David J. Green

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Singular

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Cohomology of group number 144 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 1.
• 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 exceeds the Duflot bound, which is 1.
• The Poincaré series is

  t9  −  t8  −  t6  −  t4  −  t2  −  1

  (t  +  1) · (t  −  1)3 · (t2  +  1)2 · (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 20 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. b_2_1, an element of degree 2
4. b_2_2, an element of degree 2
5. b_3_2, an element of degree 3
6. b_3_3, an element of degree 3
7. b_4_1, an element of degree 4
8. b_4_2, an element of degree 4
9. b_4_5, an element of degree 4
10. a_5_3, a nilpotent element of degree 5
11. b_5_6, an element of degree 5
12. b_5_7, an element of degree 5
13. b_6_8, an element of degree 6
14. b_6_9, an element of degree 6
15. b_7_10, an element of degree 7
16. b_7_11, an element of degree 7
17. b_8_13, an element of degree 8
18. b_8_14, an element of degree 8
19. c_8_15, a Duflot regular element of degree 8
20. b_9_18, an 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 152 minimal relations of maximal degree 18:

1. a_1_0²
2. a_1_0·a_1_1
3. a_1_1³
4. b_2_2·a_1_1 + b_2_1·a_1_1
5. b_2_2·a_1_0 + b_2_1·a_1_1
6. b_2_2² + b_2_1·b_2_2
7. a_1_1·b_3_2
8. a_1_0·b_3_2
9. a_1_0·b_3_3
10. b_2_2·b_3_2 + b_2_1·b_3_3 + b_2_1²·a_1_1
11. b_2_2·b_3_3 + b_2_2·b_3_2 + b_2_1²·a_1_1
12. a_1_1²·b_3_3
13. b_4_1·a_1_1
14. b_4_1·a_1_0
15. b_4_2·a_1_1
16. b_4_2·a_1_0
17. b_4_5·a_1_0
18. b_2_2·b_4_1 + b_2_1·b_4_2 + b_2_1·b_4_1
19. b_2_2·b_4_2
20. b_3_2² + b_2_1·b_4_5
21. b_3_2·b_3_3 + b_2_2·b_4_5
22. a_1_1·a_5_3
23. a_1_0·a_5_3
24. a_1_1·b_5_6
25. a_1_0·b_5_6
26. b_3_3² + b_3_2·b_3_3 + a_1_1·b_5_7
27. a_1_0·b_5_7
28. b_4_2·b_3_2 + b_4_1·b_3_3 + b_4_1·b_3_2
29. b_4_2·b_3_3
30. b_4_1·b_3_2 + b_2_1·b_5_6 + b_2_1²·b_3_3 + b_2_1³·a_1_1
31. b_4_1·b_3_3 + b_2_2·b_5_6 + b_2_1²·b_3_3 + b_2_1³·a_1_1
32. b_4_1·b_3_3 + b_4_1·b_3_2 + b_2_1·b_5_7 + b_2_1²·b_3_3 + b_2_2·a_5_3
33. b_2_2·b_5_7 + b_2_1²·b_3_3 + b_2_2·a_5_3
34. a_1_1²·b_5_7
35. b_6_8·a_1_1 + b_2_2·a_5_3
36. b_6_8·a_1_0 + b_2_1·a_5_3
37. b_6_9·a_1_1 + b_2_2·a_5_3 + b_2_1³·a_1_1
38. b_6_9·a_1_0 + b_2_2·a_5_3 + b_2_1³·a_1_1
39. b_4_2² + b_4_1·b_4_2
40. b_4_1² + b_2_1²·b_4_5
41. b_4_1·b_4_2 + b_4_1² + b_2_1·b_2_2·b_4_5
42. b_3_2·a_5_3
43. b_3_3·a_5_3
44. b_3_2·b_5_6 + b_4_1·b_4_5 + b_4_1·b_4_2 + b_4_1² + b_4_5·a_1_1·b_3_3
45. b_3_3·b_5_6 + b_4_2·b_4_5 + b_4_1·b_4_5 + b_4_1·b_4_2 + b_4_1²
46. b_3_2·b_5_7 + b_4_2·b_4_5 + b_4_1·b_4_2 + b_4_1² + b_4_5·a_1_1·b_3_3
47. b_4_1² + b_2_2·b_6_8 + b_2_1·b_6_9 + b_2_1²·b_4_2 + b_2_1²·b_4_1 + b_2_1³·b_2_2
48. b_4_1·b_4_2 + b_4_1² + b_2_2·b_6_9 + b_2_2·b_6_8 + b_2_1²·b_4_2 + b_2_1²·b_4_1
       + b_2_1³·b_2_2
49. a_1_1·b_7_10
50. a_1_0·b_7_10
51. b_3_3·b_5_7 + b_4_1·b_4_2 + b_4_1² + a_1_1·b_7_11
52. a_1_0·b_7_11
53. b_4_1·a_5_3
54. b_4_2·a_5_3
55. b_4_2·b_5_6 + b_2_1·b_4_5·b_3_3 + b_2_1·b_4_5·b_3_2
56. b_4_1·b_5_6 + b_2_1·b_4_5·b_3_2 + b_2_1²·b_5_7 + b_2_1²·b_5_6 + b_2_1·b_2_2·a_5_3
