a_5_5 + c_2_2·b_4_5·a_3_4
  71. b_6_10·a_3_2 + b_4_52·a_1_1 + a_4_3·a_5_8
  72. b_6_10·a_3_4 + b_4_5·a_5_9 + b_4_5·a_5_8 + b_4_5·a_5_6 + b_4_52·a_1_1 + a_4_3·a_5_8
       + c_2_2·b_4_5·a_3_3 + c_2_2·b_4_5·a_3_2
  73. a_2_1·a_7_10
  74. a_1_12·a_7_10
  75. b_4_5·a_5_8 + b_4_5·a_5_6 + a_4_3·a_5_8 + a_2_1·a_7_15 + c_2_2·b_4_5·a_3_4
  76. b_4_5·a_5_8 + b_4_5·a_5_6 + a_4_3·a_5_8 + a_2_1·a_7_16 + c_2_2·b_4_5·a_3_4
  77. b_4_5·a_5_8 + b_4_5·a_5_6 + a_4_3·a_5_8 + a_1_12·a_7_16 + c_2_2·b_4_5·a_3_4
  78. a_8_15·a_1_1 + a_4_3·a_5_8
  79. a_8_15·a_1_0 + a_4_3·a_5_8
  80. a_5_52 + b_4_5·a_3_32
  81. a_5_5·a_5_6 + b_4_5·a_3_32 + b_4_52·a_1_12
  82. a_5_5·a_5_8 + b_4_5·a_3_32 + b_4_52·a_1_12 + c_2_2·a_3_3·a_5_5
       + c_2_2·b_4_5·a_1_1·a_3_2
  83. a_5_82 + a_5_62 + c_2_22·a_1_1·a_5_6 + c_2_23·a_1_1·a_3_2 + c_2_24·a_1_12
  84. a_5_5·a_5_9 + b_4_5·a_3_32 + b_4_52·a_1_12 + c_2_2·b_4_5·a_1_1·a_3_2
  85. a_5_92 + b_4_5·a_1_1·a_5_6 + b_4_52·a_1_12 + c_2_2·b_4_5·a_1_1·a_3_2
       + c_2_22·a_3_32 + c_2_22·a_1_1·a_5_6 + c_2_23·a_1_1·a_3_2 + c_2_24·a_1_12
  86. a_4_3·a_6_9
  87. a_4_3·b_6_10 + b_4_5·a_3_32 + c_2_2·b_4_5·a_1_1·a_3_2
  88. a_3_3·a_7_10 + b_4_5·a_3_32 + b_4_52·a_1_12 + c_2_2·b_4_5·a_1_1·a_3_2
  89. a_5_8·a_5_9 + a_5_6·a_5_9 + a_3_2·a_7_10 + b_4_5·a_1_1·a_5_6 + c_2_2·b_4_5·a_1_1·a_3_4
       + c_2_22·a_3_32 + c_2_22·a_1_1·a_5_9 + c_2_22·a_1_1·a_5_6 + c_2_23·a_1_1·a_3_4
       + c_2_23·a_1_1·a_3_2 + c_2_24·a_1_12
  90. a_5_8·a_5_9 + a_3_4·a_7_10 + b_4_5·a_1_1·a_5_6 + c_2_2·b_4_5·a_1_1·a_3_4
       + c_2_22·a_3_32 + c_2_22·a_1_1·a_5_6 + c_2_24·a_1_12
  91. a_5_8·a_5_9 + a_5_6·a_5_9 + c_2_2·a_1_1·a_7_10 + c_2_2·b_4_5·a_1_1·a_3_4
       + c_2_22·a_3_32 + c_2_22·a_1_1·a_5_9 + c_2_22·b_4_5·a_1_12 + c_2_23·a_1_1·a_3_4
       + c_2_24·a_1_12
  92. b_4_5·a_6_9 + a_3_3·a_7_15 + b_4_5·a_3_32 + b_4_52·a_1_12 + c_2_2·a_3_3·a_5_5
       + c_2_22·a_3_32
  93. a_3_2·a_7_15 + b_4_5·a_1_1·a_5_9 + b_4_5·a_1_1·a_5_6 + b_4_52·a_1_12
       + c_2_2·b_4_5·a_1_1·a_3_2 + c_2_22·a_1_1·a_5_9 + c_2_22·b_4_5·a_1_12
       + c_2_23·a_1_1·a_3_4 + c_2_23·a_1_1·a_3_2
  94. b_4_5·a_6_9 + a_5_6·a_5_9 + a_5_6·a_5_8 + a_5_62 + a_3_4·a_7_15 + b_4_5·a_3_32
       + b_4_5·a_1_1·a_5_9 + b_4_5·a_1_1·a_5_6 + b_4_52·a_1_12 + c_2_2·a_3_3·a_5_5
       + c_2_2·b_4_5·a_1_1·a_3_4 + c_2_2·b_4_5·a_1_1·a_3_2 + c_2_22·a_1_1·a_5_6
       + c_2_24·a_1_12
  95. a_3_3·a_7_16 + b_4_5·a_3_32 + b_4_5·a_1_1·a_5_9 + b_4_5·a_1_1·a_5_6 + b_4_52·a_1_12
       + c_2_2·b_4_5·a_1_1·a_3_4 + c_2_2·b_4_5·a_1_1·a_3_2 + c_2_22·b_4_5·a_1_12
  96. a_5_6·a_5_9 + a_5_6·a_5_8 + a_5_62 + a_3_2·a_7_16 + b_4_5·a_1_1·a_5_9
       + b_4_5·a_1_1·a_5_6 + c_2_2·a_3_3·a_5_5 + c_2_2·b_4_5·a_1_1·a_3_2 + c_2_22·a_1_1·a_5_9
       + c_2_23·a_1_1·a_3_4 + c_2_23·a_1_1·a_3_2
  97. b_4_5·a_6_9 + a_5_6·a_5_8 + a_3_4·a_7_16 + b_4_5·a_3_32 + c_2_2·a_3_3·a_5_5
       + c_2_2·b_4_5·a_1_1·a_3_4 + c_2_22·a_1_1·a_5_9 + c_2_22·b_4_5·a_1_12
       + c_2_23·a_1_1·a_3_4 + c_2_23·a_1_1·a_3_2 + c_2_24·a_1_12
  98. a_5_6·a_5_8 + a_5_62 + c_2_2·a_1_1·a_7_16 + c_2_2·b_4_5·a_1_1·a_3_4
       + c_2_2·b_4_5·a_1_1·a_3_2 + c_2_22·a_1_1·a_5_9 + c_2_22·a_1_1·a_5_6
  99. a_5_62 + b_4_5·a_1_1·a_5_6 + b_4_52·a_1_12 + c_8_20·a_1_12
       + c_2_22·b_4_5·a_1_12 + c_2_24·a_1_12
  100. a_2_1·a_8_15
  101. a_5_62 + a_1_1·a_9_22 + b_4_52·a_1_12 + c_2_2·b_4_5·a_1_1·a_3_4
       + c_2_22·a_1_1·a_5_6 + c_2_22·b_4_5·a_1_12 + c_2_23·a_1_1·a_3_2 + c_2_24·a_1_12
