Cohomology of group number 78 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_3, a nilpotent element of degree 5
  11. a_5_5, a nilpotent element of degree 5
  12. a_5_6, 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_9, 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_24, 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 + c_2_2·a_1_12
  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 + c_2_2·a_1_1·a_3_2
  20. a_3_3·a_3_4 + a_3_32 + a_3_22 + c_2_2·a_1_1·a_3_4 + c_2_22·a_1_12
  21. a_2_1·a_4_3
  22. a_2_1·b_4_5 + a_3_32 + c_2_22·a_1_12
  23. a_3_22 + b_4_5·a_1_12
  24. a_1_1·a_5_3
  25. a_1_0·a_5_3
  26. a_1_1·a_5_5
  27. a_1_0·a_5_5
  28. a_3_42 + a_3_22 + a_1_1·a_5_6
  29. a_1_0·a_5_6
  30. a_3_42 + a_3_3·a_3_4 + a_3_32 + a_3_2·a_3_4 + a_3_22 + a_1_1·a_5_9 + c_2_2·a_1_1·a_3_2
  31. a_1_0·a_5_9
  32. a_4_3·a_3_3 + 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_3
  35. a_4_3·a_3_3 + a_2_1·a_5_5
  36. a_4_3·a_3_3 + a_2_1·a_5_6
  37. a_1_12·a_5_6
  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
  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 + a_4_3·a_3_3
  43. b_6_10·a_1_0
  44. a_4_32
  45. a_3_3·a_5_3
  46. a_3_2·a_5_3
  47. a_3_4·a_5_3
  48. a_4_3·b_4_5 + a_3_3·a_5_5 + b_4_5·a_1_1·a_3_4
  49. a_3_2·a_5_5
  50. a_4_3·b_4_5 + a_3_4·a_5_5 + b_4_5·a_1_1·a_3_4 + b_4_5·a_1_1·a_3_2
  51. a_3_3·a_5_6 + b_4_5·a_1_1·a_3_2 + c_2_2·a_1_1·a_5_6
  52. a_3_3·a_5_9 + a_3_3·a_5_6 + a_3_2·a_5_9 + a_3_2·a_5_6 + b_4_5·a_1_1·a_3_4
       + c_2_2·b_4_5·a_1_12 + c_2_22·a_1_1·a_3_4 + c_2_23·a_1_12
  53. a_4_3·b_4_5 + a_3_4·a_5_9 + a_3_4·a_5_6 + a_3_3·a_5_9 + a_3_2·a_5_6 + c_2_2·a_3_32
       + c_2_22·a_1_1·a_3_2
  54. a_3_3·a_5_9 + c_2_2·a_1_1·a_5_9 + c_2_2·b_4_5·a_1_12
  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_4
  57. a_3_2·a_5_6 + a_1_1·a_7_9 + b_4_5·a_1_1·a_3_2 + c_2_2·b_4_5·a_1_12
  58. a_1_0·a_7_9
  59. a_3_3·a_5_6 + a_1_1·a_7_15 + b_4_5·a_1_1·a_3_4 + b_4_5·a_1_1·a_3_2 + c_2_22·a_1_1·a_3_2
  60. a_1_0·a_7_15
  61. a_4_3·b_4_5 + a_3_4·a_5_6 + a_3_3·a_5_9 + a_3_2·a_5_6 + a_1_1·a_7_16 + b_4_5·a_1_1·a_3_4
  62. a_1_0·a_7_16
  63. a_4_3·a_5_3
  64. a_4_3·a_5_5
  65. b_4_5·a_5_3 + a_4_3·a_5_6
  66. b_4_5·a_5_3 + a_4_3·a_5_9 + c_2_2·a_1_12·a_5_9
  67. b_4_5·a_5_3 + a_6_9·a_3_3
  68. b_4_5·a_5_3 + a_6_9·a_3_2 + a_4_3·a_5_9
  69. a_6_9·a_3_4
  70. b_6_10·a_3_3 + b_4_5·a_5_5 + a_4_3·a_5_9 + c_2_2·b_4_5·a_3_2
  71. b_6_10·a_3_2 + b_4_5·a_5_3 + b_4_52·a_1_1 + a_4_3·a_5_9
  72. b_6_10·a_3_4 + b_4_5·a_5_9 + b_4_5·a_5_6 + b_4_5·a_5_5 + b_4_5·a_5_3 + b_4_52·a_1_1
       + c_2_2·b_4_5·a_3_4 + c_2_2·b_4_5·a_3_3 + c_2_2·b_4_5·a_3_2
  73. a_2_1·a_7_9
  74. a_1_12·a_7_9
  75. a_4_3·a_5_9 + a_2_1·a_7_15