       + b_2_1⁴·a_1_1
57. b_4_1·b_5_7 + b_4_1·b_5_6 + b_2_1·b_4_5·b_3_3 + b_4_5·a_5_3
58. b_4_2·b_5_7 + b_2_1·b_4_5·b_3_3 + b_2_1·b_4_5·b_3_2 + b_4_5·a_5_3
59. b_6_9·b_3_2 + b_6_8·b_3_3 + b_4_1·b_5_6 + b_2_1³·b_3_3 + b_2_1·b_2_2·a_5_3
       + b_2_1⁴·a_1_1
60. b_6_9·b_3_3 + b_6_8·b_3_3 + b_4_1·b_5_6 + b_2_1·b_4_5·b_3_3 + b_2_1·b_4_5·b_3_2
       + b_2_1³·b_3_3
61. b_6_8·b_3_2 + b_4_1·b_5_6 + b_2_1·b_7_10 + b_2_1·b_4_5·b_3_3 + b_2_1³·b_3_3
       + b_2_1·b_2_2·a_5_3 + b_2_1²·a_5_3 + b_2_1⁴·a_1_1
62. b_6_8·b_3_3 + b_4_1·b_5_6 + b_2_2·b_7_10 + b_2_1·b_4_5·b_3_2 + b_2_1³·b_3_3
       + b_2_1·b_2_2·a_5_3 + b_2_1⁴·a_1_1
63. b_6_8·b_3_3 + b_4_1·b_5_6 + b_2_1·b_7_11 + b_2_1·b_4_5·b_3_3 + b_2_1·b_4_5·b_3_2
       + b_2_1·b_2_2·a_5_3
64. b_6_8·b_3_3 + b_4_1·b_5_6 + b_2_2·b_7_11 + b_2_1·b_4_5·b_3_3 + b_2_1·b_4_5·b_3_2
       + b_2_1·b_2_2·a_5_3
65. b_4_5·a_5_3 + a_1_1²·b_7_11
66. b_8_13·a_1_1 + b_4_5·a_5_3 + b_2_1·b_2_2·a_5_3
67. b_8_13·a_1_0 + b_2_1·b_2_2·a_5_3
68. b_8_14·a_1_1 + b_4_5²·a_1_1
69. b_8_14·a_1_0
70. a_5_3²
71. a_5_3·b_5_6
72. b_5_6² + b_2_1·b_4_5² + b_2_1²·b_2_2·b_4_5
73. a_5_3·b_5_7
74. b_5_6·b_5_7 + b_2_2·b_4_5² + b_2_1·b_4_5² + b_2_1·b_4_2·b_4_5 + b_2_1·b_4_1·b_4_5
       + b_2_1²·b_2_2·b_4_5
75. b_4_2·b_6_8 + b_4_1·b_6_9 + b_4_1·b_6_8 + b_2_1·b_4_1·b_4_5 + b_2_1²·b_2_2·b_4_5
       + b_2_1³·b_4_2 + b_2_1³·b_4_1
76. b_4_2·b_6_9 + b_2_1·b_4_2·b_4_5
77. b_3_2·b_7_10 + b_4_5·b_6_8 + b_2_2·b_4_5² + b_2_1·b_4_5² + b_2_1·b_4_2·b_4_5
       + b_2_1·b_4_1·b_4_5 + b_2_1²·b_2_2·b_4_5 + b_4_5²·a_1_1²
78. b_3_3·b_7_10 + b_4_5·b_6_9 + b_2_1·b_4_5²
79. b_3_2·b_7_11 + b_4_5·b_6_9 + b_2_2·b_4_5² + b_2_1·b_4_5² + b_2_1²·b_2_2·b_4_5
80. b_5_7² + b_3_3·b_7_11 + b_4_5·b_6_9
81. b_5_7² + b_2_2·b_4_5² + b_2_1·b_4_5² + b_2_1²·b_2_2·b_4_5 + b_4_5·a_1_1·b_5_7
       + c_8_15·a_1_1²
82. b_4_2·b_6_8 + b_4_1·b_6_8 + b_2_1·b_8_13 + b_2_1·b_4_1·b_4_5 + b_2_1²·b_6_9
       + b_2_1³·b_4_5 + b_2_1³·b_4_1 + b_2_1⁴·b_2_2
83. b_4_2·b_6_8 + b_4_1·b_6_8 + b_2_2·b_8_13 + b_2_1·b_4_2·b_4_5 + b_2_1·b_4_1·b_4_5
       + b_2_1²·b_6_9 + b_2_1³·b_4_5 + b_2_1³·b_4_2 + b_2_1³·b_4_1 + b_2_1⁴·b_2_2
84. b_4_1·b_6_8 + b_2_1·b_8_14 + b_2_1·b_4_5² + b_2_1·b_4_2·b_4_5 + b_2_1³·b_4_5
       + b_2_1³·b_4_1
85. b_4_2·b_6_8 + b_4_1·b_6_8 + b_2_2·b_8_14 + b_2_2·b_4_5² + b_2_1²·b_2_2·b_4_5
       + b_2_1³·b_4_2 + b_2_1³·b_4_1
86. a_1_1·b_9_18 + b_4_5²·a_1_1²
87. a_1_0·b_9_18
88. b_6_9·b_5_7 + b_6_9·b_5_6 + b_6_8·b_5_7 + b_6_8·b_5_6 + b_2_1·b_4_5·b_5_7
       + b_2_1·b_4_5·b_5_6 + b_2_1²·b_4_5·b_3_3 + b_2_1³·b_5_7 + b_2_1³·b_5_6
89. b_6_9·b_5_6 + b_6_8·b_5_7 + b_4_1·b_7_10 + b_2_1·b_4_5·b_5_7 + b_2_1·b_4_5·b_5_6
       + b_2_1²·b_4_5·b_3_3 + b_2_1³·b_5_7 + b_2_1³·b_5_6 + b_2_1⁴·b_3_3 + b_6_9·a_5_3
       + b_2_1²·b_2_2·a_5_3
90. b_6_9·b_5_6 + b_6_8·b_5_6 + b_4_2·b_7_10 + b_2_1·b_4_5·b_5_7 + b_2_1·b_4_5·b_5_6
       + b_2_1⁴·b_3_3 + b_2_1⁵·a_1_1
91. b_6_9·b_5_6 + b_6_8·b_5_7 + b_6_8·b_5_6 + b_2_1·b_4_5·b_5_6 + b_2_1²·b_7_11
       + b_2_1³·b_5_7 + b_2_1³·b_5_6 + b_2_1⁴·b_3_3 + b_6_9·a_5_3 + b_2_1²·b_2_2·a_5_3
92. b_6_8·b_5_7 + b_6_8·b_5_6 + b_4_1·b_7_11 + b_2_1·b_4_5·b_5_7 + b_2_1·b_4_5·b_5_6