  102. a_1_0·a_9_22
  103. a_5_6·a_5_9 + a_1_1·a_9_25 + b_4_5·a_1_1·a_5_6 + c_2_2·a_3_3·a_5_5 + c_2_22·a_1_1·a_5_9
       + c_2_22·a_1_1·a_5_6 + c_2_22·b_4_5·a_1_12 + c_2_24·a_1_12
  104. a_1_0·a_9_25
  105. a_6_9·a_5_6 + a_6_9·a_5_5
  106. a_6_9·a_5_9 + a_6_9·a_5_5 + c_2_22·a_1_12·a_5_9
  107. b_6_10·a_5_5 + b_4_52·a_3_3 + a_6_9·a_5_5
  108. b_6_10·a_5_9 + b_4_52·a_3_4 + b_4_52·a_3_2 + a_6_9·a_5_5 + c_2_2·b_4_5·a_5_9
       + c_2_2·b_4_5·a_5_5 + c_2_22·b_4_5·a_3_4 + c_2_22·b_4_5·a_3_3 + c_2_22·b_4_5·a_3_2
  109. b_6_10·a_5_8 + b_6_10·a_5_6 + a_6_9·a_5_8 + c_2_2·b_4_5·a_5_9 + c_2_2·b_4_52·a_1_1
       + c_2_22·b_4_5·a_3_4 + c_2_22·b_4_5·a_3_3 + c_2_22·b_4_5·a_3_2
       + c_2_22·a_1_12·a_5_9
  110. a_4_3·a_7_10
  111. b_6_10·a_5_6 + b_4_5·a_7_10 + c_2_2·b_4_5·a_5_6 + c_2_2·b_4_5·a_5_5
       + c_2_22·b_4_5·a_3_2
  112. a_6_9·a_5_5 + a_4_3·a_7_15
  113. a_6_9·a_5_8 + a_6_9·a_5_5 + a_4_3·a_7_16 + c_2_22·a_1_12·a_5_9
  114. a_6_9·a_5_8 + a_6_9·a_5_5 + c_2_2·a_1_12·a_7_16 + c_2_22·a_1_12·a_5_9
  115. a_8_15·a_3_3 + a_6_9·a_5_8
  116. a_8_15·a_3_2
  117. a_8_15·a_3_4 + a_6_9·a_5_5 + c_2_22·a_1_12·a_5_9
  118. a_6_9·a_5_5 + a_2_1·a_9_22
  119. a_6_9·a_5_8 + a_2_1·a_9_25
  120. a_6_9·a_5_8 + a_1_12·a_9_25
  121. a_6_92
  122. b_6_102 + b_4_53 + b_4_52·a_1_1·a_3_4 + b_4_52·a_1_1·a_3_2 + c_2_2·b_4_5·a_3_32
  123. a_5_5·a_7_10 + b_4_5·a_3_3·a_5_5 + b_4_52·a_1_1·a_3_2 + c_2_2·b_4_52·a_1_12
  124. a_6_9·b_6_10 + a_5_5·a_7_15 + b_4_5·a_3_3·a_5_5 + b_4_52·a_1_1·a_3_2
       + c_2_2·b_4_5·a_3_32 + c_2_22·a_3_3·a_5_5
  125. a_6_9·b_6_10 + a_5_9·a_7_15 + a_5_9·a_7_10 + a_5_8·a_7_10 + a_5_6·a_7_10
       + b_4_5·a_3_3·a_5_5 + c_2_2·b_4_5·a_1_1·a_5_9 + c_2_2·b_4_52·a_1_12
       + c_2_22·a_3_3·a_5_5 + c_2_22·a_1_1·a_7_10 + c_2_23·a_3_32 + c_2_23·a_1_1·a_5_9
       + c_2_24·a_1_1·a_3_4 + c_2_24·a_1_1·a_3_2 + c_2_25·a_1_12
  126. a_5_5·a_7_16 + b_4_5·a_3_3·a_5_5 + b_4_5·a_1_1·a_7_10 + b_4_52·a_1_1·a_3_4
       + c_2_2·b_4_5·a_1_1·a_5_6
  127. a_6_9·b_6_10 + a_5_9·a_7_16 + a_5_9·a_7_10 + a_5_6·a_7_10 + b_4_5·a_3_3·a_5_5
       + b_4_5·a_1_1·a_7_10 + b_4_52·a_1_1·a_3_4 + b_4_52·a_1_1·a_3_2 + c_2_2·a_3_3·a_7_15
       + c_2_2·b_4_5·a_3_32 + c_2_2·b_4_5·a_1_1·a_5_6 + c_2_22·a_3_3·a_5_5
       + c_2_22·a_1_1·a_7_10 + c_2_22·b_4_5·a_1_1·a_3_4 + c_2_23·a_3_32
       + c_2_23·a_1_1·a_5_9 + c_2_23·a_1_1·a_5_6 + c_2_24·a_1_1·a_3_4 + c_2_24·a_1_1·a_3_2
       + c_2_25·a_1_12
  128. a_5_9·a_7_10 + a_5_8·a_7_15 + a_5_8·a_7_10 + a_5_6·a_7_15 + a_5_6·a_7_10
       + b_4_5·a_1_1·a_7_16 + b_4_5·a_1_1·a_7_10 + b_4_52·a_1_1·a_3_4 + b_4_52·a_1_1·a_3_2
       + c_2_2·a_3_3·a_7_15 + c_2_22·a_3_3·a_5_5 + c_2_22·b_4_5·a_1_1·a_3_2
       + c_2_23·a_3_32 + c_2_23·a_1_1·a_5_6 + c_2_23·b_4_5·a_1_12 + c_2_25·a_1_12
  129. a_6_9·b_6_10 + a_5_9·a_7_10 + a_5_8·a_7_16 + a_5_8·a_7_10 + a_5_6·a_7_16 + a_5_6·a_7_15
       + b_4_5·a_3_3·a_5_5 + b_4_52·a_1_1·a_3_4 + c_2_2·a_3_3·a_7_15 + c_2_2·b_4_5·a_3_32
       + c_2_23·a_3_32 + c_2_23·a_1_1·a_5_9 + c_2_24·a_1_1·a_3_4 + c_2_24·a_1_1·a_3_2
       + c_2_25·a_1_12
  130. a_5_8·a_7_15 + a_5_8·a_7_10 + a_5_6·a_7_15 + a_5_6·a_7_10 + c_2_2·a_3_3·a_7_15
       + c_2_2·b_4_5·a_1_1·a_5_9 + c_2_22·a_1_1·a_7_16 + c_2_22·a_1_1·a_7_10
       + c_2_23·a_3_32 + c_2_23·a_1_1·a_5_6 + c_2_23·b_4_5·a_1_12 + c_2_24·a_1_1·a_3_4
       + c_2_25·a_1_12
