David J. Green

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Cohomology of group number 835 of order 128

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

General information on the group

• The group has 3 minimal generators and exponent 8.
• It is non-abelian.
• It has p-Rank 3.
• Its center has rank 1.
• 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 1.
• The depth coincides with the Duflot bound.
• The Poincaré series is

  t7  −  2·t6  +  t5  −  t4  +  t2  −  t  −  1

  (t  +  1) · (t  −  1)3 · (t2  +  1) · (t4  +  1)

• The a-invariants are -∞,-4,-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 20 minimal generators of maximal degree 10:

1. a_1_0, a nilpotent element of degree 1
2. a_1_1, a nilpotent element of degree 1
3. a_1_2, a nilpotent element of degree 1
4. b_2_3, an element of degree 2
5. a_3_3, a nilpotent element of degree 3
6. a_3_4, a nilpotent element of degree 3
7. a_4_3, a nilpotent element of degree 4
8. b_4_5, an element of degree 4
9. b_4_6, an element of degree 4
10. b_5_7, an element of degree 5
11. a_6_3, a nilpotent element of degree 6
12. a_6_5, a nilpotent element of degree 6
13. a_6_6, a nilpotent element of degree 6
14. b_6_10, an element of degree 6
15. b_7_10, an element of degree 7
16. b_7_12, an element of degree 7
17. b_8_14, an element of degree 8
18. c_8_15, a Duflot regular element of degree 8
19. b_9_18, an element of degree 9
20. b_10_22, an element of degree 10

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring relations

There are 150 minimal relations of maximal degree 20:

