Cohomology of group number 4 of order 243

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 243

General information on the group

  • The group has 2 minimal generators and exponent 9.
  • It is non-abelian.
  • It has p-Rank 3.
  • Its center has rank 2.
  • It has 2 conjugacy classes of maximal elementary abelian subgroups, which are all 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) · (t2  +  1) · (t5  +  2·t3  +  1)
    (t  +  1) · (t  −  1)3 · (t2  −  t  +  1)2 · (t2  +  t  +  1)2
  • 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 243

Ring generators

The cohomology ring has 27 minimal generators of maximal degree 8:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_1, a nilpotent element of degree 1
  3. a_2_0, a nilpotent element of degree 2
  4. b_2_1, an element of degree 2
  5. b_2_2, an element of degree 2
  6. a_3_1, a nilpotent element of degree 3
  7. a_3_2, a nilpotent element of degree 3
  8. a_3_3, a nilpotent element of degree 3
  9. a_3_4, a nilpotent element of degree 3
  10. a_3_5, a nilpotent element of degree 3
  11. a_4_4, a nilpotent element of degree 4
  12. a_4_5, a nilpotent element of degree 4
  13. b_4_6, an element of degree 4
  14. a_5_6, a nilpotent element of degree 5
  15. a_5_7, a nilpotent element of degree 5
  16. a_5_8, a nilpotent element of degree 5
  17. a_5_9, a nilpotent element of degree 5
  18. a_5_10, a nilpotent element of degree 5
  19. a_6_7, a nilpotent element of degree 6
  20. a_6_9, a nilpotent element of degree 6
  21. a_6_10, a nilpotent element of degree 6
  22. b_6_12, an element of degree 6
  23. c_6_14, a Duflot regular element of degree 6
  24. c_6_15, a Duflot regular element of degree 6
  25. a_7_17, a nilpotent element of degree 7
  26. a_7_18, a nilpotent element of degree 7
  27. a_8_14, a nilpotent element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 243

Ring relations

There are 14 "obvious" relations:
   a_1_02, a_1_12, a_3_12, a_3_22, a_3_32, a_3_42, a_3_52, a_5_62, a_5_72, a_5_82, a_5_92, a_5_102, a_7_172, a_7_182

Apart from that, there are 276 minimal relations of maximal degree 16:

  1. a_1_0·a_1_1
  2. a_2_0·a_1_1
  3. a_2_0·a_1_0
  4. b_2_1·a_1_0
  5. b_2_2·a_1_1
  6. b_2_2·a_1_0
  7. a_2_02
  8. a_2_0·b_2_1
  9. a_2_0·b_2_2 + a_1_1·a_3_1
  10.  − a_2_0·b_2_2 + a_1_0·a_3_1
  11. a_2_0·b_2_2 + a_1_1·a_3_2
  12. a_1_0·a_3_2
  13. a_2_0·b_2_2 + a_1_1·a_3_3
  14.  − a_2_0·b_2_2 + a_1_0·a_3_3
  15.  − b_2_1·b_2_2 + a_2_0·b_2_2 + a_1_1·a_3_4
  16. a_1_0·a_3_4
  17. a_2_0·b_2_2 + a_1_0·a_3_5
  18. b_2_1·a_3_1
  19. a_2_0·a_3_1
  20. b_2_2·a_3_1
  21. a_2_0·a_3_2
  22. b_2_1·a_3_3 + b_2_1·a_3_2
  23. a_2_0·a_3_3
  24. b_2_2·a_3_3 − b_2_2·a_3_2
  25. a_2_0·a_3_4
  26. b_2_2·a_3_4 − b_2_2·a_3_2
  27. a_2_0·a_3_5
  28. a_4_4·a_1_1
  29. a_4_4·a_1_0
  30. a_4_5·a_1_1
  31. a_4_5·a_1_0
  32. b_4_6·a_1_1 + b_2_1·a_3_2
  33. b_4_6·a_1_0
  34. a_3_1·a_3_2
  35.  − a_3_2·a_3_3 + a_3_1·a_3_4 + a_3_1·a_3_3
  36. a_3_3·a_3_4 + a_3_2·a_3_4 − a_3_2·a_3_3 − a_3_1·a_3_3
  37. a_3_1·a_3_5 + a_3_1·a_3_3
  38. a_3_3·a_3_5 + a_3_2·a_3_5 + a_3_2·a_3_3
  39. b_2_1·a_4_4 + b_2_1·a_1_1·a_3_5 − b_2_1·a_1_1·a_3_4
  40. a_2_0·a_4_4
  41. b_2_2·a_4_4 − a_3_2·a_3_3
  42. b_2_1·a_4_5 − b_2_1·a_1_1·a_3_5
  43. a_2_0·a_4_5
  44. b_2_2·a_4_5 − a_3_2·a_3_3 + a_3_1·a_3_3
  45. a_2_0·b_4_6
  46. b_2_2·b_4_6 + a_3_2·a_3_4 − a_3_1·a_3_3
  47. a_3_2·a_3_5 + a_3_2·a_3_3 + a_1_1·a_5_6
  48. a_1_0·a_5_6
  49.  − a_3_2·a_3_3 + a_1_1·a_5_7 − b_2_1·a_1_1·a_3_5
  50. a_1_0·a_5_7
  51. a_3_2·a_3_3 − a_3_1·a_3_3 + a_1_1·a_5_8 − b_2_1·a_1_1·a_3_5
  52. a_3_1·a_3_3 + a_1_0·a_5_8
  53.  − a_3_2·a_3_4 + a_3_2·a_3_3 − a_3_1·a_3_3 + a_1_1·a_5_9
  54. a_3_2·a_3_3 − a_3_1·a_3_3 + a_1_0·a_5_9
  55.  − a_3_2·a_3_3 + a_3_1·a_3_3 + a_1_1·a_5_10 + b_2_1·a_1_1·a_3_5 − b_2_1·a_1_1·a_3_4
  56. a_3_2·a_3_3 + a_3_1·a_3_3 + a_1_0·a_5_10
  57. a_4_4·a_3_2
  58. a_4_4·a_3_1
  59. a_4_4·a_3_5 − a_1_1·a_3_4·a_3_5
  60. b_2_22·a_3_5 + b_2_22·a_3_2 + a_4_4·a_3_4 − a_1_1·a_3_4·a_3_5
  61. a_4_4·a_3_3
  62. a_4_5·a_3_2
  63. a_4_5·a_3_1
  64.  − b_2_22·a_3_5 − b_2_22·a_3_2 + a_4_5·a_3_5
  65. a_4_5·a_3_4 + a_1_1·a_3_4·a_3_5
  66. b_2_22·a_3_5 + b_2_22·a_3_2 + a_4_5·a_3_3
  67. b_4_6·a_3_1
  68. b_4_6·a_3_3 + b_4_6·a_3_2 + b_2_22·a_3_5 + b_2_22·a_3_2
  69.  − b_4_6·a_3_5 + b_4_6·a_3_2 + b_2_22·a_3_5 + b_2_22·a_3_2 + b_2_1·a_5_6 + b_2_12·a_3_2
  70. a_2_0·a_5_6
  71.  − b_4_6·a_3_2 − b_2_22·a_3_5 − b_2_22·a_3_2 + b_2_1·a_5_7 − b_2_12·a_3_5 − b_2_12·a_3_2
       − a_1_1·a_3_4·a_3_5
  72. a_2_0·a_5_7
  73.  − b_4_6·a_3_2 + b_2_1·a_5_8 − b_2_12·a_3_5 + a_1_1·a_3_4·a_3_5
  74. a_2_0·a_5_8
  75. b_2_2·a_5_8 + b_2_22·a_3_5 − a_1_1·a_3_4·a_3_5
  76. b_4_6·a_3_4 − b_4_6·a_3_2 + b_2_22·a_3_5 + b_2_22·a_3_2 + b_2_1·a_5_9 + b_2_12·a_3_2
       + a_1_1·a_3_4·a_3_5
  77. a_2_0·a_5_9
  78. b_4_6·a_3_2 + b_2_1·a_5_10 + b_2_12·a_3_5 − b_2_12·a_3_4 − b_2_12·a_3_2
       − a_1_1·a_3_4·a_3_5
  79.  − b_2_22·a_3_5 − b_2_22·a_3_2 + a_2_0·a_5_10
  80. b_2_2·a_5_10 + b_2_2·a_5_9 − b_2_22·a_3_5 + b_2_22·a_3_2 + a_1_1·a_3_4·a_3_5
  81. a_6_7·a_1_1
  82. a_6_7·a_1_0
  83. b_2_22·a_3_5 + b_2_22·a_3_2 + a_6_9·a_1_1 + a_1_1·a_3_4·a_3_5
  84. a_6_9·a_1_0
  85. b_2_22·a_3_5 + b_2_22·a_3_2 + a_6_10·a_1_1 − a_1_1·a_3_4·a_3_5
  86.  − b_2_22·a_3_5 − b_2_22·a_3_2 + a_6_10·a_1_0
  87. b_6_12·a_1_1 + b_4_6·a_3_2 + b_2_22·a_3_5 + b_2_22·a_3_2 + b_2_12·a_3_2
       + a_1_1·a_3_4·a_3_5
  88. b_6_12·a_1_0 − b_2_22·a_3_5 − b_2_22·a_3_2
  89. a_4_42
  90. a_4_4·a_4_5
  91. a_4_52
  92.  − a_4_5·b_4_6 + b_2_1·a_1_1·a_5_6
  93. a_3_1·a_5_6
  94. a_4_5·b_4_6 + a_3_5·a_5_6 − a_3_2·a_5_6
  95. a_3_3·a_5_6 + a_3_2·a_5_6
  96. a_3_1·a_5_7
  97. a_3_5·a_5_7 + a_3_2·a_5_7 + a_3_2·a_5_6
  98. a_4_5·b_4_6 + a_3_3·a_5_7 − a_3_2·a_5_7
  99. a_4_5·b_4_6 + a_3_2·a_5_8
  100. a_3_1·a_5_8
  101.  − a_4_5·b_4_6 + a_4_4·b_4_6 − a_3_5·a_5_8 + a_3_4·a_5_8 − a_3_4·a_5_7 + a_3_2·a_5_7
       − a_3_2·a_5_6
  102.  − a_4_5·b_4_6 + a_3_5·a_5_8 + a_3_3·a_5_8 + a_3_2·a_5_6
  103. a_4_5·b_4_6 + a_4_4·b_4_6 + b_2_1·a_1_1·a_5_9
  104. a_3_1·a_5_9
  105. a_4_5·b_4_6 + a_4_4·b_4_6 + a_3_5·a_5_9 + a_3_5·a_5_8 + a_3_4·a_5_7 − a_3_4·a_5_6
       + a_3_2·a_5_9 − a_3_2·a_5_7 − a_3_2·a_5_6 − b_2_1·a_3_4·a_3_5
  106. a_4_5·b_4_6 + a_4_4·b_4_6 + a_3_4·a_5_9 − a_3_2·a_5_9
  107.  − a_4_5·b_4_6 + a_4_4·b_4_6 − a_3_5·a_5_8 − a_3_4·a_5_7 + a_3_3·a_5_9 − a_3_2·a_5_9
       + a_3_2·a_5_7 − a_3_2·a_5_6 + b_2_1·a_3_4·a_3_5
  108.  − a_4_5·b_4_6 − a_4_4·b_4_6 − a_3_4·a_5_7 + a_3_2·a_5_10 + a_3_2·a_5_9 + a_3_2·a_5_7
       + b_2_1·a_3_4·a_3_5
  109. a_3_5·a_5_8 + a_3_2·a_5_6 + a_3_1·a_5_10
  110.  − a_4_4·b_4_6 + a_3_5·a_5_10 + a_3_5·a_5_8 + a_3_4·a_5_7 − a_3_2·a_5_9 − a_3_2·a_5_7
  111.  − a_4_5·b_4_6 − a_4_4·b_4_6 + a_3_5·a_5_8 + a_3_4·a_5_10 + a_3_2·a_5_9 + a_3_2·a_5_6
       + b_2_1·a_3_4·a_3_5
  112.  − a_4_5·b_4_6 − a_3_5·a_5_8 − a_3_4·a_5_7 + a_3_3·a_5_10 + a_3_2·a_5_9 + a_3_2·a_5_7