  131. a_6_9·b_6_10 + a_5_9·a_7_10 + a_5_8·a_7_15 + b_4_5·a_3_3·a_5_5 + b_4_5·a_1_1·a_7_10
       + b_4_52·a_1_1·a_3_4 + b_4_52·a_1_1·a_3_2 + c_8_20·a_1_1·a_3_2 + c_2_2·a_3_3·a_7_15
       + c_2_2·b_4_5·a_1_1·a_5_9 + c_2_2·b_4_5·a_1_1·a_5_6 + c_2_22·b_4_5·a_1_1·a_3_2
       + c_2_23·a_3_32 + c_2_23·a_1_1·a_5_9 + c_2_23·a_1_1·a_5_6 + c_2_24·a_1_1·a_3_4
       + c_2_25·a_1_12
  132. a_5_9·a_7_10 + a_5_8·a_7_15 + a_5_8·a_7_10 + a_5_6·a_7_16 + b_4_52·a_1_1·a_3_4
       + c_8_20·a_1_1·a_3_4 + c_2_2·a_3_3·a_7_15 + c_2_2·b_4_5·a_1_1·a_5_9
       + c_2_2·b_4_5·a_1_1·a_5_6 + c_2_22·a_3_3·a_5_5 + c_2_22·b_4_5·a_1_1·a_3_4
       + c_2_23·a_3_32 + c_2_23·a_1_1·a_5_6 + c_2_23·b_4_5·a_1_12 + c_2_24·a_1_1·a_3_4
       + c_2_25·a_1_12
  133. a_6_9·b_6_10 + a_5_9·a_7_10 + a_5_8·a_7_15 + a_5_6·a_7_10 + b_4_5·a_3_3·a_5_5
       + b_4_52·a_1_1·a_3_4 + c_2_2·a_3_3·a_7_15 + c_2_2·b_4_5·a_3_32
       + c_2_2·b_4_5·a_1_1·a_5_9 + c_2_2·b_4_5·a_1_1·a_5_6 + c_2_2·c_8_20·a_1_12
       + c_2_22·a_1_1·a_7_10 + c_2_22·b_4_5·a_1_1·a_3_2 + c_2_23·a_3_32
       + c_2_23·a_1_1·a_5_9 + c_2_23·b_4_5·a_1_12 + c_2_24·a_1_1·a_3_4
  134. a_4_3·a_8_15
  135. a_6_9·b_6_10 + b_4_5·a_8_15 + b_4_5·a_3_3·a_5_5 + b_4_52·a_1_1·a_3_4
       + b_4_52·a_1_1·a_3_2 + c_2_2·a_3_3·a_7_15 + c_2_2·b_4_5·a_1_1·a_5_6
       + c_2_22·a_3_3·a_5_5 + c_2_23·a_3_32
  136. a_6_9·b_6_10 + a_3_3·a_9_22 + b_4_5·a_3_3·a_5_5 + c_2_2·b_4_5·a_3_32
       + c_2_22·a_3_3·a_5_5 + c_2_23·a_3_32
  137. a_6_9·b_6_10 + a_5_9·a_7_10 + a_5_8·a_7_15 + a_3_2·a_9_22 + b_4_5·a_3_3·a_5_5
       + b_4_52·a_1_1·a_3_4 + b_4_52·a_1_1·a_3_2 + c_2_2·a_3_3·a_7_15
       + c_2_2·b_4_52·a_1_12 + c_2_22·a_1_1·a_7_10 + c_2_22·b_4_5·a_1_1·a_3_4
       + c_2_22·b_4_5·a_1_1·a_3_2 + c_2_23·a_3_32 + c_2_23·a_1_1·a_5_9
       + c_2_23·b_4_5·a_1_12 + c_2_24·a_1_1·a_3_4 + c_2_24·a_1_1·a_3_2 + c_2_25·a_1_12
  138. a_6_9·b_6_10 + a_5_8·a_7_15 + a_5_8·a_7_10 + a_5_6·a_7_16 + a_3_4·a_9_22
       + b_4_52·a_1_1·a_3_2 + c_2_2·a_3_3·a_7_15 + c_2_2·b_4_5·a_1_1·a_5_9
       + c_2_22·a_1_1·a_7_10 + c_2_24·a_1_1·a_3_4 + c_2_24·a_1_1·a_3_2 + c_2_25·a_1_12
  139. a_3_3·a_9_25 + b_4_5·a_1_1·a_7_10 + b_4_52·a_1_1·a_3_4 + b_4_52·a_1_1·a_3_2
       + c_2_2·b_4_5·a_1_1·a_5_9 + c_2_2·b_4_52·a_1_12 + c_2_22·b_4_5·a_1_1·a_3_4
       + c_2_23·b_4_5·a_1_12
  140. a_5_9·a_7_10 + a_5_8·a_7_10 + a_5_6·a_7_10 + a_3_2·a_9_25 + b_4_5·a_1_1·a_7_10
       + c_2_2·b_4_52·a_1_12 + c_2_22·b_4_5·a_1_1·a_3_2 + c_2_23·a_1_1·a_5_9
       + c_2_23·b_4_5·a_1_12 + c_2_24·a_1_1·a_3_4
  141. a_6_9·b_6_10 + a_5_8·a_7_10 + a_3_4·a_9_25 + b_4_5·a_3_3·a_5_5 + b_4_5·a_1_1·a_7_10
       + b_4_52·a_1_1·a_3_4 + c_2_2·a_3_3·a_7_15 + c_2_2·b_4_5·a_3_32
       + c_2_2·b_4_5·a_1_1·a_5_6 + c_2_23·a_3_32 + c_2_23·b_4_5·a_1_12
       + c_2_24·a_1_1·a_3_4 + c_2_25·a_1_12
  142. a_5_8·a_7_10 + a_5_6·a_7_10 + c_2_2·a_1_1·a_9_25 + c_2_22·a_3_3·a_5_5
       + c_2_22·a_1_1·a_7_10 + c_2_24·a_1_1·a_3_4 + c_2_25·a_1_12
  143. a_6_9·a_7_10 + b_4_5·a_1_12·a_7_16
  144. b_6_10·a_7_10 + b_4_52·a_5_6 + a_6_9·a_7_15 + c_2_2·b_4_5·a_7_10 + c_2_2·b_4_52·a_3_3
       + c_2_22·b_4_5·a_5_6 + c_2_22·b_4_5·a_5_5 + c_2_22·b_4_52·a_1_1
       + c_2_22·a_1_12·a_7_16 + c_2_23·b_4_5·a_3_2
  145. a_6_9·a_7_16 + a_6_9·a_7_15 + a_6_9·a_7_10 + c_2_23·a_1_12·a_5_9
  146. b_6_10·a_7_10 + b_4_52·a_5_6 + a_8_15·a_5_5 + c_2_2·b_4_5·a_7_10 + c_2_2·b_4_52·a_3_3
       + c_2_22·b_4_5·a_5_6 + c_2_22·b_4_5·a_5_5 + c_2_22·b_4_52·a_1_1