1. a_1_1·a_1_2
2. a_1_1² + a_1_0·a_1_2
3. a_1_2² + a_1_1² + a_1_0·a_1_1 + a_1_0²
4. a_1_0²·a_1_1
5. b_2_3·a_1_0·a_1_2
6. a_1_1·a_3_3 + b_2_3·a_1_0²
7. a_1_2·a_3_3 + b_2_3·a_1_0²
8. a_1_1·a_3_4 + b_2_3·a_1_0²
9. a_1_0·a_3_4 + a_1_0·a_3_3 + b_2_3·a_1_0·a_1_1
10. a_1_2·a_3_4 + a_1_0·a_3_3 + b_2_3·a_1_0·a_1_1
11. a_4_3·a_1_1
12. a_4_3·a_1_0
13. b_2_3·a_3_3 + b_2_3²·a_1_2 + b_2_3²·a_1_0 + a_4_3·a_1_2
14. b_4_5·a_1_1 + b_2_3²·a_1_1 + b_2_3²·a_1_0
15. b_4_5·a_1_0
16. b_4_5·a_1_2 + b_2_3·a_3_4 + b_2_3²·a_1_0
17. b_4_6·a_1_1 + b_2_3²·a_1_0
18. a_3_3·a_3_4 + a_3_3²
19. a_3_4²
20. a_3_3² + b_4_6·a_1_0²
21. a_1_1·b_5_7
22. a_4_3·a_3_3 + b_2_3·a_4_3·a_1_2
23. b_4_5·a_3_3 + b_2_3·b_4_6·a_1_0 + b_2_3²·a_3_4 + a_4_3·a_3_4
24. b_4_5·a_3_4 + b_4_5·a_3_3 + b_2_3·b_4_6·a_1_2 + b_2_3²·a_3_4 + b_2_3³·a_1_2
       + b_2_3³·a_1_0 + a_4_3·a_3_4 + a_4_3·a_3_3
25. b_4_5·a_3_3 + b_2_3²·a_3_4 + b_2_3³·a_1_0 + a_1_0²·b_5_7 + a_4_3·a_3_4
26. a_6_3·a_1_1
27. a_6_3·a_1_0
28. a_6_3·a_1_2 + a_4_3·a_3_4 + a_4_3·a_3_3
29. b_4_5·a_3_3 + b_2_3²·a_3_4 + b_2_3³·a_1_0 + a_6_5·a_1_1 + a_4_3·a_3_3
30. b_4_5·a_3_3 + b_2_3²·a_3_4 + b_2_3³·a_1_0 + a_6_5·a_1_0 + a_4_3·a_3_3
31. a_6_5·a_1_2 + a_4_3·a_3_3
32. b_4_5·a_3_3 + b_2_3²·a_3_4 + b_2_3³·a_1_0 + a_6_6·a_1_1
33. b_4_5·a_3_3 + b_2_3²·a_3_4 + b_2_3³·a_1_0 + a_6_6·a_1_0 + a_4_3·a_3_4
34. a_6_6·a_1_2 + a_4_3·a_3_4
35. b_6_10·a_1_1 + b_2_3³·a_1_0
36. b_6_10·a_1_0 + b_4_6·a_3_3 + b_4_5·a_3_4 + b_4_5·a_3_3 + b_2_3²·a_3_4 + b_2_3³·a_1_2
       + b_2_3³·a_1_0
37. b_6_10·a_1_2 + b_4_6·a_3_4 + b_4_6·a_3_3 + b_4_5·a_3_3 + b_2_3²·a_3_4 + b_2_3³·a_1_0
       + a_4_3·a_3_3
38. a_4_3²
39. b_4_5² + b_2_3²·b_4_6 + b_2_3⁴ + b_2_3²·a_4_3
40. b_2_3·a_1_0·b_5_7
41. a_4_3·b_4_5 + b_2_3·a_6_3 + b_2_3²·a_4_3
42. b_4_5·b_4_6 + b_4_5² + b_2_3·b_6_10 + b_2_3⁴ + a_3_3·b_5_7 + a_4_3·b_4_6 + a_4_3·b_4_5
       + b_4_6·a_1_0·a_3_3
43. a_1_1·b_7_10
44. a_1_0·b_7_10 + b_4_6·a_1_0·a_3_3
45. a_3_4·b_5_7 + a_3_3·b_5_7 + a_1_2·b_7_10 + a_4_3·b_4_6 + a_4_3·b_4_5 + b_2_3²·a_4_3
       + b_4_6·a_1_0·a_3_3
46. a_1_1·b_7_12
47. a_3_3·b_5_7 + a_1_0·b_7_12 + b_2_3·a_1_2·b_5_7 + b_4_6·a_1_0·a_3_3
48. a_3_4·b_5_7 + a_3_3·b_5_7 + a_1_2·b_7_12
49. a_6_3·a_3_3 + b_2_3·a_4_3·a_3_4 + b_2_3²·a_4_3·a_1_2
50. a_6_3·a_3_4 + a_4_3·b_4_6·a_1_2 + b_2_3·a_4_3·a_3_4 + b_2_3²·a_4_3·a_1_2
51. a_6_5·a_3_3 + b_2_3·a_4_3·a_3_4
52. a_6_5·a_3_4 + b_2_3²·a_4_3·a_1_2
53. a_6_6·a_3_3 + a_4_3·b_4_6·a_1_2 + b_2_3²·a_4_3·a_1_2
54. a_6_6·a_3_4 + b_2_3·a_4_3·a_3_4
55. b_6_10·a_3_3 + b_4_6²·a_1_0 + b_2_3·b_4_6·a_3_4 + b_2_3²·b_4_6·a_1_2 + b_2_3⁴·a_1_0
       + b_2_3·a_4_3·a_3_4 + b_2_3²·a_4_3·a_1_2
56. b_6_10·a_3_4 + b_4_6²·a_1_2 + b_4_6²·a_1_0 + b_2_3·b_4_6·a_3_4 + b_2_3²·b_4_6·a_1_2
       + b_2_3⁴·a_1_0 + a_4_3·b_4_6·a_1_2
57. b_4_5·b_5_7 + b_2_3·b_7_12 + b_2_3²·b_5_7 + a_4_3·b_5_7 + b_2_3³·a_3_4 + b_2_3⁴·a_1_2
       + b_2_3⁴·a_1_1 + a_4_3·b_4_6·a_1_2 + b_2_3²·a_4_3·a_1_2
58. b_8_14·a_1_1 + b_2_3·a_4_3·a_3_4 + b_2_3²·a_4_3·a_1_2
59. b_8_14·a_1_0 + b_4_6²·a_1_0 + b_2_3⁴·a_1_0 + a_4_3·b_4_6·a_1_2
60. b_8_14·a_1_2 + b_4_6²·a_1_2 + a_4_3·b_5_7 + b_2_3·b_4_6·a_3_4 + b_2_3²·b_4_6·a_1_2
       + b_2_3⁴·a_1_0
61. a_4_3·a_6_3
62. b_4_5·a_6_3 + b_2_3·a_4_3·b_4_6 + b_2_3²·a_6_3
63. a_4_3·a_6_5
64. b_4_5·a_6_5 + b_2_3²·a_1_2·b_5_7 + b_2_3²·a_6_3 + b_2_3³·a_4_3
65. a_4_3·a_6_6
66. b_4_6·a_1_0·b_5_7 + b_4_6·a_6_6 + b_4_6·a_6_5 + b_4_6·a_6_3 + b_2_3²·a_1_2·b_5_7
       + b_2_3²·a_6_5 + b_2_3³·a_4_3
67. b_4_5·a_6_6 + b_2_3·a_4_3·b_4_6 + b_2_3²·a_1_2·b_5_7 + b_2_3²·a_6_6 + b_2_3²·a_6_3