       + b_2_1²·b_4_5·b_3_3 + b_6_9·a_5_3
93. b_4_2·b_7_11
94. b_6_9·a_5_3 + b_2_1·c_8_15·a_1_1
95. b_6_8·a_5_3 + b_2_1²·b_2_2·a_5_3 + b_2_1·c_8_15·a_1_0
96. b_8_13·b_3_2 + b_6_9·b_5_6 + b_2_1³·b_5_7 + b_2_1²·b_2_2·a_5_3 + b_2_1⁵·a_1_1
97. b_8_13·b_3_3 + b_6_9·b_5_6 + b_2_1·b_4_5·b_5_7 + b_2_1²·b_4_5·b_3_3 + b_2_1⁴·b_3_3
       + b_2_1²·b_2_2·a_5_3 + b_2_1⁵·a_1_1
98. b_8_14·b_3_2 + b_6_9·b_5_6 + b_6_8·b_5_7 + b_4_5²·b_3_2 + b_2_1·b_4_5·b_5_7
       + b_2_1·b_4_5·b_5_6 + b_2_1²·b_4_5·b_3_2 + b_2_1³·b_5_6 + b_6_9·a_5_3
99. b_8_14·b_3_3 + b_6_8·b_5_7 + b_6_8·b_5_6 + b_4_5²·b_3_3 + b_2_1²·b_4_5·b_3_3
       + b_2_1³·b_5_7 + b_2_1³·b_5_6 + b_6_9·a_5_3 + b_2_1²·b_2_2·a_5_3 + b_2_1⁵·a_1_1
100. b_6_8·b_5_6 + b_2_1·b_9_18 + b_2_1·b_4_5·b_5_7 + b_2_1·b_4_5·b_5_6 + b_2_1²·b_7_10
        + b_2_1²·b_4_5·b_3_3 + b_2_1²·b_4_5·b_3_2 + b_2_1³·b_5_6 + b_6_8·a_5_3 + b_2_1³·a_5_3
101. b_6_8·b_5_7 + b_6_8·b_5_6 + b_2_2·b_9_18 + b_2_1·b_4_5·b_5_7 + b_2_1·b_4_5·b_5_6
102. a_5_3·b_7_10
103. a_5_3·b_7_11
104. b_5_7·b_7_10 + b_5_6·b_7_11 + b_5_6·b_7_10 + b_4_2·b_4_5² + b_4_1·b_4_5²
        + b_2_1·b_4_5·b_6_9 + b_2_1·b_2_2·b_4_5² + b_2_1²·b_4_5² + b_2_1²·b_4_2·b_4_5
        + b_2_1²·b_4_1·b_4_5 + b_2_1³·b_2_2·b_4_5
105. b_6_9² + b_6_8·b_6_9 + b_6_8² + b_2_1·b_4_5·b_6_8 + b_2_1·b_2_2·b_4_5²
        + b_2_1²·b_4_2·b_4_5 + b_2_1²·b_4_1·b_4_5 + b_2_1³·b_2_2·b_4_5 + b_2_1⁴·b_4_2
        + b_2_1⁵·b_2_2 + b_2_1²·c_8_15
106. b_6_8·b_6_9 + b_2_1·b_4_5·b_6_8 + b_2_1²·b_4_2·b_4_5 + b_2_1²·b_4_1·b_4_5
        + b_2_1·b_2_2·c_8_15
107. b_5_7·b_7_11 + b_2_1·b_4_5·b_6_9 + b_2_1·b_2_2·b_4_5² + b_2_1²·b_4_5²
        + b_2_1³·b_2_2·b_4_5 + b_4_5·a_1_1·b_7_11 + c_8_15·a_1_1·b_3_3
108. b_6_9² + b_6_8·b_6_9 + b_2_1·b_4_5·b_6_8 + b_2_1²·b_8_13 + b_2_1²·b_4_5²
        + b_2_1²·b_4_1·b_4_5 + b_2_1³·b_2_2·b_4_5 + b_2_1⁴·b_4_2 + b_2_1⁵·b_2_2
109. b_6_9² + b_6_8·b_6_9 + b_4_1·b_8_13 + b_2_1·b_4_5·b_6_9 + b_2_1·b_4_5·b_6_8
        + b_2_1²·b_4_5² + b_2_1²·b_4_2·b_4_5 + b_2_1²·b_4_1·b_4_5 + b_2_1³·b_6_9
        + b_2_1³·b_2_2·b_4_5 + b_2_1⁴·b_4_2 + b_2_1⁴·b_4_1
110. b_4_2·b_8_13 + b_2_1·b_2_2·b_4_5² + b_2_1²·b_4_5² + b_2_1³·b_2_2·b_4_5
        + b_2_1⁴·b_4_5
111. b_5_7·b_7_10 + b_5_6·b_7_10 + b_4_5·b_8_13 + b_4_1·b_4_5² + b_2_1·b_4_5·b_6_9
        + b_2_1·b_2_2·b_4_5² + b_2_1²·b_4_5² + b_2_1²·b_4_2·b_4_5 + b_2_1³·b_2_2·b_4_5
        + b_4_5·a_1_1·b_7_11
112. b_4_1·b_8_14 + b_4_1·b_4_5² + b_2_1·b_4_5·b_6_8 + b_2_1·b_2_2·b_4_5²
        + b_2_1²·b_4_5² + b_2_1²·b_4_1·b_4_5 + b_2_1⁴·b_4_5
113. b_4_2·b_8_14 + b_4_2·b_4_5² + b_2_1·b_4_5·b_6_9 + b_2_1·b_4_5·b_6_8
        + b_2_1·b_2_2·b_4_5² + b_2_1²·b_4_1·b_4_5 + b_2_1⁴·b_4_5
114. b_5_6·b_7_10 + b_4_5·b_8_14 + b_4_5³ + b_2_1·b_4_5·b_6_9 + b_2_1·b_2_2·b_4_5²
        + b_2_1²·b_4_2·b_4_5 + b_4_5²·a_1_1·b_3_3
115. b_5_6·b_7_10 + b_3_2·b_9_18 + b_4_1·b_4_5² + b_2_1·b_4_5·b_6_8 + b_2_1·b_2_2·b_4_5²
        + b_2_1²·b_4_2·b_4_5 + b_2_1³·b_2_2·b_4_5 + b_4_5²·a_1_1·b_3_3
116. b_5_7·b_7_10 + b_5_6·b_7_10 + b_3_3·b_9_18 + b_4_2·b_4_5² + b_4_1·b_4_5²
        + b_2_1·b_2_2·b_4_5² + b_2_1²·b_4_2·b_4_5 + b_2_1²·b_4_1·b_4_5