  76. a_4_3·a_5_9 + a_2_1·a_7_16
  77. a_4_3·a_5_9 + a_1_12·a_7_16
  78. b_4_5·a_5_3 + a_8_15·a_1_1
  79. b_4_5·a_5_3 + a_8_15·a_1_0 + a_4_3·a_5_9
  80. a_5_32
  81. a_5_3·a_5_5
  82. a_5_52 + b_4_5·a_3_32 + c_2_22·b_4_5·a_1_12
  83. a_5_3·a_5_6
  84. a_5_5·a_5_6 + b_4_52·a_1_12
  85. a_5_3·a_5_9
  86. a_5_5·a_5_9 + c_2_2·b_4_5·a_1_1·a_3_2
  87. a_5_92 + a_5_62 + b_4_5·a_3_32 + b_4_5·a_1_1·a_5_6 + c_2_22·a_3_32
       + c_2_22·a_1_1·a_5_6 + c_2_22·b_4_5·a_1_12
  88. a_4_3·a_6_9
  89. a_4_3·b_6_10 + 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
  90. a_3_2·a_7_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
  91. a_3_3·a_7_9 + b_4_5·a_3_32 + b_4_52·a_1_12 + c_2_2·a_3_3·a_5_5 + c_2_2·a_1_1·a_7_9
       + c_2_22·b_4_5·a_1_12
  92. b_4_5·a_6_9 + a_3_3·a_7_15 + b_4_5·a_3_32 + b_4_5·a_1_1·a_5_9
       + 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_22·b_4_5·a_1_12 + c_2_23·a_1_1·a_3_2
  93. a_3_3·a_7_9 + a_3_2·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
       + c_2_2·a_3_3·a_5_5 + c_2_2·b_4_5·a_1_1·a_3_4
  94. b_4_5·a_6_9 + a_5_6·a_5_9 + a_5_62 + a_3_4·a_7_15 + a_3_4·a_7_9 + a_3_3·a_7_9
       + b_4_5·a_1_1·a_5_9 + 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_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
  95. b_4_5·a_6_9 + a_5_6·a_5_9 + a_5_62 + a_3_4·a_7_9 + a_3_3·a_7_16 + b_4_5·a_1_1·a_5_9
       + 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_9
       + c_2_22·a_1_1·a_5_6
  96. a_3_4·a_7_9 + a_3_3·a_7_9 + a_3_2·a_7_16 + b_4_5·a_3_32 + b_4_5·a_1_1·a_5_9
       + 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·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_23·a_1_1·a_3_4 + c_2_24·a_1_12
  97. a_5_6·a_5_9 + a_3_4·a_7_16 + 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·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_23·a_1_1·a_3_2 + c_2_24·a_1_12
  98. a_5_6·a_5_9 + a_5_62 + a_3_4·a_7_9 + b_4_5·a_3_32 + b_4_5·a_1_1·a_5_9
       + b_4_52·a_1_12 + c_2_2·a_1_1·a_7_16 + 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 + c_2_22·b_4_5·a_1_12
  99. a_5_62 + b_4_5·a_3_32 + b_4_5·a_1_1·a_5_6 + c_8_20·a_1_12
       + c_2_2·b_4_5·a_1_1·a_3_2 + c_2_22·b_4_5·a_1_12 + c_2_24·a_1_12
  100. a_2_1·a_8_15
  101. a_1_1·a_9_24 + b_4_5·a_1_1·a_5_6 + c_2_2·b_4_5·a_1_1·a_3_2 + c_2_22·a_1_1·a_5_6
       + c_2_22·b_4_5·a_1_12
  102. a_1_0·a_9_24
  103. a_5_6·a_5_9 + a_5_62 + a_3_3·a_7_9 + a_1_1·a_9_25 + 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·a_1_1·a_5_6
       + c_2_22·b_4_5·a_1_12 + c_2_23·a_1_1·a_3_4 + c_2_24·a_1_12
  104. a_1_0·a_9_25
  105. a_6_9·a_5_3 + c_2_22·a_1_12·a_5_9
  106. a_6_9·a_5_9 + c_2_22·a_1_12·a_5_9
  107. b_6_10·a_5_3 + a_6_9·a_5_5