68. b_4_6·a_6_3 + a_4_3·b_6_10 + b_4_6²·a_1_0²
69. b_4_5·b_6_10 + b_2_3·b_4_6² + b_2_3²·b_6_10 + b_4_6·a_1_0·b_5_7 + b_4_6·a_6_5
       + b_4_6·a_6_3 + b_2_3·a_4_3·b_4_6 + b_2_3²·a_1_2·b_5_7 + b_2_3²·a_6_5 + b_2_3³·a_4_3
       + b_4_6²·a_1_0²
70. a_3_3·b_7_10 + b_4_6·a_6_5 + b_2_3²·a_1_2·b_5_7 + b_2_3²·a_6_5 + b_2_3²·a_6_3
       + b_2_3³·a_4_3
71. b_4_6·a_6_5 + b_2_3·a_1_2·b_7_10 + b_2_3²·a_1_2·b_5_7 + b_2_3²·a_6_5 + b_2_3²·a_6_3
       + b_2_3³·a_4_3 + b_4_6²·a_1_0²
72. a_3_4·b_7_10 + b_4_6·a_1_2·b_5_7 + b_4_6·a_6_5 + b_4_6·a_6_3 + b_2_3·a_4_3·b_4_6
       + b_2_3²·a_1_2·b_5_7 + b_2_3²·a_6_5 + b_2_3²·a_6_3 + b_2_3³·a_4_3
73. a_3_3·b_7_12 + b_4_6·a_1_0·b_5_7 + b_4_6·a_6_5 + b_2_3·a_4_3·b_4_6 + b_2_3²·a_1_2·b_5_7
       + b_2_3²·a_6_5 + b_2_3³·a_4_3
74. a_3_4·b_7_12 + b_4_6·a_1_2·b_5_7 + b_4_6·a_1_0·b_5_7 + b_4_6·a_6_5 + b_2_3·a_4_3·b_4_6
       + b_2_3²·a_1_2·b_5_7 + b_2_3²·a_6_5 + b_2_3³·a_4_3
75. b_5_7² + b_2_3·b_4_6² + b_2_3³·b_4_6 + b_4_6·a_1_2·b_5_7 + b_4_6·a_6_5
       + b_2_3·a_4_3·b_4_6 + b_2_3²·a_1_2·b_5_7 + b_2_3²·a_6_5 + b_4_6²·a_1_0²
       + c_8_15·a_1_0·a_1_2 + c_8_15·a_1_0·a_1_1 + c_8_15·a_1_0²
76. a_1_1·b_9_18
77. b_5_7² + b_2_3·b_4_6² + b_2_3³·b_4_6 + a_1_0·b_9_18 + b_4_6·a_1_2·b_5_7 + b_4_6·a_6_5
       + b_2_3·a_4_3·b_4_6 + b_2_3²·a_1_2·b_5_7 + b_2_3²·a_6_5 + c_8_15·a_1_0·a_1_1
       + c_8_15·a_1_0²
78. b_5_7² + b_2_3·b_4_6² + b_2_3³·b_4_6 + a_1_2·b_9_18 + b_4_6·a_6_5 + b_4_6·a_6_3
       + b_2_3·a_4_3·b_4_6 + b_2_3²·a_6_5 + b_2_3²·a_6_3
79. a_6_5·b_5_7 + b_2_3·a_4_3·b_5_7 + b_2_3²·b_4_6·a_3_4 + b_2_3⁵·a_1_0
       + a_4_3·b_4_6·a_3_4 + b_2_3³·a_4_3·a_1_2
80. a_6_6·b_5_7 + a_6_3·b_5_7 + b_2_3·a_4_3·b_5_7 + b_2_3²·b_4_6·a_3_4
       + b_2_3³·b_4_6·a_1_2 + b_2_3⁴·a_3_4 + b_2_3⁵·a_1_2 + b_2_3³·a_4_3·a_1_2
81. a_6_3·b_5_7 + a_4_3·b_7_10 + b_2_3·b_4_6²·a_1_2 + b_2_3³·b_4_6·a_1_2
       + a_4_3·b_4_6·a_3_4 + b_2_3³·a_4_3·a_1_2
82. a_6_3·b_5_7 + a_4_3·b_7_12 + a_4_3·b_4_6·a_3_4 + b_2_3²·a_4_3·a_3_4
       + b_2_3³·a_4_3·a_1_2
83. b_6_10·b_5_7 + b_4_6·b_7_12 + a_6_3·b_5_7 + b_4_6²·a_3_3 + b_2_3²·b_4_6·a_3_4
       + b_2_3²·a_4_3·a_3_4
84. b_4_5·b_7_12 + b_2_3·b_4_6·b_5_7 + b_2_3²·b_7_12 + a_6_3·b_5_7 + b_2_3·a_4_3·b_5_7
       + b_2_3³·b_4_6·a_1_2 + a_4_3·b_4_6·a_3_4 + b_2_3³·a_4_3·a_1_2
85. b_8_14·a_3_3 + b_4_6²·a_3_3 + b_2_3·a_4_3·b_5_7 + b_2_3²·b_4_6·a_3_4
       + b_2_3³·b_4_6·a_1_2 + a_4_3·b_4_6·a_3_4
86. b_8_14·a_3_4 + a_6_3·b_5_7 + b_4_6²·a_3_4 + b_2_3·b_4_6²·a_1_2 + b_2_3·a_4_3·b_5_7
       + b_2_3²·b_4_6·a_3_4 + b_2_3³·b_4_6·a_1_2 + a_4_3·b_4_6·a_3_4
87. b_4_5·b_7_10 + b_2_3·b_9_18 + b_2_3²·b_7_12 + b_2_3³·b_5_7 + a_6_3·b_5_7
       + b_2_3·a_4_3·b_5_7 + b_2_3²·b_4_6·a_3_4 + b_2_3³·b_4_6·a_1_2 + b_2_3⁵·a_1_0
       + b_2_3³·a_4_3·a_1_2 + b_2_3·c_8_15·a_1_2
88. b_10_22·a_1_1 + b_2_3⁵·a_1_0 + b_2_3²·a_4_3·a_3_4 + b_2_3·c_8_15·a_1_1
89. b_10_22·a_1_0 + b_4_6²·a_3_3 + b_2_3·b_4_6²·a_1_2 + b_2_3²·a_4_3·a_3_4
       + b_2_3³·a_4_3·a_1_2 + b_2_3·c_8_15·a_1_0
90. b_10_22·a_1_2 + a_6_3·b_5_7 + b_4_6²·a_3_4 + b_4_6²·a_3_3 + b_2_3²·b_4_6·a_3_4
       + b_2_3³·b_4_6·a_1_2 + b_2_3⁴·a_3_4 + b_2_3⁵·a_1_2 + a_4_3·b_4_6·a_3_4
       + b_2_3·c_8_15·a_1_2
91. a_6_3²
92. a_6_3·a_6_5
93. a_6_5²
94. a_6_3·a_6_6
95. a_6_6²
96. a_6_5·a_6_6
97. b_6_10² + b_4_6³ + a_4_3·b_4_6² + b_4_6²·a_1_0·a_3_3
98. a_6_3·b_6_10 + a_4_3·b_4_6² + b_4_6²·a_1_0·a_3_3
99. a_6_5·b_6_10 + b_2_3·b_4_6·a_1_2·b_5_7 + b_2_3·a_4_3·b_6_10 + b_2_3²·a_1_2·b_7_10