       − a_3_2·a_5_6 + b_2_1·a_3_4·a_3_5
  113.  − a_4_4·b_4_6 + b_2_1·a_6_7
  114. a_2_0·a_6_7
  115. a_4_5·b_4_6 + b_2_2·a_6_7 + a_3_2·a_5_7
  116.  − a_4_5·b_4_6 + b_2_1·a_6_9 + b_2_1·a_3_4·a_3_5 − b_2_12·a_1_1·a_3_4
  117. a_2_0·a_6_9
  118.  − a_4_4·b_4_6 + b_2_2·a_6_9 + a_3_4·a_5_7 − a_3_2·a_5_9 + a_3_2·a_5_7 − b_2_1·a_3_4·a_3_5
  119.  − a_4_4·b_4_6 + b_2_1·a_6_10 − b_2_1·a_3_4·a_3_5 − b_2_12·a_1_1·a_3_5
       − b_2_12·a_1_1·a_3_4
  120. a_2_0·a_6_10
  121. a_4_5·b_4_6 + b_2_2·a_6_10 − a_3_5·a_5_8 + a_3_2·a_5_7 − a_3_2·a_5_6
  122.  − b_4_62 + b_2_1·b_6_12 − b_2_12·b_4_6 + a_4_5·b_4_6 + b_2_1·a_3_4·a_3_5
       + b_2_12·a_1_1·a_3_5
  123. a_2_0·b_6_12
  124. b_2_2·b_6_12 + a_4_5·b_4_6 − a_4_4·b_4_6 − a_3_5·a_5_8 − a_3_2·a_5_9 − a_3_2·a_5_7
       − a_3_2·a_5_6
  125.  − a_4_5·b_4_6 − a_3_2·a_5_6 + a_1_1·a_7_17 + b_2_12·a_1_1·a_3_5
  126. a_1_0·a_7_17
  127. a_4_4·b_4_6 + a_3_5·a_5_8 + a_3_4·a_5_7 − a_3_2·a_5_7 + a_3_2·a_5_6 + a_1_1·a_7_18
       − b_2_1·a_3_4·a_3_5 − b_2_12·a_1_1·a_3_5 + b_2_12·a_1_1·a_3_4
  128.  − a_3_5·a_5_8 − a_3_2·a_5_6 + a_1_0·a_7_18
  129. a_4_5·a_5_6
  130.  − a_4_4·a_5_6 + a_1_1·a_3_4·a_5_6
  131. a_4_4·a_5_7 − b_2_1·a_1_1·a_3_4·a_3_5
  132. a_4_5·a_5_7
  133. a_4_4·a_5_8 − b_2_1·a_1_1·a_3_4·a_3_5
  134.  − b_2_22·a_5_6 − b_2_23·a_3_2 + a_4_5·a_5_8
  135. b_4_6·a_5_8 − b_4_6·a_5_7 + b_2_12·a_5_7 − b_2_13·a_3_5 − b_2_13·a_3_2 − a_4_4·a_5_6
       − b_2_1·a_1_1·a_3_4·a_3_5
  136.  − b_2_22·a_5_6 − b_2_23·a_3_2 + a_4_4·a_5_9 + a_4_4·a_5_6
  137. a_4_5·a_5_9 − a_4_4·a_5_6
  138.  − b_2_22·a_5_6 − b_2_23·a_3_2 + a_4_4·a_5_10
  139. b_2_22·a_5_6 + b_2_23·a_3_2 + a_4_5·a_5_10 + b_2_1·a_1_1·a_3_4·a_3_5
  140. b_4_6·a_5_10 + b_4_6·a_5_7 − b_2_22·a_5_6 − b_2_23·a_3_2 + b_2_12·a_5_9 + b_2_13·a_3_2
       + a_4_4·a_5_6 + b_2_1·a_1_1·a_3_4·a_3_5
  141.  − b_4_6·a_5_7 + b_2_22·a_5_6 + b_2_23·a_3_2 − b_2_12·a_5_7 + b_2_12·a_5_6
       + b_2_13·a_3_5 + a_4_4·a_5_6 + b_2_1·a_1_1·a_3_4·a_3_5 + b_2_1·c_6_14·a_1_1
  142. a_6_7·a_3_2
  143. a_6_7·a_3_1
  144. a_6_7·a_3_5 − a_4_4·a_5_6
  145. b_2_22·a_5_6 + b_2_23·a_3_2 + a_6_7·a_3_4 − a_4_4·a_5_6
  146. a_6_7·a_3_3
  147.  − b_2_22·a_5_6 − b_2_23·a_3_2 + a_6_9·a_3_2 − a_4_4·a_5_6
  148. a_6_9·a_3_1
  149. a_6_9·a_3_5 − b_2_1·a_1_1·a_3_4·a_3_5
  150. b_2_22·a_5_6 + b_2_23·a_3_2 + a_6_9·a_3_4 + a_4_4·a_5_6
  151. a_6_9·a_3_3 + a_4_4·a_5_6
  152. a_6_10·a_3_2 + a_4_4·a_5_6
  153. b_2_22·a_5_6 + b_2_23·a_3_2 + a_6_10·a_3_1
  154.  − b_2_22·a_5_6 − b_2_23·a_3_2 + a_6_10·a_3_5 − a_4_4·a_5_6 − b_2_1·a_1_1·a_3_4·a_3_5
  155. b_2_22·a_5_6 + b_2_23·a_3_2 + a_6_10·a_3_4 − a_4_4·a_5_6 + b_2_1·a_1_1·a_3_4·a_3_5
  156. b_2_22·a_5_6 + b_2_23·a_3_2 + a_6_10·a_3_3 − a_4_4·a_5_6
  157. b_6_12·a_3_2 − b_4_6·a_5_7 + b_2_22·a_5_6 + b_2_23·a_3_2 + b_2_12·a_5_7 + b_2_12·a_5_6
       − b_2_13·a_3_5 − b_2_1·a_1_1·a_3_4·a_3_5
  158. b_6_12·a_3_1 + b_2_22·a_5_6 + b_2_23·a_3_2
  159. b_6_12·a_3_5 − b_4_6·a_5_7 − b_4_6·a_5_6 + a_4_4·a_5_6
  160. b_6_12·a_3_4 + b_4_6·a_5_9 − b_4_6·a_5_7 − b_2_22·a_5_6 − b_2_23·a_3_2 + b_2_12·a_5_9
       − b_2_12·a_5_7 + b_2_12·a_5_6 + b_2_13·a_3_5 + a_4_4·a_5_6 + b_2_1·a_1_1·a_3_4·a_3_5
  161. b_6_12·a_3_3 + b_4_6·a_5_7 − b_2_12·a_5_7 − b_2_12·a_5_6 + b_2_13·a_3_5
       + b_2_1·a_1_1·a_3_4·a_3_5
  162.  − b_4_6·a_5_7 + b_4_6·a_5_6 + b_2_22·a_5_6 + b_2_23·a_3_2 + b_2_1·a_7_17 − b_2_12·a_5_7
       − b_2_13·a_3_5 − a_4_4·a_5_6 + b_2_1·a_1_1·a_3_4·a_3_5
  163. a_2_0·a_7_17
  164.  − b_4_6·a_5_9 + b_4_6·a_5_7 + b_2_1·a_7_18 + b_2_12·a_5_9 + b_2_12·a_5_7 − b_2_12·a_5_6
       + b_2_13·a_3_5 + b_2_13·a_3_4 + b_2_13·a_3_2 − b_2_1·a_1_1·a_3_4·a_3_5
       − b_2_1·c_6_15·a_1_1
  165. b_2_22·a_5_6 + b_2_23·a_3_2 + a_2_0·a_7_18
  166. b_2_2·a_7_18 − b_2_22·a_5_9 − b_2_23·a_3_2 − b_2_1·a_1_1·a_3_4·a_3_5
  167. b_2_22·a_5_6 + b_2_23·a_3_2 + a_8_14·a_1_1 + a_4_4·a_5_6
  168. a_8_14·a_1_0
  169.  − a_5_8·a_5_9 + a_5_7·a_5_10 + a_5_7·a_5_9 + a_5_7·a_5_8 + b_2_2·a_3_2·a_5_9
       − b_2_2·a_3_2·a_5_7 + b_2_12·a_3_4·a_3_5 − b_2_12·a_1_1·a_5_9 − b_2_12·a_1_1·a_5_6
  170. a_5_6·a_5_10 − a_5_6·a_5_8 − a_5_6·a_5_7 − b_2_2·a_3_2·a_5_9 − b_2_2·a_3_2·a_5_7
       + b_2_1·a_3_4·a_5_6
  171. a_5_9·a_5_10 + a_5_8·a_5_10 − a_5_8·a_5_9 + b_2_12·a_3_4·a_3_5 + b_2_12·a_1_1·a_5_9
       − b_2_12·a_1_1·a_5_6
  172.  − a_5_7·a_5_8 − b_2_2·a_3_2·a_5_7 − b_2_12·a_1_1·a_5_6 + c_6_14·a_1_0·a_3_1
  173.  − a_5_7·a_5_8 − a_5_6·a_5_8 − a_5_6·a_5_7 + b_2_2·a_3_2·a_5_7 + c_6_14·a_1_1·a_3_5
  174.  − a_5_9·a_5_10 − a_5_8·a_5_9 + a_5_6·a_5_8 − a_5_6·a_5_7 − b_2_2·a_3_2·a_5_7
       − b_2_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_5_9 + b_2_12·a_1_1·a_5_6 + c_6_15·a_1_0·a_3_1
       + c_6_14·a_1_1·a_3_4
  175. a_4_4·a_6_7
  176. a_4_5·a_6_7
  177. b_4_6·a_6_7 − a_5_8·a_5_9 − a_5_7·a_5_8 + a_5_6·a_5_8 − a_5_6·a_5_7 + b_2_2·a_3_2·a_5_9