  108. b_6_10·a_5_5 + b_4_52·a_3_3 + a_6_9·a_5_5 + c_2_2·b_4_52·a_1_1
  109. b_6_10·a_5_9 + b_6_10·a_5_6 + b_4_52·a_3_4 + b_4_52·a_3_3 + b_4_52·a_3_2
       + c_2_2·b_4_5·a_5_9 + c_2_2·b_4_5·a_5_6 + 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
  110. a_6_9·a_5_5 + a_4_3·a_7_9 + c_2_22·a_1_12·a_5_9
  111. b_6_10·a_5_6 + b_4_5·a_7_9 + b_4_52·a_3_3 + b_4_52·a_3_2 + c_2_2·b_4_5·a_5_5
       + c_2_22·a_1_12·a_5_9
  112. a_6_9·a_5_6 + a_4_3·a_7_15 + c_2_22·a_1_12·a_5_9
  113. a_6_9·a_5_6 + a_6_9·a_5_5 + a_4_3·a_7_16
  114. a_6_9·a_5_6 + 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_5
  116. a_8_15·a_3_2 + a_6_9·a_5_5 + c_2_22·a_1_12·a_5_9
  117. a_8_15·a_3_4 + a_6_9·a_5_6 + a_6_9·a_5_5
  118. a_6_9·a_5_6 + a_2_1·a_9_24 + c_2_22·a_1_12·a_5_9
  119. a_6_9·a_5_6 + a_2_1·a_9_25
  120. a_6_9·a_5_6 + 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_52·a_1_12
  123. a_5_3·a_7_9
  124. a_5_5·a_7_9 + 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_23·b_4_5·a_1_12
  125. a_5_3·a_7_15
  126. a_6_9·b_6_10 + a_5_5·a_7_15 + b_4_5·a_3_3·a_5_5 + b_4_5·a_1_1·a_7_9
       + b_4_52·a_1_1·a_3_4 + 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_4 + c_2_23·b_4_5·a_1_12
  127. a_5_3·a_7_16
  128. a_6_9·b_6_10 + a_5_5·a_7_16 + 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_5·a_1_1·a_5_6 + 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·b_4_5·a_1_12
  129. a_6_9·b_6_10 + a_5_9·a_7_16 + a_5_9·a_7_9 + a_5_6·a_7_16 + a_5_6·a_7_15
       + b_4_5·a_1_1·a_7_9 + 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·b_4_5·a_1_1·a_3_4 + c_2_23·a_1_1·a_5_6 + c_2_24·a_1_1·a_3_2
       + c_2_25·a_1_12
  130. a_5_9·a_7_15 + a_5_9·a_7_9 + a_5_6·a_7_15 + a_5_6·a_7_9 + b_4_5·a_1_1·a_7_16
       + b_4_52·a_1_1·a_3_4 + 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_52·a_1_12 + c_2_22·a_3_3·a_5_5 + c_2_22·a_1_1·a_7_16
       + c_2_22·a_1_1·a_7_9 + c_2_22·b_4_5·a_1_1·a_3_4 + 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_5_6·a_7_9 + b_4_5·a_3_3·a_5_5 + b_4_52·a_1_1·a_3_2 + c_8_20·a_1_1·a_3_2
       + c_2_2·b_4_5·a_1_1·a_5_6 + c_2_24·a_1_1·a_3_2
  132. a_6_9·b_6_10 + a_5_9·a_7_15 + a_5_6·a_7_16 + a_5_6·a_7_9 + b_4_5·a_1_1·a_7_9
       + 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_4
       + 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_9
       + c_2_22·b_4_5·a_1_1·a_3_2 + c_2_23·a_1_1·a_5_9 + c_2_23·a_1_1·a_5_6
       + c_2_25·a_1_12
  133. a_5_6·a_7_15 + b_4_5·a_3_3·a_5_5 + b_4_5·a_1_1·a_7_16 + 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 + 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_9
       + c_2_22·b_4_5·a_1_1·a_3_2 + c_2_25·a_1_12
  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_5·a_1_1·a_7_16 + b_4_5·a_1_1·a_7_9