       + b_2_3²·a_4_3·b_4_6 + b_2_3³·a_1_2·b_5_7 + b_2_3³·a_6_5 + b_2_3³·a_6_3
       + b_2_3⁴·a_4_3 + b_4_6²·a_1_0·a_3_3
100. a_6_6·b_6_10 + b_4_6·a_1_0·b_7_12 + a_4_3·b_4_6² + b_2_3·b_4_6·a_1_2·b_5_7
        + b_2_3·a_4_3·b_6_10 + b_4_6²·a_1_0·a_3_3
101. b_5_7·b_7_12 + b_2_3·b_4_6·b_6_10 + b_2_3³·b_6_10 + a_6_6·b_6_10 + a_6_5·b_6_10
        + b_4_6·a_1_2·b_7_10 + b_2_3³·a_6_5 + b_2_3⁴·a_4_3 + c_8_15·a_1_0·a_3_3
        + b_2_3·c_8_15·a_1_0·a_1_1 + b_2_3·c_8_15·a_1_0²
102. a_6_5·b_6_10 + a_4_3·b_8_14 + a_4_3·b_4_6² + b_2_3³·a_1_2·b_5_7 + b_2_3³·a_6_5
        + b_2_3⁴·a_4_3 + b_4_6²·a_1_0·a_3_3
103. b_5_7·b_7_12 + b_5_7·b_7_10 + b_4_6·b_8_14 + b_4_6³ + b_4_5·b_8_14 + b_2_3²·b_8_14
        + b_2_3²·b_4_6² + a_6_5·b_6_10 + b_4_6·a_1_2·b_7_10 + a_4_3·b_4_6²
        + b_2_3·b_4_6·a_1_2·b_5_7 + b_2_3²·a_4_3·b_4_6 + b_2_3³·a_1_2·b_5_7 + b_2_3³·a_6_5
        + b_2_3⁴·a_4_3 + b_4_6²·a_1_0·a_3_3
104. b_5_7·b_7_12 + b_2_3·b_4_6·b_6_10 + b_2_3³·b_6_10 + a_3_3·b_9_18 + a_6_6·b_6_10
        + a_6_5·b_6_10 + b_4_6·a_1_2·b_7_10 + b_2_3·b_4_6·a_1_2·b_5_7 + b_2_3·a_4_3·b_6_10
        + b_2_3³·a_1_2·b_5_7 + b_2_3³·a_6_5 + b_2_3³·a_6_3 + b_2_3⁴·a_4_3
        + b_4_6²·a_1_0·a_3_3 + c_8_15·a_1_0·a_3_3 + b_2_3·c_8_15·a_1_0·a_1_1
105. a_3_4·b_9_18 + a_6_5·b_6_10 + b_4_6·a_1_2·b_7_10 + b_2_3·a_4_3·b_6_10
        + b_2_3²·a_4_3·b_4_6 + b_2_3³·a_6_5 + b_2_3³·a_6_3 + b_2_3⁴·a_4_3
        + b_4_6²·a_1_0·a_3_3 + c_8_15·a_1_0·a_3_3 + b_2_3·c_8_15·a_1_0·a_1_1
106. b_5_7·b_7_12 + b_5_7·b_7_10 + b_4_6·b_8_14 + b_4_6³ + b_2_3·b_10_22 + b_2_3³·b_6_10
        + b_2_3⁴·b_4_5 + b_2_3⁶ + a_6_6·b_6_10 + b_4_6·a_1_2·b_7_10 + a_4_3·b_4_6²
        + b_2_3·b_4_6·a_1_2·b_5_7 + b_2_3·a_4_3·b_6_10 + b_2_3³·a_1_2·b_5_7 + b_2_3³·a_6_6
        + b_2_3³·a_6_5 + b_4_6²·a_1_0·a_3_3 + b_2_3²·c_8_15 + b_2_3·c_8_15·a_1_0·a_1_1
107. a_6_3·b_7_10 + a_4_3·b_4_6·b_5_7 + b_2_3·b_4_6²·a_3_4 + b_2_3²·b_4_6²·a_1_2
        + b_2_3³·b_4_6·a_3_4 + b_2_3⁴·b_4_6·a_1_2 + a_4_3·b_4_6²·a_1_2
108. a_6_6·b_7_10 + a_4_3·b_4_6·b_5_7 + b_2_3·b_4_6²·a_3_4 + b_2_3²·b_4_6²·a_1_2
        + b_2_3²·a_4_3·b_5_7 + b_2_3³·b_4_6·a_3_4 + b_2_3⁴·b_4_6·a_1_2 + b_2_3³·a_4_3·a_3_4
        + b_2_3⁴·a_4_3·a_1_2
109. a_6_5·b_7_10 + b_2_3³·b_4_6·a_3_4 + b_2_3⁶·a_1_0 + b_2_3⁴·a_4_3·a_1_2
110. b_6_10·b_7_12 + b_4_6²·b_5_7 + b_4_6³·a_1_0 + b_2_3·b_4_6²·a_3_4
        + b_2_3³·b_4_6·a_3_4 + b_2_3⁴·b_4_6·a_1_2 + b_2_3⁶·a_1_0
111. a_6_3·b_7_12 + a_4_3·b_4_6·b_5_7 + a_4_3·b_4_6²·a_1_2
112. a_6_6·b_7_12 + a_4_3·b_4_6·b_5_7 + b_2_3·a_4_3·b_7_10 + b_2_3³·a_4_3·a_3_4
113. a_6_5·b_7_12 + b_2_3·a_4_3·b_7_10 + b_2_3³·b_4_6·a_3_4 + b_2_3⁶·a_1_0
        + a_4_3·b_4_6²·a_1_2 + b_2_3⁴·a_4_3·a_1_2
114. b_8_14·b_5_7 + b_4_6²·b_5_7 + b_2_3·b_4_6·b_7_10 + b_2_3²·b_9_18 + b_2_3²·b_4_6·b_5_7
        + b_2_3³·b_7_12 + b_2_3³·b_7_10 + b_2_3⁴·b_5_7 + b_2_3·b_4_6²·a_3_4
        + b_2_3·a_4_3·b_7_10 + b_2_3²·b_4_6²·a_1_2 + b_2_3³·b_4_6·a_3_4
        + a_4_3·b_4_6²·a_1_2 + b_2_3⁴·a_4_3·a_1_2 + b_2_3²·c_8_15·a_1_2 + a_4_3·c_8_15·a_1_2
115. a_4_3·b_9_18 + a_4_3·b_4_6·b_5_7 + b_2_3·b_4_6²·a_3_4 + b_2_3²·a_4_3·b_5_7
        + b_2_3³·b_4_6·a_3_4 + b_2_3³·a_4_3·a_3_4 + a_4_3·c_8_15·a_1_2
116. b_6_10·b_7_10 + b_4_6·b_9_18 + b_2_3·b_4_6·b_7_12 + b_2_3·b_4_6·b_7_10
        + b_2_3²·b_4_6·b_5_7 + b_4_6³·a_1_2 + a_4_3·b_4_6·b_5_7 + b_2_3·b_4_6²·a_3_4
        + b_2_3·a_4_3·b_7_10 + b_2_3²·b_4_6²·a_1_2 + b_2_3⁴·b_4_6·a_1_2 + b_2_3⁶·a_1_0
        + b_2_3⁴·a_4_3·a_1_2 + b_4_6·c_8_15·a_1_2
117. b_4_5·b_9_18 + b_2_3·b_4_6·b_7_10 + b_2_3²·b_4_6·b_5_7 + b_2_3³·b_7_10 + b_2_3⁴·b_5_7