       + b_2_2·a_3_2·a_5_7 + b_2_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_5_9 + b_2_12·a_1_1·a_5_6
       − c_6_14·a_1_1·a_3_4
  178. a_4_4·a_6_9
  179. a_4_5·a_6_9
  180. b_4_6·a_6_9 + a_5_8·a_5_9 + a_5_7·a_5_8 − a_5_6·a_5_8 + a_5_6·a_5_7 − b_2_2·a_3_2·a_5_9
       − b_2_2·a_3_2·a_5_7 − b_2_12·a_1_1·a_5_9 − b_2_12·a_1_1·a_5_6 + c_6_14·a_1_1·a_3_4
  181. a_4_4·a_6_10
  182. a_4_5·a_6_10
  183. b_4_6·a_6_10 + a_5_8·a_5_9 + a_5_7·a_5_8 − b_2_2·a_3_2·a_5_9 + b_2_2·a_3_2·a_5_7
       + b_2_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_5_9 + b_2_12·a_1_1·a_5_6 + c_6_14·a_1_1·a_3_4
  184. a_4_4·b_6_12 − a_5_8·a_5_9 − a_5_7·a_5_8 + a_5_6·a_5_8 − a_5_6·a_5_7 + b_2_2·a_3_2·a_5_9
       + b_2_2·a_3_2·a_5_7 + b_2_1·a_3_4·a_5_6 − b_2_12·a_1_1·a_5_9 − b_2_12·a_1_1·a_5_6
       − c_6_14·a_1_1·a_3_4
  185. a_4_5·b_6_12 + a_5_6·a_5_8 − a_5_6·a_5_7 − b_2_2·a_3_2·a_5_7 − b_2_12·a_1_1·a_5_6
  186. b_4_6·b_6_12 − b_2_12·b_6_12 + a_5_8·a_5_9 + a_5_7·a_5_8 − b_2_2·a_3_2·a_5_9
       + b_2_2·a_3_2·a_5_7 − b_2_12·a_3_4·a_3_5 + b_2_12·a_1_1·a_5_9 − b_2_12·a_1_1·a_5_6
       − b_2_13·a_1_1·a_3_4 + b_2_12·c_6_14 + c_6_14·a_1_1·a_3_4
  187.  − a_5_6·a_5_8 + a_5_6·a_5_7 + b_2_2·a_3_2·a_5_7 + b_2_1·a_1_1·a_7_17
       − b_2_12·a_1_1·a_5_6 + b_2_13·a_1_1·a_3_5
  188.  − a_5_7·a_5_8 − a_5_6·a_5_7 + a_3_2·a_7_17 − b_2_2·a_3_2·a_5_9 + b_2_2·a_3_2·a_5_7
       − b_2_12·a_1_1·a_5_6
  189.  − a_5_9·a_5_10 − a_5_8·a_5_9 + a_5_6·a_5_8 − a_5_6·a_5_7 + a_3_1·a_7_17 − b_2_2·a_3_2·a_5_7
       − b_2_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_5_9 + b_2_12·a_1_1·a_5_6 + c_6_14·a_1_1·a_3_4
  190. a_5_9·a_5_10 + a_5_8·a_5_9 + a_5_6·a_5_8 + a_3_5·a_7_17 + b_2_2·a_3_2·a_5_9
       + b_2_1·a_3_4·a_5_6 − b_2_12·a_1_1·a_5_9 − c_6_14·a_1_1·a_3_4
  191. a_5_6·a_5_9 − a_5_6·a_5_7 + a_3_4·a_7_17 − b_2_2·a_3_2·a_5_7 − b_2_1·a_3_4·a_5_6
       + b_2_12·a_3_4·a_3_5 + b_2_12·a_1_1·a_5_6 + c_6_14·a_1_1·a_3_4
  192.  − a_5_9·a_5_10 − a_5_8·a_5_9 + a_5_6·a_5_8 + a_3_3·a_7_17 − b_2_2·a_3_2·a_5_9
       − b_2_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_5_9 + b_2_12·a_1_1·a_5_6 + c_6_14·a_1_1·a_3_4
  193. a_5_8·a_5_9 + a_5_7·a_5_8 + a_5_6·a_5_8 − a_5_6·a_5_7 − b_2_2·a_3_2·a_5_9
       − b_2_1·a_3_4·a_5_6 + b_2_1·a_1_1·a_7_18 − b_2_12·a_1_1·a_5_6 − b_2_13·a_1_1·a_3_5
       + b_2_13·a_1_1·a_3_4 + c_6_14·a_1_1·a_3_4
  194.  − a_5_9·a_5_10 − a_5_6·a_5_8 + a_5_6·a_5_7 + a_3_2·a_7_18 + b_2_2·a_3_2·a_5_9
       + b_2_2·a_3_2·a_5_7 + b_2_1·a_3_4·a_5_6 − b_2_12·a_1_1·a_5_9
  195.  − a_5_9·a_5_10 − a_5_8·a_5_9 + a_5_7·a_5_8 + a_5_6·a_5_8 − a_5_6·a_5_7 + a_3_1·a_7_18
       − b_2_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_5_9 − b_2_12·a_1_1·a_5_6 + c_6_14·a_1_1·a_3_4
  196. a_5_9·a_5_10 + a_5_8·a_5_9 − a_5_7·a_5_8 − a_5_6·a_5_9 + a_5_6·a_5_7 + a_3_5·a_7_18
       − b_2_1·a_3_4·a_5_6 − b_2_12·a_3_4·a_3_5 − b_2_12·a_1_1·a_5_9 − b_2_12·a_1_1·a_5_6
       + c_6_15·a_1_1·a_3_5
  197. a_5_9·a_5_10 − a_5_7·a_5_8 + a_5_6·a_5_8 − a_5_6·a_5_7 + a_3_4·a_7_18 + b_2_2·a_3_2·a_5_7
       − b_2_1·a_3_4·a_5_6 − b_2_12·a_3_4·a_3_5 + b_2_12·a_1_1·a_5_9 + c_6_15·a_1_1·a_3_4
       + c_6_14·a_1_1·a_3_4
  198. a_5_9·a_5_10 + a_5_6·a_5_8 − a_5_6·a_5_7 + a_3_3·a_7_18 − b_2_2·a_3_2·a_5_7
       − b_2_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_5_9
  199. b_2_1·a_8_14 − a_5_8·a_5_9 − a_5_7·a_5_8 − a_5_6·a_5_8 + a_5_6·a_5_7 + b_2_2·a_3_2·a_5_9
       − b_2_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_5_6 − c_6_14·a_1_1·a_3_4
  200. a_2_0·a_8_14
  201. b_2_2·a_8_14 + a_5_9·a_5_10 − a_5_8·a_5_9 + a_5_7·a_5_9 + a_5_7·a_5_8 + a_5_6·a_5_8
       − a_5_6·a_5_7 + b_2_2·a_3_2·a_5_9 − b_2_2·a_3_2·a_5_7 − b_2_1·a_3_4·a_5_6
       − b_2_12·a_1_1·a_5_6 + c_6_14·a_1_1·a_3_4
  202. a_6_7·a_5_7 − b_2_1·a_1_1·a_3_4·a_5_6
  203. a_6_7·a_5_8 − b_2_1·a_1_1·a_3_4·a_5_6
  204. a_6_7·a_5_10 + a_6_7·a_5_9 + a_6_7·a_5_6
  205. a_6_9·a_5_7 − a_6_7·a_5_9 + a_6_7·a_5_6 − b_2_1·a_1_1·a_3_4·a_5_6
       − b_2_12·a_1_1·a_3_4·a_3_5
  206. a_6_9·a_5_6 + a_6_7·a_5_6
  207. a_6_9·a_5_9 + a_6_7·a_5_9 − a_6_7·a_5_6 + b_2_1·a_1_1·a_3_4·a_5_6
  208. a_6_9·a_5_8 − a_6_7·a_5_6 − b_2_12·a_1_1·a_3_4·a_3_5
  209. a_6_9·a_5_10 − a_6_7·a_5_9 + b_2_12·a_1_1·a_3_4·a_3_5
  210. a_6_10·a_5_7 + a_6_7·a_5_6 − b_2_12·a_1_1·a_3_4·a_3_5
  211. a_6_10·a_5_6 + a_6_7·a_5_6 + b_2_1·a_1_1·a_3_4·a_5_6
  212. a_6_10·a_5_9 − a_6_7·a_5_9 + a_6_7·a_5_6 + b_2_1·a_1_1·a_3_4·a_5_6
  213. a_6_10·a_5_8 + a_6_7·a_5_6 − b_2_1·a_1_1·a_3_4·a_5_6 − b_2_12·a_1_1·a_3_4·a_3_5
  214. a_6_10·a_5_10 + a_6_7·a_5_9 + b_2_1·a_1_1·a_3_4·a_5_6 − b_2_12·a_1_1·a_3_4·a_3_5
  215.  − b_6_12·a_5_7 + b_6_12·a_5_6 + b_2_13·a_5_7 − b_2_14·a_3_5 + a_6_7·a_5_9 + a_6_7·a_5_6
       + b_2_12·a_1_1·a_3_4·a_3_5 + b_2_1·c_6_14·a_3_5 + b_2_1·c_6_14·a_3_2