       + 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_9 + c_2_22·b_4_5·a_1_1·a_3_4 + c_2_23·a_1_1·a_5_6
       + c_2_24·a_1_1·a_3_2
  136. a_6_9·b_6_10 + a_3_3·a_9_24 + b_4_5·a_1_1·a_7_9 + 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_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·b_4_5·a_1_12 + c_2_24·a_1_1·a_3_2 + c_2_25·a_1_12
  137. a_3_2·a_9_24 + b_4_5·a_1_1·a_7_9 + b_4_52·a_1_1·a_3_2 + c_2_22·a_1_1·a_7_9
       + c_2_23·b_4_5·a_1_12
  138. a_6_9·b_6_10 + a_5_9·a_7_15 + a_5_9·a_7_9 + a_5_6·a_7_15 + a_5_6·a_7_9 + a_3_4·a_9_24
       + b_4_5·a_3_3·a_5_5 + b_4_5·a_1_1·a_7_9 + 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_1_1·a_5_9 + 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_9 + 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_24·a_1_1·a_3_2
  139. a_6_9·b_6_10 + a_5_9·a_7_15 + a_5_6·a_7_15 + a_3_3·a_9_25 + 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_2·b_4_52·a_1_12 + c_2_22·a_1_1·a_7_9 + 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_2
       + c_2_25·a_1_12
  140. a_5_9·a_7_9 + a_5_6·a_7_9 + a_3_2·a_9_25 + b_4_5·a_3_3·a_5_5 + b_4_52·a_1_1·a_3_4
       + c_2_2·b_4_5·a_3_32 + c_2_2·b_4_5·a_1_1·a_5_6 + c_2_23·b_4_5·a_1_12
  141. a_5_9·a_7_15 + a_5_9·a_7_9 + a_3_4·a_9_25 + b_4_5·a_1_1·a_7_16 + b_4_5·a_1_1·a_7_9
       + 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_52·a_1_12
       + c_2_22·b_4_5·a_1_1·a_3_2 + c_2_23·a_1_1·a_5_6 + c_2_24·a_1_1·a_3_2
  142. a_5_9·a_7_15 + a_5_6·a_7_15 + b_4_5·a_3_3·a_5_5 + b_4_52·a_1_1·a_3_2
       + 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_9
  143. a_6_9·a_7_9 + c_2_23·a_1_12·a_5_9
  144. b_6_10·a_7_9 + b_4_52·a_5_6 + b_4_52·a_5_5 + b_4_53·a_1_1 + a_6_9·a_7_16 + a_6_9·a_7_15
       + b_4_5·a_1_12·a_7_16 + c_2_2·b_4_52·a_3_3 + c_2_2·b_4_52·a_3_2
       + c_2_22·b_4_52·a_1_1
  145. b_6_10·a_7_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
       + c_2_2·b_4_52·a_3_3 + c_2_2·b_4_52·a_3_2 + c_2_22·b_4_52·a_1_1
       + c_2_22·a_1_12·a_7_16
  146. a_8_15·a_5_3 + c_2_23·a_1_12·a_5_9
  147. b_6_10·a_7_9 + b_4_52·a_5_6 + b_4_52·a_5_5 + b_4_53·a_1_1 + a_8_15·a_5_5
       + b_4_5·a_1_12·a_7_16 + c_2_2·b_4_52·a_3_3 + c_2_2·b_4_52·a_3_2
       + c_2_22·b_4_52·a_1_1 + c_2_23·a_1_12·a_5_9
  148. b_6_10·a_7_9 + b_4_52·a_5_6 + b_4_52·a_5_5 + b_4_53·a_1_1 + a_8_15·a_5_6
       + b_4_5·a_1_12·a_7_16 + c_2_2·b_4_52·a_3_3 + c_2_2·b_4_52·a_3_2
       + c_2_22·b_4_52·a_1_1 + c_2_23·a_1_12·a_5_9
  149. a_8_15·a_5_9 + a_6_9·a_7_15 + b_4_5·a_1_12·a_7_16
  150. a_6_9·a_7_15 + a_4_3·a_9_24 + c_2_23·a_1_12·a_5_9
  151. b_6_10·a_7_15 + b_6_10·a_7_9 + b_4_5·a_9_24 + b_4_52·a_5_9 + b_4_52·a_5_6 + a_6_9·a_7_15