        + a_4_3·b_4_6·b_5_7 + b_2_3²·a_4_3·b_5_7 + b_2_3³·b_4_6·a_3_4 + b_2_3⁴·b_4_6·a_1_2
        + b_2_3⁵·a_3_4 + b_2_3⁶·a_1_2 + b_2_3⁶·a_1_1 + b_2_3⁶·a_1_0 + b_2_3³·a_4_3·a_3_4
        + b_2_3⁴·a_4_3·a_1_2 + b_2_3·c_8_15·a_3_4 + b_2_3²·c_8_15·a_1_0
118. b_10_22·a_3_3 + b_4_6³·a_1_0 + b_2_3·b_4_6²·a_3_4 + b_2_3·a_4_3·b_7_10
        + b_2_3³·b_4_6·a_3_4 + b_2_3⁵·a_3_4 + b_2_3⁶·a_1_2 + b_2_3⁶·a_1_0
        + a_4_3·b_4_6²·a_1_2 + b_2_3³·a_4_3·a_3_4 + b_2_3²·c_8_15·a_1_2
        + b_2_3²·c_8_15·a_1_0 + a_4_3·c_8_15·a_1_2
119. b_10_22·a_3_4 + b_4_6³·a_1_2 + b_4_6³·a_1_0 + a_4_3·b_4_6·b_5_7 + b_2_3·b_4_6²·a_3_4
        + b_2_3·a_4_3·b_7_10 + b_2_3²·b_4_6²·a_1_2 + b_2_3³·b_4_6·a_3_4
        + b_2_3⁴·b_4_6·a_1_2 + b_2_3⁵·a_3_4 + b_2_3⁶·a_1_2 + b_2_3⁶·a_1_0
        + b_2_3·c_8_15·a_3_4
120. b_7_12² + b_7_10² + b_2_3·b_4_6³ + b_2_3²·b_4_6·b_6_10 + b_2_3³·b_4_6²
        + b_2_3⁴·b_6_10 + b_4_6²·a_1_2·b_5_7 + b_2_3²·a_4_3·b_6_10 + b_2_3³·a_4_3·b_4_6
        + b_2_3⁴·a_1_2·b_5_7 + b_4_6³·a_1_0²
121. b_7_10² + b_2_3²·b_4_6·b_6_10 + b_2_3⁴·b_6_10 + b_2_3·b_4_6·a_1_2·b_7_10
        + b_2_3³·a_4_3·b_4_6 + b_2_3⁴·a_1_2·b_5_7 + b_4_6·c_8_15·a_1_0²
122. a_6_3·b_8_14 + a_4_3·b_4_6·b_6_10 + b_2_3·b_4_6·a_1_2·b_7_10
        + b_2_3²·b_4_6·a_1_2·b_5_7 + b_2_3²·a_4_3·b_6_10 + b_4_6³·a_1_0²
123. b_7_10·b_7_12 + b_7_10² + b_6_10·b_8_14 + b_4_6²·b_6_10 + b_2_3·b_4_6·b_8_14
        + b_2_3·b_4_6³ + b_2_3³·b_4_6² + b_2_3⁴·b_6_10 + a_4_3·b_4_6·b_6_10
        + b_2_3·b_4_6·a_1_2·b_7_10 + b_2_3·a_4_3·b_4_6² + b_2_3²·b_4_6·a_1_2·b_5_7
        + b_2_3³·a_1_2·b_7_10 + b_2_3⁴·a_1_2·b_5_7 + b_2_3⁴·a_6_3 + b_4_6³·a_1_0²
124. a_6_6·b_8_14 + b_4_6²·a_6_6 + b_2_3·b_4_6·a_1_2·b_7_10 + b_2_3²·b_4_6·a_1_2·b_5_7
        + b_2_3²·a_4_3·b_6_10 + b_2_3³·a_1_2·b_7_10 + b_2_3³·a_4_3·b_4_6
125. a_6_5·b_8_14 + b_2_3·b_4_6·a_1_2·b_7_10 + b_2_3²·b_4_6·a_1_2·b_5_7
        + b_2_3²·a_4_3·b_6_10 + b_2_3³·a_1_2·b_7_10 + b_2_3⁴·a_6_3 + b_4_6³·a_1_0²
126. b_7_10² + b_5_7·b_9_18 + b_6_10·b_8_14 + b_4_6²·b_6_10 + b_2_3²·b_10_22
        + b_2_3⁵·b_4_6 + b_2_3⁵·b_4_5 + b_2_3⁷ + b_4_6²·a_1_2·b_5_7 + a_4_3·b_4_6·b_6_10
        + b_2_3·b_4_6·a_1_2·b_7_10 + b_2_3·a_4_3·b_4_6² + b_2_3³·a_4_3·b_4_6 + b_2_3⁴·a_6_6
        + b_2_3⁴·a_6_5 + b_2_3⁵·a_4_3 + b_2_3³·c_8_15 + c_8_15·a_1_2·b_5_7
127. a_4_3·b_10_22 + a_4_3·b_4_6·b_6_10 + b_2_3·b_4_6·a_1_2·b_7_10 + b_2_3·a_4_3·b_4_6²
        + b_2_3²·b_4_6·a_1_2·b_5_7 + b_2_3⁴·a_6_3 + b_2_3·a_4_3·c_8_15
128. b_6_10·b_8_14 + b_4_6·b_10_22 + b_2_3·b_4_6³ + b_2_3²·b_4_6·b_6_10 + b_2_3⁴·b_6_10
        + b_4_6²·a_6_6 + b_2_3·b_4_6·a_1_2·b_7_10 + b_2_3·a_4_3·b_4_6² + b_2_3⁴·a_6_5
        + b_2_3⁴·a_6_3 + b_2_3⁵·a_4_3 + b_2_3·b_4_6·c_8_15
129. b_7_10·b_7_12 + b_5_7·b_9_18 + b_4_5·b_10_22 + b_2_3·b_4_6³ + b_2_3²·b_4_6·b_6_10
        + b_2_3⁴·b_6_10 + b_2_3⁵·b_4_5 + b_2_3⁷ + b_4_6²·a_1_2·b_5_7 + b_4_6²·a_6_6
        + b_2_3·b_4_6·a_1_2·b_7_10 + b_2_3·a_4_3·b_4_6² + b_2_3²·a_4_3·b_6_10
        + b_2_3³·a_4_3·b_4_6 + b_2_3⁴·a_1_2·b_5_7 + b_2_3⁴·a_6_6 + b_2_3⁵·a_4_3
        + b_2_3·b_4_5·c_8_15 + c_8_15·a_1_2·b_5_7
130. b_8_14·b_7_10 + b_4_6²·b_7_10 + b_2_3²·b_4_6·b_7_12 + b_2_3²·b_4_6·b_7_10
        + b_2_3³·b_4_6·b_5_7 + a_4_3·b_4_6·b_7_10 + b_2_3·a_4_3·b_4_6·b_5_7
        + b_2_3²·b_4_6²·a_3_4 + b_2_3²·a_4_3·b_7_10 + b_2_3³·a_4_3·b_5_7
        + b_2_3⁴·b_4_6·a_3_4 + b_2_3⁵·b_4_6·a_1_2 + a_4_3·c_8_15·a_3_4
        + b_2_3·a_4_3·c_8_15·a_1_2
131. b_8_14·b_7_12 + b_6_10·b_9_18 + b_4_6²·b_7_12 + b_4_6²·b_7_10 + b_2_3·b_4_6²·b_5_7