       + c_2_23·b_4_5·a_3_2
  147. b_6_10·a_7_10 + b_4_52·a_5_6 + a_8_15·a_5_6 + a_6_9·a_7_10 + c_2_2·b_4_5·a_7_10
       + c_2_2·b_4_52·a_3_3 + c_2_22·b_4_5·a_5_6 + c_2_22·b_4_5·a_5_5
       + c_2_22·b_4_52·a_1_1 + c_2_23·b_4_5·a_3_2
  148. b_6_10·a_7_10 + b_4_52·a_5_6 + a_8_15·a_5_9 + a_6_9·a_7_15 + a_6_9·a_7_10
       + c_2_2·b_4_5·a_7_10 + c_2_2·b_4_52·a_3_3 + c_2_22·b_4_5·a_5_6 + c_2_22·b_4_5·a_5_5
       + c_2_22·b_4_52·a_1_1 + c_2_23·b_4_5·a_3_2
  149. a_8_15·a_5_8 + c_2_23·a_1_12·a_5_9
  150. a_6_9·a_7_10 + a_4_3·a_9_22 + c_2_23·a_1_12·a_5_9
  151. b_6_10·a_7_15 + b_6_10·a_7_10 + b_4_5·a_9_22 + b_4_52·a_5_9 + b_4_52·a_5_6
       + b_4_52·a_5_5 + b_4_53·a_1_1 + a_6_9·a_7_15 + a_6_9·a_7_10 + b_4_5·c_8_20·a_1_1
       + c_2_2·b_4_5·a_7_10 + c_2_2·b_4_52·a_3_4 + c_2_2·b_4_52·a_3_2 + c_2_22·b_4_5·a_5_9
       + c_2_22·b_4_5·a_5_5 + c_2_23·b_4_5·a_3_4 + c_2_23·b_4_5·a_3_2
       + c_2_23·a_1_12·a_5_9
  152. a_6_9·a_7_15 + a_6_9·a_7_10 + a_4_3·a_9_25 + c_2_23·a_1_12·a_5_9
  153. b_6_10·a_7_16 + b_4_5·a_9_25 + b_4_52·a_5_9 + c_2_2·b_4_5·a_7_16 + c_2_2·b_4_52·a_3_4
       + c_2_22·b_4_5·a_5_9 + c_2_22·b_4_5·a_5_5 + c_2_22·b_4_52·a_1_1
       + c_2_23·b_4_5·a_3_4 + c_2_23·b_4_5·a_3_3 + c_2_23·b_4_5·a_3_2
       + c_2_23·a_1_12·a_5_9 + c_2_24·b_4_5·a_1_1
  154. a_6_9·a_7_15 + a_6_9·a_7_10 + c_2_2·a_1_12·a_9_25 + c_2_23·a_1_12·a_5_9
  155. a_7_162 + a_7_152 + b_4_52·a_1_1·a_5_6 + b_4_53·a_1_12 + c_8_20·a_1_1·a_5_6
       + c_2_2·b_4_5·a_1_1·a_7_10 + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_2·c_8_20·a_1_1·a_3_2
       + c_2_22·b_4_5·a_3_32 + c_2_22·b_4_52·a_1_12 + c_2_24·a_1_1·a_5_6
       + c_2_24·b_4_5·a_1_12 + c_2_25·a_1_1·a_3_2
  156. a_7_152 + b_4_53·a_1_12 + c_8_20·a_3_32 + b_4_5·c_8_20·a_1_12
       + c_2_2·b_4_5·a_3_3·a_5_5 + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_22·b_4_5·a_3_32
       + c_2_22·b_4_5·a_1_1·a_5_6 + c_2_23·b_4_5·a_1_1·a_3_2 + c_2_24·a_1_1·a_5_6
       + c_2_25·a_1_1·a_3_2 + c_2_26·a_1_12
  157. a_7_152 + a_7_102 + b_4_52·a_1_1·a_5_6 + c_8_20·a_3_32 + c_2_2·b_4_5·a_3_3·a_5_5
       + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_22·c_8_20·a_1_12 + c_2_23·b_4_5·a_1_1·a_3_2
       + c_2_24·a_1_1·a_5_6 + c_2_24·b_4_5·a_1_12 + c_2_25·a_1_1·a_3_2
  158. b_6_10·a_8_15 + a_7_162 + a_7_15·a_7_16 + a_7_152 + a_7_102 + c_8_20·a_1_1·a_5_9
       + c_8_20·a_1_1·a_5_6 + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_2·c_8_20·a_1_1·a_3_4
       + c_2_22·a_3_3·a_7_15 + c_2_22·b_4_5·a_3_32 + c_2_22·b_4_5·a_1_1·a_5_9
       + c_2_22·b_4_52·a_1_12 + c_2_23·a_1_1·a_7_16 + c_2_24·a_3_32
       + c_2_24·a_1_1·a_5_9 + c_2_24·b_4_5·a_1_12 + c_2_26·a_1_12
  159. a_6_9·a_8_15
  160. a_5_5·a_9_22 + b_4_5·a_3_3·a_7_15 + b_4_53·a_1_12 + c_2_23·a_3_3·a_5_5
  161. a_7_102 + a_5_6·a_9_22 + b_4_5·a_3_3·a_7_15 + b_4_52·a_3_32 + b_4_52·a_1_1·a_5_9
       + b_4_52·a_1_1·a_5_6 + b_4_53·a_1_12 + c_8_20·a_1_1·a_5_6 + c_2_2·b_4_5·a_3_3·a_5_5
       + c_2_2·b_4_5·a_1_1·a_7_16 + c_2_22·b_4_5·a_1_1·a_5_9 + c_2_22·b_4_5·a_1_1·a_5_6
       + c_2_23·a_3_3·a_5_5 + c_2_23·a_1_1·a_7_10 + c_2_23·b_4_5·a_1_1·a_3_2
       + c_2_24·a_1_1·a_5_6 + c_2_24·b_4_5·a_1_12 + c_2_25·a_1_1·a_3_2
  162. a_7_162 + a_7_15·a_7_16 + a_7_152 + a_7_102 + b_4_5·a_3_3·a_7_15
       + b_4_52·a_1_1·a_5_9 + b_4_53·a_1_12 + c_8_20·a_1_1·a_5_9 + c_8_20·a_1_1·a_5_6
       + c_2_2·a_3_3·a_9_22 + c_2_2·b_4_5·a_3_3·a_5_5 + c_2_2·b_4_5·a_1_1·a_7_10