       + c_2_2·b_4_5·a_7_15 + c_2_2·b_4_5·a_7_9 + c_2_2·b_4_52·a_3_3 + c_2_22·b_4_52·a_1_1
       + 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
  152. a_6_9·a_7_15 + a_4_3·a_9_25
  153. b_6_10·a_7_16 + b_4_5·a_9_25 + b_4_53·a_1_1 + a_6_9·a_7_15 + b_4_5·a_1_12·a_7_16
       + c_2_2·b_4_5·a_7_16 + 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_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_3 + c_2_24·b_4_5·a_1_1
  154. a_6_9·a_7_15 + c_2_2·a_1_12·a_9_25
  155. a_7_152 + b_4_52·a_1_1·a_5_6 + b_4_53·a_1_12 + c_8_20·a_3_32
       + c_2_2·b_4_5·a_3_3·a_5_5 + 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·b_4_5·a_1_12 + c_2_26·a_1_12
  156. a_7_15·a_7_16 + a_7_152 + a_7_9·a_7_15 + b_4_52·a_1_1·a_5_6 + b_4_53·a_1_12
       + c_2_2·b_4_5·a_1_1·a_7_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_23·a_1_1·a_7_16 + c_2_23·a_1_1·a_7_9 + c_2_23·b_4_5·a_1_1·a_3_2
       + c_2_26·a_1_12
  157. a_7_92 + b_4_52·a_1_1·a_5_6 + b_4_53·a_1_12 + b_4_5·c_8_20·a_1_12
       + 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_52·a_1_12
  158. a_7_162 + a_7_92 + c_8_20·a_1_1·a_5_6 + c_2_2·b_4_5·a_1_1·a_7_9
       + c_2_2·b_4_52·a_1_1·a_3_2 + c_2_22·b_4_52·a_1_12 + c_2_22·c_8_20·a_1_12
       + c_2_23·b_4_5·a_1_1·a_3_2
  159. b_6_10·a_8_15 + a_7_9·a_7_15 + b_4_52·a_3_32 + 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_52·a_1_12 + c_2_25·a_1_1·a_3_2
  160. a_6_9·a_8_15
  161. a_5_3·a_9_24
  162. a_7_162 + a_5_6·a_9_24 + 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_1_1·a_5_6 + c_2_2·b_4_5·a_1_1·a_7_9 + c_2_22·b_4_52·a_1_12
       + c_2_26·a_1_12
  163. a_5_5·a_9_24 + b_4_5·a_3_3·a_7_15 + b_4_52·a_3_32 + c_2_2·a_3_3·a_9_24
       + c_2_2·b_4_52·a_1_1·a_3_4 + c_2_22·a_3_3·a_7_15 + c_2_22·b_4_52·a_1_12
       + c_2_23·b_4_5·a_1_1·a_3_4 + c_2_24·a_3_32 + c_2_24·b_4_5·a_1_12
       + c_2_25·a_1_1·a_3_2 + c_2_26·a_1_12
  164. a_7_15·a_7_16 + a_7_152 + a_7_9·a_7_16 + a_7_92 + a_5_9·a_9_24 + b_4_5·a_3_3·a_7_15
       + b_4_52·a_3_32 + 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·b_4_5·a_3_3·a_5_5 + c_2_2·b_4_5·a_1_1·a_7_16 + c_2_2·b_4_5·a_1_1·a_7_9
       + 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_5·a_1_1·a_5_6
       + c_2_23·a_3_3·a_5_5 + 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_25·a_1_1·a_3_4 + c_2_25·a_1_1·a_3_2 + c_2_26·a_1_12
  165. a_5_3·a_9_25
  166. a_5_5·a_9_25 + a_5_5·a_9_24 + b_4_52·a_3_32 + b_4_52·a_1_1·a_5_9
       + c_2_2·b_4_5·a_1_1·a_7_9 + c_2_2·b_4_52·a_1_1·a_3_2
  167. a_7_162 + a_7_15·a_7_16 + a_7_152 + a_7_9·a_7_16 + a_7_92 + a_5_6·a_9_25
       + a_5_5·a_9_24 + b_4_5·a_3_3·a_7_15 + b_4_52·a_1_1·a_5_9 + 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_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_3_32 + c_2_23·a_1_1·a_7_16