        + b_2_3²·b_4_6·b_7_10 + b_4_6³·a_3_4 + b_4_6³·a_3_3 + b_2_3·b_4_6³·a_1_2
        + b_2_3²·a_4_3·b_7_10 + b_2_3⁵·b_4_6·a_1_2 + a_4_3·b_4_6²·a_3_4
        + b_2_3⁵·a_4_3·a_1_2 + b_4_6·c_8_15·a_3_4 + b_4_6·c_8_15·a_3_3 + a_6_5·c_8_15·a_1_0
        + a_4_3·c_8_15·a_3_4 + b_2_3·a_4_3·c_8_15·a_1_2
132. a_6_3·b_9_18 + a_4_3·b_4_6·b_7_10 + b_2_3²·b_4_6²·a_3_4 + b_2_3²·a_4_3·b_7_10
        + b_2_3⁴·b_4_6·a_3_4 + a_4_3·b_4_6²·a_3_4 + b_2_3⁴·a_4_3·a_3_4 + a_4_3·c_8_15·a_3_4
        + b_2_3·a_4_3·c_8_15·a_1_2
133. b_8_14·b_7_12 + b_4_6²·b_7_12 + b_2_3·b_4_6·b_9_18 + b_2_3³·b_4_6·b_5_7
        + b_2_3²·b_4_6²·a_3_4 + b_2_3²·a_4_3·b_7_10 + b_2_3³·b_4_6²·a_1_2 + b_2_3⁷·a_1_0
        + a_4_3·b_4_6²·a_3_4 + b_2_3⁴·a_4_3·a_3_4 + b_2_3⁵·a_4_3·a_1_2
        + b_2_3·b_4_6·c_8_15·a_1_2 + a_4_3·c_8_15·a_3_4 + b_2_3·a_4_3·c_8_15·a_1_2
134. a_6_6·b_9_18 + a_4_3·b_4_6·b_7_10 + b_2_3²·b_4_6²·a_3_4 + b_2_3²·a_4_3·b_7_10
        + b_2_3³·b_4_6²·a_1_2 + b_2_3⁶·a_3_4 + b_2_3⁷·a_1_2 + a_4_3·c_8_15·a_3_4
135. a_6_5·b_9_18 + b_2_3²·a_4_3·b_7_10 + b_2_3³·b_4_6²·a_1_2 + b_2_3³·a_4_3·b_5_7
        + b_2_3⁵·b_4_6·a_1_2 + b_2_3⁵·a_4_3·a_1_2 + b_2_3·a_4_3·c_8_15·a_1_2
136. b_10_22·b_5_7 + b_8_14·b_7_12 + b_2_3·b_4_6²·b_5_7 + b_2_3²·b_4_6·b_7_12
        + b_2_3⁴·b_7_12 + b_4_6³·a_3_3 + b_2_3·a_4_3·b_4_6·b_5_7 + b_2_3²·b_4_6²·a_3_4
        + b_2_3²·a_4_3·b_7_10 + b_2_3³·a_4_3·b_5_7 + b_2_3⁴·b_4_6·a_3_4
        + b_2_3⁵·b_4_6·a_1_2 + b_2_3⁷·a_1_1 + a_4_3·b_4_6²·a_3_4 + b_2_3·c_8_15·b_5_7
137. b_8_14² + b_4_6⁴ + b_2_3³·b_4_6·b_6_10 + b_2_3⁴·b_4_6² + b_2_3⁵·b_6_10
        + b_2_3²·a_4_3·b_4_6² + b_2_3³·b_4_6·a_1_2·b_5_7 + b_2_3³·a_4_3·b_6_10
        + b_2_3⁴·a_4_3·b_4_6 + b_2_3⁵·a_1_2·b_5_7
138. b_7_12·b_9_18 + b_4_6²·b_8_14 + b_4_6⁴ + b_2_3²·b_4_6·b_8_14 + b_2_3²·b_4_6³
        + b_2_3³·b_4_6·b_6_10 + b_2_3⁵·b_6_10 + b_4_6²·a_1_2·b_7_10
        + b_2_3·b_4_6²·a_1_2·b_5_7 + b_2_3·a_4_3·b_4_6·b_6_10 + b_2_3²·b_4_6·a_1_2·b_7_10
        + b_2_3²·a_4_3·b_4_6² + b_2_3³·a_4_3·b_6_10 + b_2_3⁴·a_4_3·b_4_6
        + b_2_3⁵·a_1_2·b_5_7 + c_8_15·a_1_2·b_7_10 + a_4_3·b_4_6·c_8_15 + b_2_3·a_6_3·c_8_15
139. b_6_10·b_10_22 + b_4_6²·b_8_14 + b_2_3·b_4_6²·b_6_10 + b_2_3²·b_4_6³
        + b_2_3⁴·b_4_6² + b_4_6²·a_1_0·b_7_12 + b_2_3·b_4_6²·a_1_2·b_5_7
        + b_2_3²·b_4_6·a_1_2·b_7_10 + b_2_3²·a_4_3·b_4_6² + b_2_3³·a_4_3·b_6_10
        + b_2_3⁵·a_1_2·b_5_7 + b_2_3⁵·a_6_5 + b_2_3⁶·a_4_3 + b_2_3·b_6_10·c_8_15
140. a_6_3·b_10_22 + a_4_3·b_4_6³ + b_2_3·b_4_6²·a_1_2·b_5_7
        + b_2_3²·b_4_6·a_1_2·b_7_10 + b_2_3³·a_4_3·b_6_10 + b_2_3⁴·a_4_3·b_4_6
        + b_4_6³·a_1_0·a_3_3 + b_2_3·a_6_3·c_8_15
141. b_7_10·b_9_18 + b_2_3·b_4_6·b_10_22 + b_2_3·b_4_6²·b_6_10 + b_2_3³·b_10_22
        + b_2_3⁶·b_4_5 + b_2_3⁸ + b_4_6²·a_1_2·b_7_10 + b_2_3·b_4_6²·a_1_2·b_5_7
        + b_2_3·a_4_3·b_4_6·b_6_10 + b_2_3²·b_4_6·a_1_2·b_7_10 + b_2_3⁴·a_4_3·b_4_6
        + b_2_3⁵·a_1_2·b_5_7 + b_2_3⁵·a_6_6 + b_2_3⁵·a_6_3 + b_2_3⁶·a_4_3
        + b_2_3²·b_4_6·c_8_15 + b_2_3⁴·c_8_15 + c_8_15·a_1_2·b_7_10
        + b_4_6·c_8_15·a_1_0·a_3_3
142. a_6_6·b_10_22 + b_4_6²·a_1_0·b_7_12 + a_4_3·b_4_6³ + b_2_3·a_4_3·b_4_6·b_6_10
        + b_2_3³·a_4_3·b_6_10 + b_2_3⁵·a_1_2·b_5_7 + b_2_3⁵·a_6_3 + b_4_6³·a_1_0·a_3_3
        + b_2_3·a_6_6·c_8_15
143. a_6_5·b_10_22 + b_2_3·b_4_6²·a_1_2·b_5_7 + b_2_3·a_4_3·b_4_6·b_6_10
        + b_2_3²·a_4_3·b_4_6² + b_2_3³·b_4_6·a_1_2·b_5_7 + b_2_3⁵·a_1_2·b_5_7
        + b_2_3⁵·a_6_5 + b_2_3⁵·a_6_3 + b_2_3⁶·a_4_3 + b_4_6³·a_1_0·a_3_3