       + b_2_12·c_6_14·a_1_1
  216. b_6_12·a_5_8 − b_6_12·a_5_7 + b_2_13·a_5_7 − b_2_14·a_3_5 + a_6_7·a_5_9
       − b_2_12·a_1_1·a_3_4·a_3_5 + b_2_12·c_6_14·a_1_1
  217. b_6_12·a_5_10 + b_6_12·a_5_9 + b_6_12·a_5_7 + b_2_13·a_5_7 − b_2_14·a_3_5 − a_6_7·a_5_9
       + a_6_7·a_5_6 + b_2_1·a_1_1·a_3_4·a_5_6 − b_2_12·a_1_1·a_3_4·a_3_5
       − b_2_1·c_6_14·a_3_4 + b_2_1·c_6_14·a_3_2 + b_2_12·c_6_14·a_1_1
  218. b_6_12·a_5_7 + b_2_12·a_7_17 − b_2_13·a_5_7 + b_2_13·a_5_6 − b_2_14·a_3_5
       − a_6_7·a_5_9 − b_2_1·a_1_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_3_4·a_3_5
       + b_2_1·c_6_14·a_3_2 − b_2_12·c_6_14·a_1_1
  219. b_2_22·a_7_17 − b_2_23·a_5_9 − b_2_24·a_3_2 + a_6_7·a_5_9 + a_6_7·a_5_6
  220. a_6_7·a_5_6 + a_4_4·a_7_17 − b_2_1·a_1_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_3_4·a_3_5
  221. a_4_5·a_7_17
  222. a_6_7·a_5_6 + a_1_1·a_3_4·a_7_17 − b_2_1·a_1_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_3_4·a_3_5
  223.  − b_6_12·a_5_7 + b_4_6·a_7_17 − b_2_13·a_5_7 + b_2_14·a_3_5 + a_6_7·a_5_9 + a_6_7·a_5_6
       − b_2_1·a_1_1·a_3_4·a_5_6 − b_2_12·a_1_1·a_3_4·a_3_5 − b_2_1·c_6_14·a_3_5
       + b_2_1·c_6_14·a_3_2 − b_2_12·c_6_14·a_1_1
  224.  − b_6_12·a_5_9 + b_2_12·a_7_18 − b_2_13·a_5_9 − b_2_14·a_3_5 + b_2_14·a_3_4
       + b_2_14·a_3_2 − a_6_7·a_5_9 + a_6_7·a_5_6 − b_2_1·a_1_1·a_3_4·a_5_6
       + b_2_1·c_6_14·a_3_4 − b_2_1·c_6_14·a_3_2 − b_2_12·c_6_15·a_1_1
  225. a_6_7·a_5_6 + a_4_4·a_7_18 − b_2_1·a_1_1·a_3_4·a_5_6
  226.  − a_6_7·a_5_6 + a_4_5·a_7_18 + b_2_1·a_1_1·a_3_4·a_5_6 − b_2_12·a_1_1·a_3_4·a_3_5
  227. b_6_12·a_5_9 + b_4_6·a_7_18 + b_2_13·a_5_7 − b_2_13·a_5_6 − b_2_14·a_3_5 + a_6_7·a_5_9
       + a_6_7·a_5_6 − b_2_1·a_1_1·a_3_4·a_5_6 + b_2_12·a_1_1·a_3_4·a_3_5
       + b_2_1·c_6_15·a_3_2 + b_2_1·c_6_14·a_3_4 + b_2_1·c_6_14·a_3_2 − b_2_12·c_6_14·a_1_1
  228. a_8_14·a_3_2 − a_6_7·a_5_9 + a_6_7·a_5_6
  229. a_8_14·a_3_1
  230. a_8_14·a_3_5 + a_6_7·a_5_9 − a_6_7·a_5_6
  231. a_8_14·a_3_4 − a_6_7·a_5_9 − a_6_7·a_5_6
  232. a_8_14·a_3_3 − a_6_7·a_5_9
  233. a_6_72
  234. a_6_92
  235. a_6_7·a_6_9
  236. a_6_102
  237. a_6_9·a_6_10
  238. a_6_7·a_6_10
  239.  − b_6_122 − b_2_13·b_6_12 + a_6_10·b_6_12 + a_6_7·b_6_12 − b_2_13·a_3_4·a_3_5
       − b_2_13·a_1_1·a_5_9 + b_2_13·a_1_1·a_5_6 − b_2_14·a_1_1·a_3_4 − b_2_1·b_4_6·c_6_14
       + b_2_13·c_6_14 − b_2_1·c_6_14·a_1_1·a_3_4
  240.  − a_6_10·b_6_12 − a_6_9·b_6_12 + a_5_7·a_7_17 − b_2_2·a_5_7·a_5_9 + b_2_22·a_3_2·a_5_7
       + c_6_14·a_1_1·a_5_6 − c_6_14·a_1_0·a_5_9 − c_6_14·a_1_0·a_5_8
       − b_2_1·c_6_14·a_1_1·a_3_5 − b_2_1·c_6_14·a_1_1·a_3_4
  241. a_6_10·b_6_12 + a_6_9·b_6_12 + a_5_6·a_7_17 + b_2_22·a_3_2·a_5_9 + c_6_14·a_1_1·a_5_6
       + b_2_1·c_6_14·a_1_1·a_3_4
  242. a_6_10·b_6_12 + a_6_9·b_6_12 + b_2_12·a_1_1·a_7_17 + b_2_13·a_1_1·a_5_6
       + b_2_14·a_1_1·a_3_5 + b_2_1·c_6_14·a_1_1·a_3_4
  243.  − b_6_122 − b_2_13·b_6_12 + a_6_10·b_6_12 − a_6_9·b_6_12 + b_2_1·a_3_4·a_7_17
       + b_2_12·a_3_4·a_5_6 − b_2_13·a_1_1·a_5_9 + b_2_13·a_1_1·a_5_6 − b_2_14·a_1_1·a_3_4
       − b_2_1·b_4_6·c_6_14 + b_2_13·c_6_14
  244. b_6_122 + b_2_13·b_6_12 + a_6_10·b_6_12 + a_6_9·b_6_12 + a_5_9·a_7_17
       + b_2_22·a_3_2·a_5_9 + b_2_13·a_3_4·a_3_5 + b_2_13·a_1_1·a_5_9 − b_2_13·a_1_1·a_5_6
       + b_2_14·a_1_1·a_3_4 + b_2_1·b_4_6·c_6_14 − b_2_13·c_6_14 − c_6_15·a_1_0·a_5_9
       + c_6_14·a_3_4·a_3_5 − c_6_14·a_1_1·a_5_9 + c_6_14·a_1_1·a_5_6 + c_6_14·a_1_0·a_5_9
       − c_6_14·a_1_0·a_5_8 − b_2_1·c_6_14·a_1_1·a_3_5 + b_2_1·c_6_14·a_1_1·a_3_4
  245. a_6_10·b_6_12 + a_6_9·b_6_12 + a_5_8·a_7_17 − b_2_22·a_3_2·a_5_9 − c_6_15·a_1_0·a_5_8
       + c_6_14·a_1_1·a_5_6 + c_6_14·a_1_0·a_5_9 + c_6_14·a_1_0·a_5_8
       + b_2_1·c_6_14·a_1_1·a_3_5 + b_2_1·c_6_14·a_1_1·a_3_4
  246.  − b_6_122 − b_2_13·b_6_12 + a_6_10·b_6_12 − a_6_9·b_6_12 + a_5_10·a_7_17
       + b_2_22·a_3_2·a_5_9 + b_2_12·a_3_4·a_5_6 − b_2_13·a_1_1·a_5_9 + b_2_13·a_1_1·a_5_6
       − b_2_14·a_1_1·a_3_4 − b_2_1·b_4_6·c_6_14 + b_2_13·c_6_14 − c_6_15·a_1_0·a_5_9
       + c_6_15·a_1_0·a_5_8 − c_6_14·a_1_1·a_5_6 − c_6_14·a_1_0·a_5_8
  247.  − a_6_10·b_6_12 + a_5_7·a_7_18 − b_2_2·a_5_7·a_5_9 + b_2_22·a_3_2·a_5_7
       − b_2_12·a_3_4·a_5_6 − b_2_13·a_3_4·a_3_5 − c_6_15·a_1_0·a_5_9 − c_6_15·a_1_0·a_5_8
       − c_6_14·a_1_1·a_5_9 − c_6_14·a_1_0·a_5_9 + c_6_14·a_1_0·a_5_8
       + b_2_1·c_6_15·a_1_1·a_3_5 + b_2_1·c_6_14·a_1_1·a_3_5 − b_2_1·c_6_14·a_1_1·a_3_4
  248.  − b_6_122 − b_2_13·b_6_12 − a_6_10·b_6_12 + a_5_6·a_7_18 + b_2_22·a_3_2·a_5_9
       − b_2_13·a_3_4·a_3_5 − b_2_13·a_1_1·a_5_9 + b_2_13·a_1_1·a_5_6 − b_2_14·a_1_1·a_3_4
       − b_2_1·b_4_6·c_6_14 + b_2_13·c_6_14 + c_6_15·a_1_1·a_5_6 + c_6_14·a_3_4·a_3_5
       + c_6_14·a_1_1·a_5_9 − c_6_14·a_1_0·a_5_8 + b_2_1·c_6_14·a_1_1·a_3_5