       + c_2_2·b_4_52·a_1_1·a_3_4 + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_2·c_8_20·a_1_1·a_3_4
       + c_2_22·a_3_3·a_7_15 + c_2_22·b_4_5·a_3_32 + c_2_22·b_4_5·a_1_1·a_5_9
       + c_2_22·b_4_5·a_1_1·a_5_6 + c_2_22·b_4_52·a_1_12 + c_2_23·a_3_3·a_5_5
       + c_2_23·a_1_1·a_7_16 + c_2_23·b_4_5·a_1_1·a_3_2 + c_2_24·a_1_1·a_5_9
       + c_2_24·b_4_5·a_1_12 + c_2_26·a_1_12
  163. a_7_15·a_7_16 + a_7_152 + a_7_10·a_7_16 + a_7_10·a_7_15 + a_5_9·a_9_22
       + b_4_52·a_3_32 + b_4_52·a_1_1·a_5_9 + b_4_53·a_1_12 + c_8_20·a_3_32
       + c_8_20·a_1_1·a_5_9 + c_2_2·b_4_52·a_1_1·a_3_4 + c_2_2·c_8_20·a_1_1·a_3_4
       + c_2_22·a_3_3·a_7_15 + c_2_22·b_4_5·a_3_32 + c_2_22·b_4_5·a_1_1·a_5_9
       + c_2_22·b_4_5·a_1_1·a_5_6 + c_2_22·b_4_52·a_1_12 + c_2_23·a_3_3·a_5_5
       + c_2_23·a_1_1·a_7_10 + c_2_23·b_4_5·a_1_1·a_3_4 + c_2_23·b_4_5·a_1_1·a_3_2
       + c_2_24·a_3_32 + c_2_24·b_4_5·a_1_12 + c_2_25·a_1_1·a_3_4 + c_2_25·a_1_1·a_3_2
  164. a_7_162 + a_7_15·a_7_16 + a_7_152 + a_5_8·a_9_22 + b_4_52·a_3_32
       + b_4_52·a_1_1·a_5_6 + c_8_20·a_1_1·a_5_9 + c_2_2·b_4_5·a_3_3·a_5_5
       + c_2_2·b_4_52·a_1_1·a_3_4 + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_22·a_3_3·a_7_15
       + c_2_22·b_4_5·a_1_1·a_5_9 + c_2_22·b_4_5·a_1_1·a_5_6 + c_2_22·b_4_52·a_1_12
       + c_2_23·a_3_3·a_5_5 + c_2_23·a_1_1·a_7_10 + c_2_23·b_4_5·a_1_1·a_3_4
       + c_2_23·b_4_5·a_1_1·a_3_2 + c_2_24·a_1_1·a_5_9 + c_2_24·b_4_5·a_1_12
       + c_2_25·a_1_1·a_3_4 + c_2_26·a_1_12
  165. a_5_5·a_9_25 + b_4_52·a_1_1·a_5_9 + b_4_52·a_1_1·a_5_6 + c_2_2·b_4_5·a_1_1·a_7_10
       + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_22·b_4_5·a_1_1·a_5_6
  166. a_7_162 + a_7_10·a_7_16 + a_7_10·a_7_15 + a_5_6·a_9_25 + b_4_5·a_3_3·a_7_15
       + b_4_52·a_1_1·a_5_9 + b_4_53·a_1_12 + c_8_20·a_3_32 + c_8_20·a_1_1·a_5_6
       + c_2_2·b_4_5·a_1_1·a_7_10 + c_2_2·b_4_52·a_1_1·a_3_4 + c_2_22·b_4_5·a_3_32
       + c_2_23·a_3_3·a_5_5 + c_2_23·a_1_1·a_7_16 + c_2_23·a_1_1·a_7_10
       + c_2_23·b_4_5·a_1_1·a_3_4 + c_2_23·b_4_5·a_1_1·a_3_2 + c_2_24·a_1_1·a_5_9
       + c_2_24·a_1_1·a_5_6 + c_2_24·b_4_5·a_1_12 + c_2_26·a_1_12
  167. a_7_15·a_7_16 + a_7_152 + a_7_10·a_7_16 + a_7_10·a_7_15 + a_7_102 + a_5_9·a_9_25
       + b_4_52·a_1_1·a_5_9 + b_4_52·a_1_1·a_5_6 + c_8_20·a_3_32 + c_2_2·b_4_5·a_3_3·a_5_5
       + c_2_2·b_4_52·a_1_1·a_3_4 + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_2·c_8_20·a_1_1·a_3_4
       + c_2_22·b_4_5·a_3_32 + c_2_22·b_4_5·a_1_1·a_5_6 + c_2_22·b_4_52·a_1_12
       + c_2_24·a_1_1·a_5_6 + c_2_24·b_4_5·a_1_12 + c_2_26·a_1_12
  168. a_7_162 + a_7_10·a_7_15 + b_4_5·a_3_3·a_7_15 + b_4_5·a_1_1·a_9_25
       + b_4_52·a_1_1·a_5_9 + b_4_52·a_1_1·a_5_6 + b_4_53·a_1_12 + c_8_20·a_3_32
       + c_8_20·a_1_1·a_5_6 + c_2_2·b_4_5·a_1_1·a_7_16 + c_2_2·b_4_52·a_1_1·a_3_4
       + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_22·b_4_5·a_1_1·a_5_9 + c_2_22·b_4_5·a_1_1·a_5_6
       + c_2_23·a_3_3·a_5_5 + c_2_23·a_1_1·a_7_16 + c_2_23·b_4_5·a_1_1·a_3_4
       + c_2_23·b_4_5·a_1_1·a_3_2 + c_2_24·a_1_1·a_5_6 + c_2_25·a_1_1·a_3_4
       + c_2_26·a_1_12
  169. a_7_10·a_7_15 + a_5_8·a_9_25 + b_4_52·a_1_1·a_5_9 + b_4_52·a_1_1·a_5_6
       + c_8_20·a_1_1·a_5_9 + c_2_2·b_4_5·a_1_1·a_7_16 + c_2_2·b_4_5·a_1_1·a_7_10
       + c_2_22·a_3_3·a_7_15 + c_2_22·b_4_5·a_3_32 + c_2_22·b_4_5·a_1_1·a_5_9