       + c_2_23·a_1_1·a_7_9 + c_2_23·b_4_5·a_1_1·a_3_2 + c_2_24·b_4_5·a_1_12
       + c_2_25·a_1_1·a_3_4
  168. a_7_162 + a_7_9·a_7_15 + a_5_9·a_9_25 + b_4_5·a_3_3·a_7_15 + b_4_52·a_3_32
       + b_4_53·a_1_12 + 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_5·a_1_1·a_7_9 + 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_6 + c_2_23·a_1_1·a_7_9 + c_2_23·b_4_5·a_1_1·a_3_2
       + c_2_24·a_3_32 + c_2_24·a_1_1·a_5_9 + c_2_24·a_1_1·a_5_6
  169. a_7_9·a_7_15 + a_5_5·a_9_24 + b_4_5·a_1_1·a_9_25 + c_2_2·b_4_5·a_1_1·a_7_16
       + c_2_2·b_4_5·a_1_1·a_7_9 + 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_2 + c_2_22·b_4_5·a_3_32 + c_2_22·b_4_52·a_1_12
       + c_2_23·a_3_3·a_5_5 + 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_25·a_1_1·a_3_2
  170. a_7_162 + a_7_15·a_7_16 + a_7_152 + a_7_9·a_7_16 + a_7_9·a_7_15 + a_7_92
       + a_5_5·a_9_24 + b_4_5·a_3_3·a_7_15 + b_4_52·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·b_4_52·a_1_1·a_3_2 + c_2_22·a_1_1·a_9_25
       + c_2_22·b_4_5·a_3_32 + 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_9 + 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
  171. a_8_15·a_7_16 + a_8_15·a_7_15 + a_8_15·a_7_9 + c_8_20·a_1_12·a_5_9
       + c_2_24·a_1_12·a_5_9
  172. b_6_10·a_9_24 + b_4_52·a_7_15 + b_4_52·a_7_9 + b_4_53·a_3_4 + b_4_53·a_3_3
       + b_4_53·a_3_2 + a_8_15·a_7_15 + c_2_2·b_4_5·a_9_24 + c_2_2·b_4_52·a_5_5
       + c_2_2·b_4_53·a_1_1 + c_2_2·b_4_5·a_1_12·a_7_16 + c_2_22·b_4_5·a_7_15
       + c_2_22·b_4_5·a_7_9 + c_2_22·b_4_52·a_3_4 + c_2_23·b_4_5·a_5_5
       + c_2_24·b_4_5·a_3_3 + c_2_24·b_4_5·a_3_2 + c_2_24·a_1_12·a_5_9
       + c_2_25·b_4_5·a_1_1
  173. a_8_15·a_7_15 + a_6_9·a_9_24 + c_2_2·b_4_5·a_1_12·a_7_16 + c_2_24·a_1_12·a_5_9
  174. b_6_10·a_9_25 + b_4_52·a_7_16 + b_4_53·a_3_2 + a_8_15·a_7_16 + a_8_15·a_7_15
       + 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_6 + 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_2·b_4_5·a_1_12·a_7_16
       + c_2_22·b_4_5·a_7_16 + c_2_22·b_4_52·a_3_4 + c_2_22·b_4_52·a_3_3
       + c_2_23·b_4_52·a_1_1 + c_2_24·b_4_5·a_3_4 + c_2_25·b_4_5·a_1_1
  175. 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
  176. a_8_15·a_7_16 + a_8_15·a_7_15 + a_6_9·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
  177. a_8_15·a_7_16 + c_8_20·a_1_12·a_5_9 + c_2_22·a_1_12·a_9_25 + 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_15·a_9_24 + b_4_5·a_3_3·a_9_24 + b_4_52·a_3_3·a_5_5 + b_4_52·a_1_1·a_7_16
       + b_4_52·a_1_1·a_7_9 + c_8_20·a_3_3·a_5_5 + 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_3_32 + c_2_2·b_4_5·c_8_20·a_1_12