       − b_2_1·c_6_14·a_1_1·a_3_4
  249. b_6_122 + b_2_13·b_6_12 + a_6_9·b_6_12 + b_2_12·a_1_1·a_7_18 + b_2_13·a_3_4·a_3_5
       − b_2_13·a_1_1·a_5_6 − b_2_14·a_1_1·a_3_5 − b_2_14·a_1_1·a_3_4 + b_2_1·b_4_6·c_6_14
       − b_2_13·c_6_14 − b_2_1·c_6_14·a_1_1·a_3_5
  250.  − b_6_122 − b_2_13·b_6_12 + a_6_10·b_6_12 + a_5_9·a_7_18 + b_2_22·a_3_2·a_5_9
       + b_2_12·a_3_4·a_5_6 − b_2_13·a_3_4·a_3_5 − b_2_13·a_1_1·a_5_9 − b_2_13·a_1_1·a_5_6
       − b_2_14·a_1_1·a_3_4 − b_2_1·b_4_6·c_6_14 + b_2_13·c_6_14 + c_6_15·a_1_1·a_5_9
       − c_6_14·a_1_1·a_5_9 + b_2_1·c_6_14·a_1_1·a_3_5 + b_2_1·c_6_14·a_1_1·a_3_4
  251.  − b_6_122 − b_2_13·b_6_12 − a_6_10·b_6_12 − a_6_9·b_6_12 + a_5_8·a_7_18
       − b_2_22·a_3_2·a_5_9 − b_2_12·a_3_4·a_5_6 + b_2_13·a_3_4·a_3_5 − b_2_13·a_1_1·a_5_9
       − b_2_14·a_1_1·a_3_4 − b_2_1·b_4_6·c_6_14 + b_2_13·c_6_14 + c_6_15·a_1_0·a_5_9
       − c_6_14·a_1_1·a_5_9 − c_6_14·a_1_0·a_5_9 + b_2_1·c_6_15·a_1_1·a_3_5
       − b_2_1·c_6_14·a_1_1·a_3_5 + b_2_1·c_6_14·a_1_1·a_3_4
  252. b_6_122 + b_2_13·b_6_12 + a_6_10·b_6_12 + a_6_9·b_6_12 + a_5_10·a_7_18
       + b_2_22·a_3_2·a_5_9 + b_2_12·a_3_4·a_5_6 + b_2_13·a_3_4·a_3_5 + b_2_13·a_1_1·a_5_9
       + b_2_13·a_1_1·a_5_6 + b_2_14·a_1_1·a_3_4 + b_2_1·b_4_6·c_6_14 − b_2_13·c_6_14
       − c_6_15·a_1_0·a_5_9 + c_6_15·a_1_0·a_5_8 + c_6_14·a_1_1·a_5_9 + c_6_14·a_1_0·a_5_9
       − c_6_14·a_1_0·a_5_8 − b_2_1·c_6_15·a_1_1·a_3_5 + b_2_1·c_6_15·a_1_1·a_3_4
       + b_2_1·c_6_14·a_1_1·a_3_5
  253. a_4_4·a_8_14
  254. a_4_5·a_8_14
  255. a_6_10·b_6_12 + b_4_6·a_8_14 − b_2_12·a_3_4·a_5_6 − b_2_13·a_1_1·a_5_9
       − b_2_1·c_6_14·a_1_1·a_3_5
  256. b_6_12·a_7_17 − b_2_13·a_7_17 − b_2_14·a_5_7 − b_2_14·a_5_6 − a_3_2·a_5_7·a_5_9
       + b_2_12·a_1_1·a_3_4·a_5_6 + b_2_13·a_1_1·a_3_4·a_3_5 + b_2_1·c_6_14·a_5_7
       − b_2_1·c_6_14·a_5_6 − b_2_12·c_6_14·a_3_5 − b_2_13·c_6_14·a_1_1
       + a_2_0·c_6_15·a_5_10 − a_2_0·c_6_14·a_5_10
  257. a_6_10·a_7_17 + a_3_2·a_5_7·a_5_9 − b_2_1·a_1_1·a_3_4·a_7_17
       − b_2_12·a_1_1·a_3_4·a_5_6 + a_2_0·c_6_15·a_5_10
  258. a_6_9·a_7_17 − a_3_2·a_5_7·a_5_9 − b_2_12·a_1_1·a_3_4·a_5_6
       + b_2_13·a_1_1·a_3_4·a_3_5 + a_2_0·c_6_14·a_5_10 − c_6_14·a_1_1·a_3_4·a_3_5
  259. a_6_7·a_7_17 + a_3_2·a_5_7·a_5_9 − b_2_12·a_1_1·a_3_4·a_5_6
       − c_6_14·a_1_1·a_3_4·a_3_5
  260. b_6_12·a_7_18 − b_2_13·a_7_18 + b_2_13·a_7_17 + b_2_14·a_5_9 − b_2_14·a_5_7
       + b_2_14·a_5_6 − b_2_15·a_3_4 − b_2_15·a_3_2 − a_3_2·a_5_7·a_5_9
       + b_2_1·a_1_1·a_3_4·a_7_17 − b_2_13·a_1_1·a_3_4·a_3_5 + b_2_1·c_6_15·a_5_7
       + b_2_1·c_6_14·a_5_9 − b_2_1·c_6_14·a_5_7 − b_2_12·c_6_15·a_3_5 + b_2_12·c_6_14·a_3_5
       + b_2_13·c_6_15·a_1_1 − b_2_13·c_6_14·a_1_1 + a_2_0·c_6_14·a_5_10
       − c_6_14·a_1_1·a_3_4·a_3_5
  261. a_6_10·a_7_18 + a_3_2·a_5_7·a_5_9 + b_2_13·a_1_1·a_3_4·a_3_5 + a_2_0·c_6_15·a_5_10
       + a_2_0·c_6_14·a_5_10 − c_6_15·a_1_1·a_3_4·a_3_5 − c_6_14·a_1_1·a_3_4·a_3_5
  262. a_6_9·a_7_18 − a_3_2·a_5_7·a_5_9 + b_2_1·a_1_1·a_3_4·a_7_17
       − b_2_12·a_1_1·a_3_4·a_5_6 + a_2_0·c_6_15·a_5_10 + c_6_15·a_1_1·a_3_4·a_3_5
       + c_6_14·a_1_1·a_3_4·a_3_5
  263. a_6_7·a_7_18 + a_3_2·a_5_7·a_5_9 + b_2_12·a_1_1·a_3_4·a_5_6 − a_2_0·c_6_14·a_5_10
       − c_6_14·a_1_1·a_3_4·a_3_5
  264. a_8_14·a_5_7 + a_3_2·a_5_7·a_5_9 − b_2_1·a_1_1·a_3_4·a_7_17
       − b_2_13·a_1_1·a_3_4·a_3_5 + a_2_0·c_6_14·a_5_10 + c_6_14·a_1_1·a_3_4·a_3_5
  265. a_8_14·a_5_6 − a_3_2·a_5_7·a_5_9 − b_2_12·a_1_1·a_3_4·a_5_6
       + c_6_14·a_1_1·a_3_4·a_3_5
  266. a_8_14·a_5_9 − a_3_2·a_5_7·a_5_9 − b_2_12·a_1_1·a_3_4·a_5_6
       + c_6_14·a_1_1·a_3_4·a_3_5
  267. a_8_14·a_5_8 + a_3_2·a_5_7·a_5_9 + b_2_1·a_1_1·a_3_4·a_7_17
       + b_2_12·a_1_1·a_3_4·a_5_6 + b_2_13·a_1_1·a_3_4·a_3_5 − a_2_0·c_6_14·a_5_10
       + c_6_14·a_1_1·a_3_4·a_3_5
  268. a_8_14·a_5_10 − a_3_2·a_5_7·a_5_9 + b_2_12·a_1_1·a_3_4·a_5_6 + a_2_0·c_6_15·a_5_10
       − c_6_14·a_1_1·a_3_4·a_3_5
  269. a_7_17·a_7_18 − b_2_12·a_3_4·a_7_17 − b_2_13·a_1_1·a_7_17 − b_2_14·a_1_1·a_5_6
       − b_2_15·a_1_1·a_3_5 + c_6_15·a_1_1·a_7_17 + c_6_15·a_1_0·a_7_18 − c_6_14·a_3_4·a_5_6
       − c_6_14·a_1_1·a_7_18 − c_6_14·a_1_0·a_7_18 − b_2_1·c_6_14·a_3_4·a_3_5
       − b_2_1·c_6_14·a_1_1·a_5_9 − b_2_1·c_6_14·a_1_1·a_5_6 − b_2_12·c_6_14·a_1_1·a_3_5
       − b_2_12·c_6_14·a_1_1·a_3_4
  270. b_6_12·a_8_14 − b_2_12·a_3_4·a_7_17 − b_2_13·a_3_4·a_5_6 − b_2_14·a_3_4·a_3_5
       − b_2_1·c_6_14·a_3_4·a_3_5 + b_2_1·c_6_14·a_1_1·a_5_9
  271. a_6_10·a_8_14
  272. a_6_9·a_8_14
  273. a_6_7·a_8_14
  274. a_8_14·a_7_18 − b_2_13·a_1_1·a_3_4·a_5_6 + c_6_15·a_1_1·a_3_4·a_5_6
       + b_2_1·c_6_14·a_1_1·a_3_4·a_3_5
  275. a_8_14·a_7_17 − b_2_12·a_1_1·a_3_4·a_7_17 − b_2_13·a_1_1·a_3_4·a_5_6
       − b_2_14·a_1_1·a_3_4·a_3_5 − a_2_0·c_6_14·a_7_18 − b_2_1·c_6_14·a_1_1·a_3_4·a_3_5
  276. a_8_142