       + c_2_22·b_4_5·a_1_1·a_5_6 + c_2_23·a_1_1·a_7_16 + c_2_23·b_4_5·a_1_1·a_3_4
       + c_2_23·b_4_5·a_1_1·a_3_2 + c_2_24·a_3_32 + c_2_24·b_4_5·a_1_12
       + c_2_25·a_1_1·a_3_4 + c_2_26·a_1_12
  170. a_7_162 + a_7_15·a_7_16 + a_7_152 + a_7_10·a_7_16 + b_4_52·a_1_1·a_5_9
       + b_4_52·a_1_1·a_5_6 + b_4_53·a_1_12 + c_8_20·a_1_1·a_5_6
       + c_2_2·b_4_5·a_1_1·a_7_16 + c_2_2·b_4_52·a_1_1·a_3_4 + c_2_2·c_8_20·a_1_1·a_3_4
       + c_2_22·a_3_3·a_7_15 + c_2_22·a_1_1·a_9_25 + c_2_22·b_4_5·a_3_32
       + c_2_22·b_4_5·a_1_1·a_5_6 + c_2_23·a_1_1·a_7_16 + c_2_23·a_1_1·a_7_10
       + c_2_24·a_3_32 + c_2_24·b_4_5·a_1_12 + c_2_25·a_1_1·a_3_4
  171. a_8_15·a_7_10
  172. a_8_15·a_7_16 + a_8_15·a_7_15 + c_8_20·a_1_12·a_5_9 + c_2_2·b_4_5·a_1_12·a_7_16
  173. b_6_10·a_9_22 + b_4_52·a_7_15 + b_4_53·a_3_4 + b_4_53·a_3_3 + b_4_5·c_8_20·a_3_2
       + c_8_20·a_1_12·a_5_9 + c_2_2·b_4_5·a_1_12·a_7_16 + c_2_22·b_4_5·a_7_10
       + c_2_22·b_4_52·a_3_4 + c_2_23·b_4_5·a_5_6 + c_2_23·b_4_52·a_1_1
       + c_2_23·a_1_12·a_7_16 + c_2_24·b_4_5·a_3_2
  174. a_8_15·a_7_15 + a_6_9·a_9_22 + c_8_20·a_1_12·a_5_9 + c_2_2·b_4_5·a_1_12·a_7_16
       + c_2_23·a_1_12·a_7_16
  175. b_6_10·a_9_25 + b_4_52·a_7_16 + b_4_53·a_3_4 + b_4_53·a_3_2 + c_2_2·b_4_5·a_9_25
       + c_2_2·b_4_52·a_5_9 + c_2_2·b_4_52·a_5_5 + c_2_2·b_4_53·a_1_1
       + c_8_20·a_1_12·a_5_9 + c_2_22·b_4_5·a_7_16 + c_2_22·b_4_52·a_3_3
       + c_2_23·b_4_5·a_5_9 + c_2_23·b_4_5·a_5_5 + c_2_23·b_4_52·a_1_1
       + c_2_24·b_4_5·a_3_4 + c_2_24·b_4_5·a_3_3 + c_2_25·b_4_5·a_1_1
  176. a_8_15·a_7_15 + b_4_5·a_1_12·a_9_25 + c_8_20·a_1_12·a_5_9
       + c_2_2·b_4_5·a_1_12·a_7_16 + c_2_22·a_1_12·a_9_25 + c_2_23·a_1_12·a_7_16
  177. a_6_9·a_9_25 + b_4_5·a_1_12·a_9_25 + c_2_2·b_4_5·a_1_12·a_7_16
       + c_2_23·a_1_12·a_7_16 + c_2_24·a_1_12·a_5_9
  178. a_8_152
  179. a_7_16·a_9_22 + a_7_10·a_9_22 + b_4_5·a_3_3·a_9_22 + b_4_53·a_1_1·a_3_4
       + c_8_20·a_1_1·a_7_16 + c_8_20·a_1_1·a_7_10 + b_4_5·c_8_20·a_1_1·a_3_4
       + c_2_2·b_4_5·a_3_3·a_7_15 + c_2_2·b_4_52·a_3_32 + c_2_2·b_4_5·c_8_20·a_1_12
       + c_2_22·a_3_3·a_9_22 + c_2_22·b_4_5·a_1_1·a_7_16 + c_2_22·b_4_5·a_1_1·a_7_10
       + c_2_22·b_4_52·a_1_1·a_3_4 + c_2_22·c_8_20·a_1_1·a_3_4
       + c_2_22·c_8_20·a_1_1·a_3_2 + c_2_23·b_4_5·a_3_32 + c_2_23·b_4_5·a_1_1·a_5_9
       + c_2_23·b_4_5·a_1_1·a_5_6 + c_2_23·b_4_52·a_1_12 + c_2_24·a_3_3·a_5_5
       + c_2_24·a_1_1·a_7_16 + c_2_25·a_3_32 + c_2_25·a_1_1·a_5_6
  180. a_7_15·a_9_25 + a_7_15·a_9_22 + b_4_52·a_1_1·a_7_10 + b_4_53·a_1_1·a_3_2
       + c_8_20·a_3_3·a_5_5 + c_8_20·a_1_1·a_7_10 + b_4_5·c_8_20·a_1_1·a_3_2
       + c_2_2·b_4_5·a_3_3·a_7_15 + c_2_2·b_4_52·a_1_1·a_5_9 + c_2_2·c_8_20·a_1_1·a_5_6
       + c_2_22·b_4_5·a_3_3·a_5_5 + c_2_22·b_4_5·a_1_1·a_7_16 + c_2_22·b_4_5·a_1_1·a_7_10
       + c_2_22·c_8_20·a_1_1·a_3_4 + c_2_22·c_8_20·a_1_1·a_3_2 + c_2_23·b_4_5·a_3_32
       + c_2_23·b_4_5·a_1_1·a_5_6 + c_2_23·c_8_20·a_1_12 + c_2_24·a_3_3·a_5_5
       + c_2_24·b_4_5·a_1_1·a_3_4 + c_2_24·b_4_5·a_1_1·a_3_2 + c_2_25·a_3_32
       + c_2_25·b_4_5·a_1_12 + c_2_26·a_1_1·a_3_4 + c_2_26·a_1_1·a_3_2
  181. a_7_10·a_9_22 + b_4_5·a_3_3·a_9_22 + b_4_52·a_3_3·a_5_5 + b_4_53·a_1_1·a_3_4
       + c_8_20·a_1_1·a_7_10 + b_4_5·c_8_20·a_1_1·a_3_2 + c_2_2·b_4_5·a_1_1·a_9_25
       + c_2_2·b_4_52·a_1_1·a_5_9 + c_2_2·b_4_53·a_1_12 + c_2_2·b_4_5·c_8_20·a_1_12