       + c_2_22·a_3_3·a_9_24 + 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_9 + c_2_22·b_4_52·a_1_1·a_3_2 + 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_3_3·a_5_5 + c_2_24·a_1_1·a_7_9
       + c_2_25·a_3_32 + c_2_25·a_1_1·a_5_6 + c_2_25·b_4_5·a_1_12
  180. a_7_15·a_9_24 + a_7_9·a_9_24 + b_4_52·a_1_1·a_7_16 + b_4_53·a_1_1·a_3_4
       + c_8_20·a_3_3·a_5_5 + 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_3_32 + c_2_2·b_4_52·a_1_1·a_5_9 + c_2_2·b_4_53·a_1_12
       + c_2_2·c_8_20·a_3_32 + c_2_2·b_4_5·c_8_20·a_1_12 + c_2_22·b_4_5·a_1_1·a_7_16
       + 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·b_4_5·a_1_1·a_5_9 + 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_9 + 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_1_1·a_5_6 + c_2_27·a_1_12
  181. a_7_15·a_9_25 + a_7_15·a_9_24 + b_4_52·a_3_3·a_5_5 + b_4_52·a_1_1·a_7_9
       + b_4_53·a_1_1·a_3_4 + b_4_53·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_3_32 + c_2_2·b_4_52·a_1_1·a_5_9 + 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_2·b_4_5·c_8_20·a_1_12
       + c_2_22·a_3_3·a_9_24 + c_2_22·b_4_5·a_1_1·a_7_16 + 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·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_23·b_4_5·a_1_1·a_5_6 + c_2_23·c_8_20·a_1_12
       + c_2_24·a_1_1·a_7_9 + c_2_25·a_3_32 + c_2_25·a_1_1·a_5_9 + c_2_25·a_1_1·a_5_6
       + c_2_25·b_4_5·a_1_12
  182. a_7_16·a_9_24 + b_4_52·a_3_3·a_5_5 + b_4_52·a_1_1·a_7_16 + b_4_52·a_1_1·a_7_9
       + b_4_53·a_1_1·a_3_2 + c_8_20·a_3_3·a_5_5 + 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_52·a_1_1·a_5_6
       + c_2_2·b_4_53·a_1_12 + c_2_2·c_8_20·a_3_32 + c_2_22·b_4_5·a_1_1·a_7_16
       + c_2_22·b_4_5·a_1_1·a_7_9 + c_2_22·b_4_52·a_1_1·a_3_2
       + 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·a_1_1·a_9_25 + c_2_23·b_4_5·a_1_1·a_5_9 + c_2_24·a_1_1·a_7_9
       + c_2_24·b_4_5·a_1_1·a_3_4 + c_2_25·a_1_1·a_5_9
  183. a_7_16·a_9_25 + a_7_16·a_9_24 + b_4_52·a_3_3·a_5_5 + 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_9 + 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_52·a_1_1·a_5_9
       + 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_6
       + c_2_2·b_4_5·c_8_20·a_1_12 + c_2_22·b_4_5·a_1_1·a_7_16
       + 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·a_3_3·a_7_15 + 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_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_1_1·a_5_9
       + 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
  184. a_7_15·a_9_25 + a_7_15·a_9_24 + a_7_9·a_9_25 + b_4_52·a_3_3·a_5_5 + b_4_52·a_1_1·a_7_9