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 243

Data used for Benson′s test

  • Benson′s completion test succeeded in degree 16.
  • The completion test was perfect: It applied in the last degree in which a generator or relation was found.
  • The following is a filter regular homogeneous system of parameters:
    1. c_6_14, a Duflot regular element of degree 6
    2. c_6_15, a Duflot regular element of degree 6
    3. b_2_22 + b_2_12, an element of degree 4
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 9, 13].
  • 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 243

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_0 → 0, an element of degree 2
  4. b_2_1 → 0, an element of degree 2
  5. b_2_2 → 0, an element of degree 2
  6. a_3_1 → 0, an element of degree 3
  7. a_3_2 → 0, an element of degree 3
  8. a_3_3 → 0, an element of degree 3
  9. a_3_4 → 0, an element of degree 3
  10. a_3_5 → 0, an element of degree 3
  11. a_4_4 → 0, an element of degree 4
  12. a_4_5 → 0, an element of degree 4
  13. b_4_6 → 0, an element of degree 4
  14. a_5_6 → 0, an element of degree 5
  15. a_5_7 → 0, an element of degree 5
  16. a_5_8 → 0, an element of degree 5
  17. a_5_9 → 0, an element of degree 5
  18. a_5_10 → 0, an element of degree 5
  19. a_6_7 → 0, an element of degree 6
  20. a_6_9 → 0, an element of degree 6
  21. a_6_10 → 0, an element of degree 6
  22. b_6_12 → 0, an element of degree 6
  23. c_6_14 →  − c_2_13, an element of degree 6
  24. c_6_15 → c_2_23 − c_2_13, an element of degree 6
  25. a_7_17 → 0, an element of degree 7
  26. a_7_18 → 0, an element of degree 7
  27. a_8_14 → 0, an element of degree 8