        + b_2_3·a_6_5·c_8_15
144. b_8_14·b_9_18 + b_4_6²·b_9_18 + b_2_3²·b_4_6²·b_5_7 + b_2_3³·b_4_6·b_7_12
        + b_2_3³·b_4_6·b_7_10 + b_2_3⁴·b_9_18 + b_2_3⁵·b_7_12 + b_2_3⁵·b_7_10 + b_2_3⁶·b_5_7
        + b_2_3²·b_4_6³·a_1_2 + b_2_3²·a_4_3·b_4_6·b_5_7 + b_2_3³·b_4_6²·a_3_4
        + b_2_3⁴·a_4_3·b_5_7 + b_2_3⁵·b_4_6·a_3_4 + b_2_3⁶·b_4_6·a_1_2 + a_4_3·b_4_6³·a_1_2
        + a_4_3·c_8_15·b_5_7 + b_2_3·b_4_6·c_8_15·a_3_4 + b_2_3²·b_4_6·c_8_15·a_1_2
        + b_2_3⁴·c_8_15·a_1_2 + b_2_3⁴·c_8_15·a_1_0 + a_4_3·b_4_6·c_8_15·a_1_2
        + b_2_3²·a_4_3·c_8_15·a_1_2
145. b_10_22·b_7_12 + b_4_6³·b_5_7 + b_2_3·b_4_6²·b_7_12 + b_2_3·b_4_6²·b_7_10
        + b_2_3²·b_4_6·b_9_18 + b_2_3³·b_4_6·b_7_12 + b_2_3³·b_4_6·b_7_10 + b_4_6⁴·a_1_0
        + a_4_3·b_4_6²·b_5_7 + b_2_3·a_4_3·b_4_6·b_7_10 + b_2_3³·a_4_3·b_7_10
        + b_2_3⁴·a_4_3·b_5_7 + b_2_3⁶·b_4_6·a_1_2 + b_2_3⁸·a_1_0 + b_2_3⁵·a_4_3·a_3_4
        + b_2_3⁶·a_4_3·a_1_2 + b_2_3·c_8_15·b_7_12 + b_2_3²·b_4_6·c_8_15·a_1_2
        + a_4_3·b_4_6·c_8_15·a_1_2
146. b_10_22·b_7_10 + b_8_14·b_9_18 + b_2_3·b_4_6²·b_7_12 + b_2_3²·b_4_6²·b_5_7
        + b_2_3³·b_4_6·b_7_10 + b_4_6⁴·a_1_2 + a_4_3·b_4_6²·b_5_7 + b_2_3·b_4_6³·a_3_4
        + b_2_3·a_4_3·b_4_6·b_7_10 + b_2_3²·a_4_3·b_4_6·b_5_7 + b_2_3³·b_4_6²·a_3_4
        + b_2_3⁴·a_4_3·b_5_7 + b_2_3⁵·b_4_6·a_3_4 + b_2_3⁸·a_1_0 + b_2_3⁵·a_4_3·a_3_4
        + b_2_3⁶·a_4_3·a_1_2 + b_2_3·c_8_15·b_7_10 + b_4_6²·c_8_15·a_1_2 + a_4_3·c_8_15·b_5_7
        + b_2_3·b_4_6·c_8_15·a_3_4 + b_2_3²·b_4_6·c_8_15·a_1_2 + b_2_3⁴·c_8_15·a_1_0
        + b_2_3²·a_4_3·c_8_15·a_1_2
147. b_9_18² + b_2_3²·b_4_6²·b_6_10 + b_2_3³·b_4_6³ + b_2_3⁶·b_6_10 + b_2_3⁷·b_4_6
        + b_2_3·b_4_6²·a_1_2·b_7_10 + b_2_3²·b_4_6²·a_1_2·b_5_7
        + b_2_3²·a_4_3·b_4_6·b_6_10 + b_2_3³·a_4_3·b_4_6² + b_2_3⁵·a_1_2·b_7_10
        + b_2_3⁶·a_1_2·b_5_7 + b_2_3⁶·a_6_3 + b_2_3⁷·a_4_3 + b_4_6⁴·a_1_0²
        + b_4_6²·c_8_15·a_1_0² + c_8_15²·a_1_0·a_1_2 + c_8_15²·a_1_0·a_1_1
        + c_8_15²·a_1_0²
148. b_8_14·b_10_22 + b_4_6³·b_6_10 + b_2_3·b_4_6²·b_8_14 + b_2_3²·b_4_6·b_10_22
        + b_2_3⁴·b_10_22 + b_2_3⁷·b_4_5 + b_2_3⁹ + b_4_6³·a_6_6 + b_2_3·a_4_3·b_4_6³
        + b_2_3³·b_4_6·a_1_2·b_7_10 + b_2_3³·a_4_3·b_4_6² + b_2_3⁴·b_4_6·a_1_2·b_5_7
        + b_2_3⁴·a_4_3·b_6_10 + b_2_3⁵·a_1_2·b_7_10 + b_2_3⁶·a_1_2·b_5_7 + b_2_3⁶·a_6_6
        + b_2_3⁶·a_6_3 + b_2_3⁷·a_4_3 + b_2_3·b_8_14·c_8_15 + b_2_3³·b_4_6·c_8_15
        + b_2_3⁵·c_8_15
149. b_10_22·b_9_18 + b_4_6³·b_7_10 + b_2_3·b_4_6³·b_5_7 + b_2_3²·b_4_6²·b_7_12
        + b_2_3³·b_4_6²·b_5_7 + b_2_3⁴·b_4_6·b_7_12 + b_2_3⁵·b_9_18 + b_2_3⁵·b_4_6·b_5_7
        + b_2_3⁶·b_7_10 + b_2_3⁷·b_5_7 + b_4_6⁴·a_3_4 + b_4_6⁴·a_3_3 + a_4_3·b_4_6²·b_7_10
        + b_2_3·b_4_6⁴·a_1_2 + b_2_3·a_4_3·b_4_6²·b_5_7 + b_2_3²·b_4_6³·a_3_4
        + b_2_3³·b_4_6³·a_1_2 + b_2_3⁵·b_4_6²·a_1_2 + b_2_3⁹·a_1_1 + a_4_3·b_4_6³·a_3_4
        + b_2_3⁶·a_4_3·a_3_4 + b_2_3⁷·a_4_3·a_1_2 + b_2_3·c_8_15·b_9_18
        + b_4_6²·c_8_15·a_3_4 + b_4_6²·c_8_15·a_3_3 + a_4_3·c_8_15·b_7_10
        + b_2_3·b_4_6²·c_8_15·a_1_2 + b_2_3²·b_4_6·c_8_15·a_3_4 + b_2_3⁴·c_8_15·a_3_4
        + a_4_3·b_4_6·c_8_15·a_3_4 + b_2_3³·a_4_3·c_8_15·a_1_2
150. b_10_22² + b_4_6⁵ + b_2_3²·b_4_6⁴ + b_2_3³·b_4_6²·b_6_10 + b_2_3⁵·b_4_6·b_6_10
        + b_2_3⁸·b_4_6 + a_4_3·b_4_6⁴ + b_2_3²·a_4_3·b_4_6³ + b_2_3³·b_4_6²·a_1_2·b_5_7
        + b_2_3⁴·a_4_3·b_4_6² + b_2_3⁵·b_4_6·a_1_2·b_5_7 + b_2_3⁵·a_4_3·b_6_10
        + b_2_3⁸·a_4_3 + b_4_6⁴·a_1_0·a_3_3 + b_2_3²·c_8_15²