        + b_4_5²·a_1_1·b_3_3
117. b_6_9·b_7_11 + b_6_9·b_7_10 + b_2_1·b_4_5·b_7_10 + b_2_1·b_4_5²·b_3_3 + b_2_1³·b_7_11
        + b_2_1⁵·b_3_3 + b_2_1⁶·a_1_1
118. b_6_8·b_7_10 + b_2_1·b_4_5·b_7_11 + b_2_1·b_4_5·b_7_10 + b_2_1·b_4_5²·b_3_3
        + b_2_1²·b_4_5·b_5_7 + b_2_1²·b_4_5·b_5_6 + b_2_1³·b_4_5·b_3_3 + b_2_1⁴·b_5_7
        + b_2_1⁵·b_3_3 + b_2_1³·b_2_2·a_5_3 + b_2_1·c_8_15·b_3_2 + b_2_1²·c_8_15·a_1_1
        + b_2_1²·c_8_15·a_1_0
119. b_6_9·b_7_11 + b_6_9·b_7_10 + b_6_8·b_7_11 + b_2_1·b_4_5·b_7_11 + b_2_1·b_4_5·b_7_10
        + b_2_1³·b_4_5·b_3_3 + b_2_1⁴·b_5_7 + b_2_1⁴·b_5_6 + b_2_1⁵·b_3_3
        + b_2_1³·b_2_2·a_5_3 + b_4_5·a_1_1²·b_7_11 + b_2_1·c_8_15·b_3_3
        + b_2_1²·c_8_15·a_1_1
120. b_8_13·a_5_3 + b_2_1³·b_2_2·a_5_3 + b_2_1²·c_8_15·a_1_1
121. b_8_13·b_5_6 + b_6_9·b_7_11 + b_6_9·b_7_10 + b_2_1·b_4_5·b_7_11 + b_2_1·b_4_5·b_7_10
        + b_2_1·b_4_5²·b_3_2 + b_2_1³·b_4_5·b_3_2 + b_2_1⁴·b_5_7 + b_2_1⁴·b_5_6
        + b_2_1⁵·b_3_3 + b_2_1³·b_2_2·a_5_3
122. b_8_13·b_5_7 + b_6_9·b_7_11 + b_6_8·b_7_11 + b_2_1·b_4_5·b_7_11 + b_2_1·b_4_5²·b_3_3
        + b_2_1·b_4_5²·b_3_2 + b_2_1³·b_4_5·b_3_3 + b_2_1³·b_4_5·b_3_2 + b_2_1⁴·b_5_7
        + b_2_1⁴·b_5_6 + b_2_1³·b_2_2·a_5_3 + b_2_1⁶·a_1_1 + b_4_5·a_1_1²·b_7_11
        + b_2_1²·c_8_15·a_1_1
123. b_8_14·a_5_3 + b_4_5·a_1_1²·b_7_11
124. b_8_14·b_5_6 + b_6_9·b_7_10 + b_6_8·b_7_11 + b_4_5²·b_5_6 + b_2_1·b_4_5·b_7_11
        + b_2_1·b_4_5²·b_3_3 + b_2_1²·b_4_5·b_5_6 + b_2_1³·b_4_5·b_3_2 + b_2_1⁴·b_5_7
        + b_2_1⁴·b_5_6 + b_2_1⁵·b_3_3 + b_2_1³·b_2_2·a_5_3 + b_4_5·a_1_1²·b_7_11
125. b_8_14·b_5_7 + b_6_9·b_7_10 + b_6_8·b_7_11 + b_4_5²·b_5_7 + b_2_1²·b_4_5·b_5_6
        + b_2_1³·b_4_5·b_3_3 + b_2_1³·b_4_5·b_3_2 + b_2_1⁴·b_5_7 + b_2_1⁴·b_5_6
        + b_2_1⁵·b_3_3 + b_2_1³·b_2_2·a_5_3
126. b_6_9·b_7_10 + b_6_8·b_7_11 + b_2_1·b_4_5·b_7_11 + b_2_1·b_4_5·b_7_10
        + b_2_1·b_4_5²·b_3_3 + b_2_1·b_2_2·b_9_18 + b_2_1³·b_4_5·b_3_3 + b_2_1⁵·b_3_3
        + b_2_1⁶·a_1_1 + b_4_5·a_1_1²·b_7_11 + b_2_1²·c_8_15·a_1_1
127. b_6_9·b_7_11 + b_6_8·b_7_11 + b_4_1·b_9_18 + b_2_1·b_4_5·b_7_11 + b_2_1·b_4_5·b_7_10
        + b_2_1·b_4_5²·b_3_2 + b_2_1²·b_9_18 + b_2_1²·b_4_5·b_5_7 + b_2_1²·b_4_5·b_5_6
        + b_2_1³·b_7_10 + b_2_1³·b_4_5·b_3_3 + b_2_1⁴·b_5_7 + b_2_1⁴·a_5_3 + b_2_1⁶·a_1_1
        + b_4_5·a_1_1²·b_7_11 + b_2_1²·c_8_15·a_1_0
128. b_6_9·b_7_11 + b_6_8·b_7_11 + b_4_2·b_9_18 + b_2_1·b_4_5·b_7_10 + b_2_1·b_4_5²·b_3_2
        + b_2_1²·b_9_18 + b_2_1³·b_7_10 + b_2_1³·b_4_5·b_3_3 + b_2_1⁴·b_5_7 + b_2_1⁴·a_5_3
        + b_2_1⁶·a_1_1 + b_4_5·a_1_1²·b_7_11 + b_2_1²·c_8_15·a_1_0
129. b_7_10·b_7_11 + b_7_10² + b_4_5²·b_6_9 + b_2_1·b_4_5³ + b_2_1²·b_4_5·b_6_9
        + b_2_1³·b_4_5² + b_2_1³·b_4_2·b_4_5 + b_2_2·b_4_5·c_8_15 + b_2_1·b_4_5·c_8_15
130. b_7_11² + b_7_10·b_7_11 + b_4_5²·b_6_9 + b_2_2·b_4_5³ + b_2_1·b_4_5³
        + b_2_1²·b_4_5·b_6_9 + b_2_1³·b_4_5² + b_2_1⁴·b_2_2·b_4_5 + b_4_5²·a_1_1·b_5_7
        + c_8_15·a_1_1·b_5_7 + b_4_5·c_8_15·a_1_1²
131. b_6_9·b_8_13 + b_2_1·b_4_1·b_4_5² + b_2_1²·b_4_5·b_6_9 + b_2_1³·b_4_5²