       + b_4_53·a_1_1·a_3_4 + b_4_53·a_1_1·a_3_2 + 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_5·a_3_3·a_7_15 + 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_22·b_4_5·a_3_3·a_5_5 + c_2_22·b_4_5·a_1_1·a_7_9
       + c_2_22·b_4_52·a_1_1·a_3_4 + c_2_22·b_4_52·a_1_1·a_3_2
       + 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_24·a_1_1·a_7_9 + c_2_24·b_4_5·a_1_1·a_3_2 + 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
  185. a_8_15·a_9_24 + c_2_2·b_4_5·a_1_12·a_9_25 + c_2_23·a_1_12·a_9_25
       + c_2_25·a_1_12·a_5_9
  186. a_8_15·a_9_25 + a_8_15·a_9_24 + 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
  187. a_9_242 + b_4_53·a_3_32 + b_4_53·a_1_1·a_5_6 + 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_2_2·b_4_53·a_1_1·a_3_2
       + c_2_22·b_4_52·a_3_32 + c_2_22·c_8_20·a_3_32 + 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_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_25·b_4_5·a_1_1·a_3_2 + c_2_26·a_3_32
       + c_2_26·b_4_5·a_1_12
  188. a_9_24·a_9_25 + b_4_52·a_1_1·a_9_25 + b_4_53·a_3_32 + 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_9 + 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_1_1·a_7_16 + c_2_2·b_4_52·a_1_1·a_7_9
       + 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_5·a_3_3·a_7_15 + c_2_22·b_4_52·a_1_1·a_5_6 + c_2_22·c_8_20·a_3_32
       + c_2_22·c_8_20·a_1_1·a_5_9 + c_2_22·c_8_20·a_1_1·a_5_6 + c_2_23·a_3_3·a_9_24
       + 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·a_3_3·a_7_15
       + c_2_24·a_1_1·a_9_25 + c_2_24·b_4_5·a_3_32 + c_2_24·b_4_5·a_1_1·a_5_9
       + c_2_24·b_4_5·a_1_1·a_5_6 + c_2_24·c_8_20·a_1_12 + c_2_25·a_1_1·a_7_16
       + c_2_25·b_4_5·a_1_1·a_3_4 + c_2_26·a_1_1·a_5_9 + c_2_26·a_1_1·a_5_6
       + c_2_27·a_1_1·a_3_4 + c_2_28·a_1_12
  189. a_9_252 + b_4_53·a_1_1·a_5_6 + 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_1_1·a_7_9 + 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_1_1·a_5_6 + c_2_23·b_4_5·a_1_1·a_7_9
       + c_2_23·b_4_52·a_1_1·a_3_2 + 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·b_4_5·a_1_1·a_3_2
       + c_2_26·a_1_1·a_5_6 + c_2_28·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_3 → 0, an element of degree 5
  11. a_5_5 → 0, an element of degree 5
  12. a_5_6 → 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_9 → 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_24 → 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_22 + 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_3 → 0, an element of degree 5
  11. a_5_5 → 0, an element of degree 5
  12. a_5_6 → 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_9 → 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_24 → 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