       + c_2_22·b_4_5·a_1_1·a_7_10 + c_2_22·b_4_52·a_1_1·a_3_4
       + c_2_22·c_8_20·a_1_1·a_3_2 + c_2_23·b_4_5·a_3_32 + c_2_23·b_4_52·a_1_12
       + c_2_23·c_8_20·a_1_12 + c_2_24·b_4_5·a_1_1·a_3_4 + c_2_24·b_4_5·a_1_1·a_3_2
       + c_2_26·a_1_1·a_3_2 + c_2_27·a_1_12
  182. a_7_15·a_9_22 + b_4_52·a_1_1·a_7_16 + b_4_53·a_1_1·a_3_2 + c_8_20·a_3_3·a_5_5
       + c_8_20·a_1_1·a_7_10 + b_4_5·c_8_20·a_1_1·a_3_4 + b_4_5·c_8_20·a_1_1·a_3_2
       + c_2_2·b_4_52·a_1_1·a_5_9 + c_2_2·c_8_20·a_1_1·a_5_9 + c_2_2·c_8_20·a_1_1·a_5_6
       + c_2_2·b_4_5·c_8_20·a_1_12 + c_2_22·b_4_52·a_1_1·a_3_2
       + c_2_22·c_8_20·a_1_1·a_3_2 + c_2_23·a_3_3·a_7_15 + c_2_23·a_1_1·a_9_25
       + c_2_23·b_4_5·a_1_1·a_5_9 + c_2_23·b_4_52·a_1_12 + c_2_24·a_1_1·a_7_10
       + c_2_25·b_4_5·a_1_12 + c_2_26·a_1_1·a_3_4 + c_2_26·a_1_1·a_3_2 + c_2_27·a_1_12
  183. a_7_15·a_9_22 + a_7_10·a_9_25 + b_4_5·a_3_3·a_9_22 + b_4_52·a_1_1·a_7_10
       + b_4_53·a_1_1·a_3_4 + c_8_20·a_3_3·a_5_5 + c_8_20·a_1_1·a_7_10
       + b_4_5·c_8_20·a_1_1·a_3_2 + c_2_2·b_4_52·a_3_32 + c_2_2·b_4_52·a_1_1·a_5_9
       + c_2_2·b_4_52·a_1_1·a_5_6 + c_2_2·b_4_53·a_1_12 + c_2_2·c_8_20·a_1_1·a_5_9
       + c_2_2·c_8_20·a_1_1·a_5_6 + c_2_22·a_3_3·a_9_22 + c_2_22·b_4_5·a_3_3·a_5_5
       + c_2_22·b_4_5·a_1_1·a_7_16 + c_2_22·b_4_5·a_1_1·a_7_10
       + c_2_22·c_8_20·a_1_1·a_3_4 + c_2_22·c_8_20·a_1_1·a_3_2 + c_2_23·a_3_3·a_7_15
       + c_2_23·b_4_5·a_1_1·a_5_6 + c_2_23·c_8_20·a_1_12 + c_2_24·a_3_3·a_5_5
       + c_2_24·a_1_1·a_7_10 + c_2_24·b_4_5·a_1_1·a_3_4 + c_2_24·b_4_5·a_1_1·a_3_2
       + c_2_25·a_3_32 + c_2_26·a_1_1·a_3_4 + c_2_26·a_1_1·a_3_2 + c_2_27·a_1_12
  184. a_7_16·a_9_25 + a_7_15·a_9_22 + b_4_5·a_3_3·a_9_22 + b_4_5·c_8_20·a_1_1·a_3_4
       + b_4_5·c_8_20·a_1_1·a_3_2 + c_2_2·b_4_52·a_1_1·a_5_6 + c_2_2·c_8_20·a_3_32
       + c_2_2·c_8_20·a_1_1·a_5_9 + c_2_2·c_8_20·a_1_1·a_5_6 + c_2_2·b_4_5·c_8_20·a_1_12
       + c_2_22·a_3_3·a_9_22 + c_2_22·b_4_5·a_3_3·a_5_5 + c_2_23·a_3_3·a_7_15
       + c_2_23·b_4_5·a_3_32 + c_2_23·b_4_5·a_1_1·a_5_9 + c_2_24·a_3_3·a_5_5
       + c_2_24·b_4_5·a_1_1·a_3_2 + c_2_25·a_3_32 + c_2_25·a_1_1·a_5_6
       + c_2_25·b_4_5·a_1_12 + c_2_26·a_1_1·a_3_4 + c_2_26·a_1_1·a_3_2 + c_2_27·a_1_12
  185. a_8_15·a_9_22 + b_4_52·a_1_12·a_7_16 + c_2_2·b_4_5·a_1_12·a_9_25
       + c_2_22·b_4_5·a_1_12·a_7_16 + c_2_24·a_1_12·a_7_16 + c_2_25·a_1_12·a_5_9
  186. a_8_15·a_9_25 + a_8_15·a_9_22 + b_4_52·a_1_12·a_7_16 + c_2_2·c_8_20·a_1_12·a_5_9
       + c_2_22·b_4_5·a_1_12·a_7_16 + c_2_24·a_1_12·a_7_16 + c_2_25·a_1_12·a_5_9
  187. a_9_222 + b_4_53·a_3_32 + b_4_53·a_1_1·a_5_6 + b_4_54·a_1_12
       + b_4_5·c_8_20·a_3_32 + b_4_52·c_8_20·a_1_12 + c_2_2·b_4_52·a_3_3·a_5_5
       + c_8_202·a_1_12 + c_2_22·b_4_52·a_3_32 + c_2_22·b_4_52·a_1_1·a_5_6
       + c_2_22·b_4_53·a_1_12 + c_2_23·b_4_52·a_1_1·a_3_2 + c_2_24·b_4_5·a_1_1·a_5_6
       + c_2_24·b_4_52·a_1_12 + c_2_24·c_8_20·a_1_12 + c_2_26·a_3_32
       + c_2_28·a_1_12
  188. a_9_22·a_9_25 + b_4_52·a_3_3·a_7_15 + b_4_52·a_1_1·a_9_25 + b_4_53·a_1_1·a_5_9
       + b_4_54·a_1_12 + c_8_20·a_1_1·a_9_25 + b_4_5·c_8_20·a_1_1·a_5_9
       + c_2_2·b_4_52·a_3_3·a_5_5 + c_2_2·b_4_52·a_1_1·a_7_10 + c_2_2·b_4_53·a_1_1·a_3_4
       + c_2_2·b_4_53·a_1_1·a_3_2 + c_2_22·b_4_5·a_1_1·a_9_25 + c_2_22·b_4_52·a_3_32
       + c_2_22·b_4_52·a_1_1·a_5_6 + c_2_22·c_8_20·a_1_1·a_5_9
       + c_2_22·b_4_5·c_8_20·a_1_12 + c_2_23·a_3_3·a_9_22 + c_2_23·b_4_5·a_1_1·a_7_16