        + b_2_1³·b_4_1·b_4_5 + b_2_1⁴·b_2_2·b_4_5 + b_2_1·b_4_2·c_8_15 + b_2_1·b_4_1·c_8_15
        + b_2_1²·b_2_2·c_8_15
132. b_7_10² + b_2_1·b_4_5·b_8_13 + b_2_1·b_4_2·b_4_5² + b_2_1²·b_2_2·b_4_5²
        + b_2_1⁴·b_2_2·b_4_5 + b_2_1·b_4_5·c_8_15
133. b_7_10² + b_6_8·b_8_14 + b_6_8·b_8_13 + b_4_5²·b_6_8 + b_2_1·b_4_1·b_4_5²
        + b_2_1²·b_4_5·b_6_9 + b_2_1²·b_4_5·b_6_8 + b_2_1²·b_2_2·b_4_5² + b_2_1³·b_4_5²
        + b_2_1³·b_4_2·b_4_5 + b_2_1⁴·b_6_9 + b_2_1⁴·b_2_2·b_4_5 + b_2_1⁵·b_4_2
        + b_2_1⁵·b_4_1 + b_2_1⁶·b_2_2 + b_2_1·b_4_5·c_8_15 + b_2_1·b_4_2·c_8_15
        + b_2_1²·b_2_2·c_8_15
134. b_6_9·b_8_14 + b_6_8·b_8_13 + b_4_5²·b_6_9 + b_2_1·b_4_2·b_4_5² + b_2_1³·b_8_14
        + b_2_1³·b_4_2·b_4_5 + b_2_1³·b_4_1·b_4_5 + b_2_1⁴·b_6_9 + b_2_1⁵·b_4_1
        + b_2_1⁶·b_2_2 + b_2_1²·b_2_2·c_8_15
135. b_6_9·b_8_14 + b_4_5²·b_6_9 + b_2_1·b_4_5·b_8_14 + b_2_1·b_4_5³ + b_2_1²·b_4_5·b_6_9
        + b_2_1²·b_2_2·b_4_5² + b_2_1³·b_8_13 + b_2_1³·b_4_5² + b_2_1³·b_4_1·b_4_5
        + b_2_1⁴·b_6_9 + b_2_1⁴·b_2_2·b_4_5 + b_2_1⁵·b_4_5 + b_2_1⁵·b_4_2 + b_2_1⁶·b_2_2
        + b_2_1·b_4_2·c_8_15 + b_2_1·b_4_1·c_8_15
136. a_5_3·b_9_18
137. b_5_6·b_9_18 + b_6_9·b_8_14 + b_4_5²·b_6_9 + b_4_5²·b_6_8 + b_2_2·b_4_5³
        + b_2_1·b_4_1·b_4_5² + b_2_1²·b_4_5·b_6_9 + b_2_1³·b_8_13 + b_2_1³·b_4_5²
        + b_2_1⁴·b_6_9 + b_2_1⁴·b_2_2·b_4_5 + b_2_1⁵·b_4_5 + b_2_1⁵·b_4_2 + b_2_1⁶·b_2_2
        + b_4_5³·a_1_1² + b_2_1·b_4_2·c_8_15 + b_2_1·b_4_1·c_8_15
138. b_5_7·b_9_18 + b_6_9·b_8_14 + b_4_5²·b_6_8 + b_2_1·b_4_5³ + b_2_1·b_4_2·b_4_5²
        + b_2_1²·b_4_5·b_6_9 + b_2_1²·b_2_2·b_4_5² + b_2_1³·b_8_13 + b_2_1³·b_4_5²
        + b_2_1⁴·b_6_9 + b_2_1⁴·b_2_2·b_4_5 + b_2_1⁵·b_4_5 + b_2_1⁵·b_4_2 + b_2_1⁶·b_2_2
        + b_4_5²·a_1_1·b_5_7 + b_4_5³·a_1_1² + b_2_1·b_4_2·c_8_15 + b_2_1·b_4_1·c_8_15
139. b_8_14·b_7_11 + b_8_14·b_7_10 + b_8_13·b_7_11 + b_8_13·b_7_10 + b_6_9·b_9_18
        + b_4_5²·b_7_11 + b_4_5²·b_7_10 + b_2_1·b_4_5²·b_5_7 + b_2_1²·b_4_5·b_7_11
        + b_2_1²·b_4_5²·b_3_2 + b_2_1³·b_4_5·b_5_7 + b_2_1⁴·b_7_11 + b_2_1⁴·b_4_5·b_3_2
        + b_2_1·c_8_15·b_5_6 + b_2_1²·c_8_15·b_3_3 + b_2_2·c_8_15·a_5_3
140. b_8_14·b_7_11 + b_8_14·b_7_10 + b_6_8·b_9_18 + b_4_5²·b_7_11 + b_4_5²·b_7_10
        + b_2_1·b_4_5²·b_5_7 + b_2_1²·b_4_5·b_7_10 + b_2_1²·b_4_5²·b_3_2
        + b_2_1³·b_4_5·b_5_7 + b_2_1⁴·b_4_5·b_3_3 + b_2_1⁵·b_5_6 + b_2_1⁶·b_3_3
        + b_2_1⁷·a_1_1 + b_2_1·c_8_15·b_5_7 + b_2_1·c_8_15·b_5_6 + b_2_1²·c_8_15·b_3_3
        + b_2_1²·c_8_15·b_3_2 + b_2_2·c_8_15·a_5_3 + b_2_1·c_8_15·a_5_3
141. b_8_14·b_7_10 + b_4_5²·b_7_10 + b_2_1²·b_4_5·b_7_10 + b_2_1²·b_4_5²·b_3_3
        + b_2_1³·b_9_18 + b_2_1³·b_4_5·b_5_6 + b_2_1⁴·b_7_11 + b_2_1⁴·b_7_10
        + b_2_1⁴·b_4_5·b_3_3 + b_2_1⁵·b_5_6 + b_2_1⁴·b_2_2·a_5_3 + b_2_1⁵·a_5_3
        + b_2_1·c_8_15·b_5_6 + b_2_1²·c_8_15·b_3_3 + b_2_1³·c_8_15·a_1_1
        + b_2_1³·c_8_15·a_1_0
142. b_8_13·b_7_11 + b_2_1·b_4_5²·b_5_7 + b_2_1·b_4_5²·b_5_6 + b_2_1²·b_4_5·b_7_11
        + b_2_1²·b_4_5²·b_3_3 + b_2_1²·b_2_2·b_9_18 + b_2_1³·b_4_5·b_5_7
        + b_2_1³·b_4_5·b_5_6 + b_2_1⁴·b_7_11 + b_2_1⁴·b_4_5·b_3_3 + b_2_1⁵·b_5_7