About the group

Ring generators

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Data used for Benson′s test

• Benson′s completion test succeeded in degree 20.
• The completion test was perfect: It applied in the last degree in which a generator or relation was found.
• The following is a filter regular homogeneous system of parameters:
  1. c_8_15, a Duflot regular element of degree 8
  2. b_4_6 + b_4_5, an element of degree 4
  3. b_2_3, an element of degree 2
• The Raw Filter Degree Type of that HSOP is [-1, 4, 9, 11].
• The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].

About the group

Ring generators

Ring relations

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Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 1

1. a_1_0 → 0, an element of degree 1
2. a_1_1 → 0, an element of degree 1
3. a_1_2 → 0, an element of degree 1
4. b_2_3 → 0, an element of degree 2
5. a_3_3 → 0, an element of degree 3
6. a_3_4 → 0, an element of degree 3
7. a_4_3 → 0, an element of degree 4
8. b_4_5 → 0, an element of degree 4
9. b_4_6 → 0, an element of degree 4
10. b_5_7 → 0, an element of degree 5
11. a_6_3 → 0, an element of degree 6
12. a_6_5 → 0, an element of degree 6
13. a_6_6 → 0, an element of degree 6
14. b_6_10 → 0, an element of degree 6
15. b_7_10 → 0, an element of degree 7
16. b_7_12 → 0, an element of degree 7
17. b_8_14 → 0, an element of degree 8
18. c_8_15 → c_1_0⁸, an element of degree 8
19. b_9_18 → 0, an element of degree 9
20. b_10_22 → 0, an element of degree 10

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_1_2 → 0, an element of degree 1
4. b_2_3 → c_1_2², an element of degree 2
5. a_3_3 → 0, an element of degree 3
6. a_3_4 → 0, an element of degree 3
7. a_4_3 → 0, an element of degree 4
8. b_4_5 → c_1_2⁴ + c_1_1²·c_1_2², an element of degree 4
9. b_4_6 → c_1_1⁴, an element of degree 4
10. b_5_7 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2, an element of degree 5
11. a_6_3 → 0, an element of degree 6
12. a_6_5 → 0, an element of degree 6
13. a_6_6 → 0, an element of degree 6
14. b_6_10 → c_1_1⁶, an element of degree 6
15. b_7_10 → c_1_1³·c_1_2⁴ + c_1_1⁵·c_1_2², an element of degree 7
16. b_7_12 → c_1_1⁴·c_1_2³ + c_1_1⁶·c_1_2, an element of degree 7
17. b_8_14 → c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_2⁴ + c_1_1⁵·c_1_2³ + c_1_1⁸, an element of degree 8
18. c_8_15 → c_1_2⁸ + c_1_1²·c_1_2⁶ + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2²
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1²·c_1_2² + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8
19. b_9_18 → c_1_1²·c_1_2⁷ + c_1_1³·c_1_2⁶ + c_1_1⁶·c_1_2³ + c_1_1⁷·c_1_2², an element of degree 9
20. b_10_22 → c_1_2¹⁰ + c_1_1⁵·c_1_2⁵ + c_1_1⁷·c_1_2³ + c_1_1⁸·c_1_2² + c_1_1¹⁰
       + c_1_0²·c_1_1²·c_1_2⁶ + c_1_0²·c_1_1⁴·c_1_2⁴ + c_1_0⁴·c_1_2⁶
       + c_1_0⁴·c_1_1²·c_1_2⁴ + c_1_0⁴·c_1_1⁴·c_1_2² + c_1_0⁸·c_1_2², an element of degree 10

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128