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 → a_1_2, an element of degree 1
  3. a_2_0 → 0, an element of degree 2
  4. b_2_1 → c_2_5, an element of degree 2
  5. b_2_2 →  − a_1_1·a_1_2 − a_1_0·a_1_2, an element of degree 2
  6. a_3_1 → 0, an element of degree 3
  7. a_3_2 →  − c_2_3·a_1_2, an element of degree 3
  8. a_3_3 → c_2_3·a_1_2, an element of degree 3
  9. a_3_4 → c_2_5·a_1_1 + c_2_5·a_1_0 − c_2_4·a_1_2 − c_2_3·a_1_2, an element of degree 3
  10. a_3_5 → c_2_5·a_1_0 − c_2_3·a_1_2, an element of degree 3
  11. a_4_4 →  − c_2_5·a_1_1·a_1_2, an element of degree 4
  12. a_4_5 →  − c_2_5·a_1_0·a_1_2, an element of degree 4
  13. b_4_6 →  − c_2_5·a_1_1·a_1_2 − c_2_5·a_1_0·a_1_2 + c_2_3·c_2_5, an element of degree 4
  14. a_5_6 →  − c_2_5·a_1_0·a_1_1·a_1_2 + c_2_3·c_2_5·a_1_2 + c_2_3·c_2_5·a_1_0, an element of degree 5
  15. a_5_7 →  − c_2_5·a_1_0·a_1_1·a_1_2 + c_2_52·a_1_0 + c_2_3·c_2_5·a_1_2 − c_2_32·a_1_2, an element of degree 5
  16. a_5_8 → c_2_5·a_1_0·a_1_1·a_1_2 + c_2_52·a_1_0 − c_2_3·c_2_5·a_1_2 − c_2_32·a_1_2, an element of degree 5
  17. a_5_9 → c_2_5·a_1_0·a_1_1·a_1_2 + c_2_3·c_2_5·a_1_2 − c_2_3·c_2_5·a_1_1 − c_2_3·c_2_5·a_1_0
       + c_2_3·c_2_4·a_1_2, an element of degree 5
  18. a_5_10 →  − c_2_5·a_1_0·a_1_1·a_1_2 + c_2_52·a_1_1 − c_2_4·c_2_5·a_1_2 − c_2_3·c_2_5·a_1_2
       + c_2_32·a_1_2, an element of degree 5
  19. a_6_7 →  − c_2_3·c_2_5·a_1_1·a_1_2, an element of degree 6
  20. a_6_9 →  − c_2_52·a_1_1·a_1_2 − c_2_52·a_1_0·a_1_2 + c_2_52·a_1_0·a_1_1
       − c_2_4·c_2_5·a_1_0·a_1_2 + c_2_3·c_2_5·a_1_1·a_1_2 − c_2_3·c_2_5·a_1_0·a_1_2, an element of degree 6
  21. a_6_10 →  − c_2_52·a_1_1·a_1_2 + c_2_52·a_1_0·a_1_2 − c_2_52·a_1_0·a_1_1
       + c_2_4·c_2_5·a_1_0·a_1_2 + c_2_3·c_2_5·a_1_1·a_1_2, an element of degree 6
  22. b_6_12 →  − c_2_52·a_1_1·a_1_2 + c_2_52·a_1_0·a_1_1 − c_2_4·c_2_5·a_1_0·a_1_2
       − c_2_3·c_2_5·a_1_1·a_1_2 − c_2_3·c_2_5·a_1_0·a_1_2 + c_2_3·c_2_52 + c_2_32·c_2_5, an element of degree 6
  23. c_6_14 → c_2_52·a_1_1·a_1_2 − c_2_52·a_1_0·a_1_2 + c_2_3·c_2_52 − c_2_33, an element of degree 6
  24. c_6_15 → c_2_52·a_1_0·a_1_2 − c_2_3·c_2_5·a_1_1·a_1_2 + c_2_3·c_2_5·a_1_0·a_1_2
       − c_2_4·c_2_52 + c_2_43 + c_2_3·c_2_52 − c_2_32·c_2_5 − c_2_33, an element of degree 6
  25. a_7_17 →  − c_2_52·a_1_0·a_1_1·a_1_2 − c_2_53·a_1_0 + c_2_3·c_2_52·a_1_0 − c_2_32·c_2_5·a_1_2
       − c_2_32·c_2_5·a_1_0 − c_2_33·a_1_2, an element of degree 7
  26. a_7_18 →  − c_2_52·a_1_0·a_1_1·a_1_2 − c_2_3·c_2_5·a_1_0·a_1_1·a_1_2 − c_2_53·a_1_1
       + c_2_43·a_1_2 + c_2_3·c_2_52·a_1_1 + c_2_3·c_2_52·a_1_0 − c_2_3·c_2_4·c_2_5·a_1_2
       − c_2_32·c_2_5·a_1_1 − c_2_32·c_2_5·a_1_0 + c_2_32·c_2_4·a_1_2, an element of degree 7
  27. a_8_14 → c_2_3·c_2_52·a_1_0·a_1_1 − c_2_3·c_2_4·c_2_5·a_1_0·a_1_2
       − c_2_32·c_2_5·a_1_1·a_1_2 + c_2_32·c_2_5·a_1_0·a_1_2, an element of degree 8

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_0 → 0, an element of degree 2
  4. b_2_1 → 0, an element of degree 2
  5. b_2_2 →  − c_2_5, an element of degree 2
  6. a_3_1 → 0, an element of degree 3
  7. a_3_2 → c_2_5·a_1_2, an element of degree 3
  8. a_3_3 → c_2_5·a_1_2, an element of degree 3
  9. a_3_4 → c_2_5·a_1_2, an element of degree 3
  10. a_3_5 →  − c_2_5·a_1_2, an element of degree 3
  11. a_4_4 → 0, an element of degree 4
  12. a_4_5 → 0, an element of degree 4
  13. b_4_6 → 0, an element of degree 4
  14. a_5_6 → c_2_52·a_1_2, an element of degree 5
  15. a_5_7 → c_2_52·a_1_2 + c_2_52·a_1_0 − c_2_3·c_2_5·a_1_2, an element of degree 5
  16. a_5_8 →  − c_2_52·a_1_2, an element of degree 5
  17. a_5_9 → c_2_52·a_1_1 − c_2_4·c_2_5·a_1_2, an element of degree 5
  18. a_5_10 →  − c_2_52·a_1_2 − c_2_52·a_1_1 + c_2_4·c_2_5·a_1_2, an element of degree 5
  19. a_6_7 →  − c_2_52·a_1_0·a_1_2, an element of degree 6
  20. a_6_9 → c_2_52·a_1_1·a_1_2 + c_2_52·a_1_0·a_1_2, an element of degree 6
  21. a_6_10 →  − c_2_52·a_1_0·a_1_2, an element of degree 6
  22. b_6_12 → c_2_52·a_1_1·a_1_2 + c_2_52·a_1_0·a_1_2, an element of degree 6
  23. c_6_14 → c_2_52·a_1_1·a_1_2 + c_2_53 + c_2_3·c_2_52 − c_2_33, an element of degree 6
  24. c_6_15 → c_2_52·a_1_1·a_1_2 − c_2_52·a_1_0·a_1_2 − c_2_53 − c_2_4·c_2_52 + c_2_43
       + c_2_3·c_2_52 − c_2_33, an element of degree 6
  25. a_7_17 →  − c_2_52·a_1_0·a_1_1·a_1_2 + c_2_53·a_1_2 − c_2_53·a_1_1 + c_2_4·c_2_52·a_1_2, an element of degree 7
  26. a_7_18 → c_2_53·a_1_2 − c_2_53·a_1_1 + c_2_4·c_2_52·a_1_2, an element of degree 7
  27. a_8_14 → c_2_53·a_1_1·a_1_2 − c_2_53·a_1_0·a_1_2 + c_2_53·a_1_0·a_1_1
       − c_2_4·c_2_52·a_1_0·a_1_2 + c_2_3·c_2_52·a_1_1·a_1_2, an element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 243


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