        + b_2_1⁵·b_5_6 + b_2_1⁴·b_2_2·a_5_3 + b_2_1⁷·a_1_1 + b_2_1·c_8_15·b_5_7
        + b_2_1·c_8_15·b_5_6 + b_2_1²·c_8_15·b_3_3 + b_2_2·c_8_15·a_5_3 + b_2_1³·c_8_15·a_1_1
143. b_8_14·b_7_10 + b_8_13·b_7_11 + b_8_13·b_7_10 + b_4_5²·b_7_10 + b_2_1·b_4_5·b_9_18
        + b_2_1·b_4_5²·b_5_7 + b_2_1²·b_4_5²·b_3_3 + b_2_1²·b_4_5²·b_3_2
        + b_2_1³·b_4_5·b_5_7 + b_2_1⁴·b_7_11 + b_2_1⁴·b_4_5·b_3_3 + b_2_1⁴·b_4_5·b_3_2
        + b_2_1·c_8_15·b_5_6 + b_2_1²·c_8_15·b_3_3 + b_2_1³·c_8_15·a_1_1
144. b_8_14·b_7_11 + b_4_5²·b_7_11 + b_2_2·b_4_5·b_9_18 + b_2_1·b_4_5²·b_5_7
        + b_2_1·b_4_5²·b_5_6 + b_2_1²·b_4_5·b_7_11 + b_2_1²·b_4_5²·b_3_3
        + b_2_1³·b_4_5·b_5_7 + b_2_1³·b_4_5·b_5_6 + b_2_1⁴·b_4_5·b_3_3 + b_2_1·c_8_15·b_5_7
        + b_2_1·c_8_15·b_5_6 + b_2_2·c_8_15·a_5_3 + b_2_1³·c_8_15·a_1_1
145. b_8_13² + b_2_1²·b_4_5·b_8_13 + b_2_1²·b_4_5³ + b_2_1²·b_4_2·b_4_5²
        + b_2_1⁴·b_8_13 + b_2_1⁵·b_2_2·b_4_5 + b_2_1⁶·b_4_5 + b_2_1⁶·b_4_2
        + b_2_1·b_2_2·b_4_5·c_8_15 + b_2_1³·b_2_2·c_8_15
146. b_8_13·b_8_14 + b_4_5²·b_8_13 + b_2_1·b_4_5²·b_6_8 + b_2_1·b_2_2·b_4_5³
        + b_2_1²·b_4_5³ + b_2_1²·b_4_2·b_4_5² + b_2_1³·b_4_5·b_6_9 + b_2_1³·b_4_5·b_6_8
        + b_2_1⁴·b_4_5² + b_2_1⁴·b_4_1·b_4_5 + b_2_1⁶·b_4_5 + b_2_1·b_2_2·b_4_5·c_8_15
        + b_2_1²·b_4_2·c_8_15 + b_2_1²·b_4_1·c_8_15
147. b_8_14² + b_8_13² + b_4_5⁴ + b_2_1²·b_4_5³ + b_2_1⁴·b_8_13 + b_2_1⁴·b_4_5²
        + b_2_1⁵·b_2_2·b_4_5 + b_2_1⁶·b_4_2 + b_2_1·b_2_2·b_4_5·c_8_15 + b_2_1²·b_4_5·c_8_15
        + b_2_1³·b_2_2·c_8_15
148. b_7_10·b_9_18 + b_8_13² + b_4_5²·b_8_14 + b_4_5⁴ + b_2_1·b_4_5²·b_6_9
        + b_2_1·b_4_5²·b_6_8 + b_2_1·b_2_2·b_4_5³ + b_2_1²·b_4_5·b_8_14 + b_2_1²·b_4_5³
        + b_2_1²·b_4_2·b_4_5² + b_2_1³·b_4_5·b_6_9 + b_2_1⁴·b_8_13 + b_2_1⁴·b_4_5²
        + b_2_1⁴·b_4_2·b_4_5 + b_2_1⁶·b_4_5 + b_2_1⁶·b_4_2 + b_4_5³·a_1_1·b_3_3
        + b_4_1·b_4_5·c_8_15 + b_2_1²·b_4_5·c_8_15 + b_2_1³·b_2_2·c_8_15
        + b_4_5·c_8_15·a_1_1·b_3_3
149. b_7_11·b_9_18 + b_8_13² + b_4_2·b_4_5³ + b_4_1·b_4_5³ + b_2_1²·b_4_5³
        + b_2_1²·b_4_2·b_4_5² + b_2_1²·b_4_1·b_4_5² + b_2_1³·b_4_5·b_6_9
        + b_2_1⁴·b_8_13 + b_2_1⁴·b_4_5² + b_2_1⁴·b_4_1·b_4_5 + b_2_1⁶·b_4_5 + b_2_1⁶·b_4_2
        + b_4_5²·a_1_1·b_7_11 + b_4_2·b_4_5·c_8_15 + b_4_1·b_4_5·c_8_15
        + b_2_1·b_2_2·b_4_5·c_8_15 + b_2_1³·b_2_2·c_8_15
150. b_8_13·b_9_18 + b_2_1·b_4_5²·b_7_11 + b_2_1·b_4_5²·b_7_10 + b_2_1·b_4_5³·b_3_3
        + b_2_1·b_4_5³·b_3_2 + b_2_1·b_2_2·b_4_5·b_9_18 + b_2_1²·b_4_5·b_9_18
        + b_2_1²·b_4_5²·b_5_7 + b_2_1²·b_4_5²·b_5_6 + b_2_1³·b_4_5²·b_3_3
        + b_2_1³·b_4_5²·b_3_2 + b_2_1⁴·b_9_18 + b_2_1⁴·b_4_5·b_5_6 + b_2_1⁵·b_7_11
        + b_2_1⁵·b_7_10 + b_2_1⁶·b_5_7 + b_2_1⁶·a_5_3 + b_2_1⁸·a_1_1 + b_4_5²·a_1_1²·b_7_11
        + b_2_1·b_4_5·c_8_15·b_3_3 + b_2_1²·c_8_15·b_5_7 + b_2_1²·c_8_15·b_5_6
        + b_2_1⁴·c_8_15·a_1_1 + b_2_1⁴·c_8_15·a_1_0
151. b_8_14·b_9_18 + b_4_5²·b_9_18 + b_2_1·b_4_5²·b_7_10 + b_2_1²·b_4_5²·b_5_6
        + b_2_1³·b_4_5·b_7_11 + b_2_1³·b_4_5·b_7_10 + b_2_1³·b_2_2·b_9_18 + b_2_1⁴·b_9_18
        + b_2_1⁵·b_7_11 + b_2_1⁵·b_7_10 + b_2_1⁵·b_4_5·b_3_3 + b_2_1⁵·b_4_5·b_3_2