       + c_2_23·b_4_5·a_1_1·a_7_10 + c_2_24·b_4_5·a_3_32 + c_2_24·b_4_5·a_1_1·a_5_6
       + c_2_24·b_4_52·a_1_12 + c_2_24·c_8_20·a_1_12 + c_2_25·a_3_3·a_5_5
       + c_2_25·a_1_1·a_7_16 + c_2_25·b_4_5·a_1_1·a_3_4 + c_2_25·b_4_5·a_1_1·a_3_2
       + c_2_26·a_3_32 + c_2_26·a_1_1·a_5_9 + c_2_26·b_4_5·a_1_12 + c_2_27·a_1_1·a_3_4
       + c_2_28·a_1_12
  189. a_9_252 + b_4_54·a_1_12 + b_4_5·c_8_20·a_3_32 + b_4_5·c_8_20·a_1_1·a_5_6
       + b_4_52·c_8_20·a_1_12 + c_2_2·b_4_52·a_3_3·a_5_5 + c_2_2·b_4_52·a_1_1·a_7_10
       + c_2_2·b_4_53·a_1_1·a_3_2 + c_2_2·b_4_5·c_8_20·a_1_1·a_3_2
       + c_2_22·b_4_52·a_3_32 + c_2_22·b_4_53·a_1_12 + c_2_22·c_8_20·a_3_32
       + c_2_22·c_8_20·a_1_1·a_5_6 + c_2_22·b_4_5·c_8_20·a_1_12
       + c_2_23·b_4_5·a_3_3·a_5_5 + c_2_23·b_4_5·a_1_1·a_7_10
       + c_2_23·b_4_52·a_1_1·a_3_2 + c_2_23·c_8_20·a_1_1·a_3_2 + c_2_24·b_4_5·a_3_32
       + c_2_26·b_4_5·a_1_12

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 18.
  • The completion test was perfect: It applied in the last degree in which a generator or relation was found.
  • The following is a filter regular homogeneous system of parameters:
    1. c_2_2, a Duflot regular element of degree 2
    2. c_8_20, a Duflot regular element of degree 8
    3. b_4_5, an element of degree 4
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 7, 11].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].

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_1 → 0, an element of degree 1
  3. a_2_1 → 0, an element of degree 2
  4. c_2_2 → c_1_02, an element of degree 2
  5. a_3_2 → 0, an element of degree 3
  6. a_3_3 → 0, an element of degree 3
  7. a_3_4 → 0, an element of degree 3
  8. a_4_3 → 0, an element of degree 4
  9. b_4_5 → 0, an element of degree 4
  10. a_5_5 → 0, an element of degree 5
  11. a_5_6 → 0, an element of degree 5
  12. a_5_8 → 0, an element of degree 5
  13. a_5_9 → 0, an element of degree 5
  14. a_6_9 → 0, an element of degree 6
  15. b_6_10 → 0, an element of degree 6
  16. a_7_10 → 0, an element of degree 7
  17. a_7_15 → 0, an element of degree 7
  18. a_7_16 → 0, an element of degree 7
  19. a_8_15 → 0, an element of degree 8
  20. c_8_20 → c_1_18, an element of degree 8
  21. a_9_22 → 0, an element of degree 9
  22. a_9_25 → 0, an element of degree 9

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

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. a_2_1 → 0, an element of degree 2
  4. c_2_2 → c_1_02, an element of degree 2
  5. a_3_2 → 0, an element of degree 3
  6. a_3_3 → 0, an element of degree 3
  7. a_3_4 → 0, an element of degree 3
  8. a_4_3 → 0, an element of degree 4
  9. b_4_5 → c_1_24, an element of degree 4
  10. a_5_5 → 0, an element of degree 5
  11. a_5_6 → 0, an element of degree 5
  12. a_5_8 → 0, an element of degree 5
  13. a_5_9 → 0, an element of degree 5
  14. a_6_9 → 0, an element of degree 6
  15. b_6_10 → c_1_26, an element of degree 6
  16. a_7_10 → 0, an element of degree 7
  17. a_7_15 → 0, an element of degree 7
  18. a_7_16 → 0, an element of degree 7
  19. a_8_15 → 0, an element of degree 8
  20. c_8_20 → c_1_14·c_1_24 + c_1_18 + c_1_02·c_1_26 + c_1_04·c_1_24, an element of degree 8
  21. a_9_22 → 0, an element of degree 9
  22. a_9_25 → 0, an element of degree 9

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