        + b_2_1⁶·b_5_7 + b_2_1⁶·a_5_3 + b_2_1⁸·a_1_1 + b_2_1·b_4_5·c_8_15·b_3_2
        + b_2_1²·c_8_15·b_5_7 + b_2_1³·c_8_15·b_3_3 + b_2_1·b_2_2·c_8_15·a_5_3
        + b_2_1⁴·c_8_15·a_1_1 + b_2_1⁴·c_8_15·a_1_0
152. b_9_18² + b_2_1·b_4_5²·b_8_13 + b_2_1·b_4_5⁴ + b_2_1·b_4_2·b_4_5³
        + b_2_1²·b_2_2·b_4_5³ + b_2_1³·b_4_5³ + b_2_1⁴·b_2_2·b_4_5² + b_2_1⁵·b_4_5²
        + b_2_1⁵·b_4_2·b_4_5 + b_4_5⁴·a_1_1² + b_2_1·b_4_5²·c_8_15
        + b_2_1²·b_2_2·b_4_5·c_8_15 + b_2_1³·b_4_5·c_8_15

About the group

Ring generators

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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_8_15, a Duflot regular element of degree 8
  2. b_4_5 + b_2_1², an element of degree 4
  3. b_3_2, an element of degree 3
• The Raw Filter Degree Type of that HSOP is [-1, -1, 9, 12].
• 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 1

1. a_1_0 → 0, an element of degree 1
2. a_1_1 → 0, an element of degree 1
3. b_2_1 → 0, an element of degree 2
4. b_2_2 → 0, an element of degree 2
5. b_3_2 → 0, an element of degree 3
6. b_3_3 → 0, an element of degree 3
7. b_4_1 → 0, an element of degree 4
8. b_4_2 → 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. b_5_6 → 0, an element of degree 5
12. b_5_7 → 0, an element of degree 5
13. b_6_8 → 0, an element of degree 6
14. b_6_9 → 0, an element of degree 6
15. b_7_10 → 0, an element of degree 7
16. b_7_11 → 0, an element of degree 7
17. b_8_13 → 0, an element of degree 8
18. b_8_14 → 0, an element of degree 8
19. c_8_15 → c_1_0⁸, an element of degree 8
20. b_9_18 → 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. b_2_1 → c_1_1², an element of degree 2
4. b_2_2 → 0, an element of degree 2
5. b_3_2 → c_1_1·c_1_2² + c_1_1²·c_1_2, an element of degree 3
6. b_3_3 → 0, an element of degree 3
7. b_4_1 → c_1_1²·c_1_2² + c_1_1³·c_1_2, an element of degree 4
8. b_4_2 → c_1_1²·c_1_2² + c_1_1³·c_1_2, an element of degree 4
9. b_4_5 → c_1_2⁴ + c_1_1²·c_1_2², an element of degree 4
10. a_5_3 → 0, an element of degree 5
11. b_5_6 → c_1_1·c_1_2⁴ + c_1_1³·c_1_2², an element of degree 5
12. b_5_7 → c_1_1·c_1_2⁴ + c_1_1³·c_1_2², an element of degree 5
13. b_6_8 → c_1_1⁴·c_1_2² + c_1_1⁵·c_1_2 + c_1_0·c_1_1³·c_1_2² + c_1_0·c_1_1⁴·c_1_2
       + c_1_0²·c_1_1²·c_1_2² + c_1_0²·c_1_1³·c_1_2 + c_1_0²·c_1_1⁴
       + c_1_0⁴·c_1_1², an element of degree 6
14. b_6_9 → c_1_1²·c_1_2⁴ + c_1_1⁴·c_1_2², an element of degree 6
15. b_7_10 → c_1_1·c_1_2⁶ + c_1_1²·c_1_2⁵ + c_1_1⁴·c_1_2³ + c_1_1⁵·c_1_2²
       + c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2² + c_1_0²·c_1_1·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
16. b_7_11 → 0, an element of degree 7
17. b_8_13 → c_1_1²·c_1_2⁶ + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_2⁴ + c_1_1⁵·c_1_2³
       + c_1_1⁶·c_1_2² + c_1_1⁷·c_1_2, an element of degree 8
18. b_8_14 → c_1_2⁸ + c_1_1²·c_1_2⁶ + c_1_1³·c_1_2⁵ + c_1_1⁵·c_1_2³ + c_1_1⁶·c_1_2²
       + c_1_1⁷·c_1_2 + c_1_0·c_1_1³·c_1_2⁴ + c_1_0·c_1_1⁵·c_1_2²
       + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁵·c_1_2 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1³·c_1_2, an element of degree 8
19. c_8_15 → c_1_2⁸ + c_1_1⁷·c_1_2 + 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
20. b_9_18 → c_1_1³·c_1_2⁶ + c_1_1⁴·c_1_2⁵ + c_1_1⁵·c_1_2⁴ + c_1_1⁶·c_1_2³
       + c_1_0·c_1_1²·c_1_2⁶ + c_1_0·c_1_1³·c_1_2⁵ + c_1_0·c_1_1⁵·c_1_2³
       + c_1_0·c_1_1⁶·c_1_2² + c_1_0²·c_1_1·c_1_2⁶ + c_1_0²·c_1_1²·c_1_2⁵
       + c_1_0²·c_1_1³·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2³ + c_1_0²·c_1_1⁵·c_1_2²
       + c_1_0²·c_1_1⁶·c_1_2 + c_1_0⁴·c_1_1·c_1_2⁴ + c_1_0⁴·c_1_1⁴·c_1_2, 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. b_2_1 → c_1_2², an element of degree 2
4. b_2_2 → c_1_2², an element of degree 2
5. b_3_2 → c_1_1·c_1_2² + c_1_1²·c_1_2, an element of degree 3
6. b_3_3 → c_1_1·c_1_2² + c_1_1²·c_1_2, an element of degree 3
7. b_4_1 → c_1_1·c_1_2³ + c_1_1²·c_1_2², an element of degree 4
8. b_4_2 → 0, an element of degree 4
9. b_4_5 → c_1_1²·c_1_2² + c_1_1⁴, an element of degree 4
10. a_5_3 → 0, an element of degree 5
11. b_5_6 → c_1_1·c_1_2⁴ + c_1_1⁴·c_1_2, an element of degree 5
12. b_5_7 → c_1_1·c_1_2⁴ + c_1_1²·c_1_2³, an element of degree 5
13. b_6_8 → c_1_1·c_1_2⁵ + c_1_1⁴·c_1_2² + c_1_0·c_1_1·c_1_2⁴ + c_1_0·c_1_1²·c_1_2³
       + c_1_0²·c_1_2⁴ + c_1_0²·c_1_1·c_1_2³ + c_1_0²·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_2², an element of degree 6
14. b_6_9 → c_1_2⁶ + c_1_0·c_1_1·c_1_2⁴ + c_1_0·c_1_1²·c_1_2³ + c_1_0²·c_1_2⁴
       + c_1_0²·c_1_1·c_1_2³ + c_1_0²·c_1_1²·c_1_2² + c_1_0⁴·c_1_2², an element of degree 6
15. b_7_10 → c_1_1·c_1_2⁶ + c_1_1²·c_1_2⁵ + c_1_1³·c_1_2⁴ + c_1_1⁴·c_1_2³
       + c_1_1⁵·c_1_2² + c_1_1⁶·c_1_2 + c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2²
       + c_1_0²·c_1_1·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1·c_1_2²
       + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
16. b_7_11 → c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2² + c_1_0²·c_1_1·c_1_2⁴
       + c_1_0²·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
17. b_8_13 → c_1_1·c_1_2⁷ + c_1_1²·c_1_2⁶ + c_1_0·c_1_1·c_1_2⁶ + c_1_0·c_1_1⁴·c_1_2³
       + c_1_0²·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_1·c_1_2³ + c_1_0⁴·c_1_1²·c_1_2², an element of degree 8
18. b_8_14 → c_1_1·c_1_2⁷ + c_1_1²·c_1_2⁶ + c_1_1³·c_1_2⁵ + c_1_1⁵·c_1_2³
       + c_1_1⁶·c_1_2² + c_1_1⁸ + c_1_0·c_1_1²·c_1_2⁵ + c_1_0·c_1_1⁴·c_1_2³
       + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_1·c_1_2³
       + c_1_0⁴·c_1_1²·c_1_2², an element of degree 8
19. c_8_15 → c_1_1·c_1_2⁷ + c_1_1⁸ + c_1_0·c_1_1·c_1_2⁶ + c_1_0·c_1_1⁴·c_1_2³
       + c_1_0²·c_1_2⁶ + c_1_0⁴·c_1_1·c_1_2³ + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8
20. b_9_18 → c_1_1³·c_1_2⁶ + c_1_1⁴·c_1_2⁵ + c_1_1⁵·c_1_2⁴ + c_1_1⁶·c_1_2³
       + c_1_0·c_1_1³·c_1_2⁵ + c_1_0·c_1_1⁴·c_1_2⁴ + c_1_0·c_1_1⁵·c_1_2³
       + c_1_0·c_1_1⁶·c_1_2² + c_1_0²·c_1_1²·c_1_2⁵ + c_1_0²·c_1_1³·c_1_2⁴
       + c_1_0²·c_1_1⁵·c_1_2² + c_1_0²·c_1_1⁶·c_1_2 + c_1_0⁴·c_1_1²·c_1_2³
       + c_1_0⁴·c_1_1⁴·c_1_2, an element of degree 9

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128