David J. Green

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Cohomology of group number 1933 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 4 minimal generators and exponent 8.
• It is non-abelian.
• It has p-Rank 3.
• Its center has rank 2.
• It has 4 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) · (t8  +  t7  +  2·t5  +  t4  +  t3  +  t2  +  t  +  1)

  (t  −  1)3 · (t2  +  1)2 · (t4  +  1)

• The a-invariants are -∞,-∞,-5,-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 14 minimal generators of maximal degree 8:

1. a_1_2, a nilpotent element of degree 1
2. b_1_0, an element of degree 1
3. b_1_1, an element of degree 1
4. b_1_3, an element of degree 1
5. a_3_11, a nilpotent element of degree 3
6. b_3_10, an element of degree 3
7. b_4_15, an element of degree 4
8. c_4_16, a Duflot regular element of degree 4
9. b_5_22, an element of degree 5
10. b_5_23, an element of degree 5
11. b_5_24, an element of degree 5
12. b_7_40, an element of degree 7
13. b_8_47, an element of degree 8
14. c_8_49, a Duflot regular element of degree 8

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring relations

There are 57 minimal relations of maximal degree 16:

1. a_1_2·b_1_0
2. b_1_0·b_1_3 + b_1_0·b_1_1 + a_1_2·b_1_1
3. a_1_2·b_1_1·b_1_3
4. b_1_1·b_1_3² + b_1_1²·b_1_3 + b_1_0·b_1_1² + a_1_2·b_1_1² + a_1_2³
5. b_1_0·a_3_11
6. b_1_3·b_3_10 + b_1_1·b_3_10 + b_1_1·a_3_11
7. a_1_2·b_3_10
8. a_1_2³·b_1_3²
9. b_1_1²·b_3_10 + b_1_1⁴·b_1_3 + b_1_0·b_1_1⁴ + b_4_15·b_1_3 + b_1_3²·a_3_11
      + b_1_1·b_1_3·a_3_11 + b_1_1²·a_3_11 + a_1_2·b_1_1⁴ + a_1_2²·b_1_3³
      + a_1_2²·a_3_11
10. b_1_0·b_1_1⁴ + b_4_15·b_1_0 + b_1_1²·a_3_11 + a_1_2·b_1_1⁴
11. b_1_1·b_1_3·a_3_11 + b_1_1²·a_3_11 + b_4_15·a_1_2 + a_1_2·b_1_3·a_3_11
12. a_3_11² + a_1_2·b_1_3²·a_3_11 + a_1_2²·b_1_3⁴ + a_1_2³·a_3_11 + c_4_16·a_1_2²
13. b_4_15·b_1_0·b_1_1 + a_3_11·b_3_10 + b_1_1³·a_3_11
14. b_3_10² + b_1_1⁵·b_1_3 + b_1_0³·b_3_10 + b_1_1³·a_3_11 + b_4_15·a_1_2·b_1_1
       + c_4_16·b_1_0²
15. b_3_10² + b_1_1⁵·b_1_3 + b_1_0³·b_3_10 + b_1_1³·a_3_11 + a_1_2·b_5_22
       + a_1_2²·b_1_3·a_3_11 + a_1_2³·a_3_11 + c_4_16·b_1_0² + c_4_16·a_1_2·b_1_3
       + c_4_16·a_1_2·b_1_1
16. b_3_10² + b_1_1·b_5_22 + b_1_1⁵·b_1_3 + b_1_0·b_5_23 + b_1_0⁵·b_1_1
       + b_4_15·b_1_1·b_1_3 + b_4_15·b_1_1² + a_3_11·b_3_10 + a_1_2³·a_3_11
       + c_4_16·b_1_1·b_1_3 + c_4_16·b_1_1² + c_4_16·a_1_2·b_1_1
17. b_3_10² + b_1_3·b_5_22 + b_1_1·b_5_22 + b_1_1⁵·b_1_3 + b_1_0³·b_3_10
       + b_4_15·b_1_1·b_1_3 + b_4_15·b_1_1² + a_3_11·b_3_10 + a_1_2·b_5_23 + a_3_11²
       + a_1_2·b_1_3²·a_3_11 + a_1_2²·b_1_3⁴ + a_1_2²·b_1_3·a_3_11 + c_4_16·b_1_3²
       + c_4_16·b_1_1² + c_4_16·b_1_0² + c_4_16·a_1_2·b_1_3 + c_4_16·a_1_2·b_1_1
18. b_3_10² + b_1_3·b_5_22 + b_1_1·b_5_24 + b_1_1·b_5_23 + b_1_1·b_5_22
       + b_1_0²·b_1_1·b_3_10 + b_1_0³·b_3_10 + a_1_2·b_1_3²·a_3_11 + a_1_2³·a_3_11
       + c_4_16·b_1_3² + c_4_16·b_1_1·b_1_3 + c_4_16·b_1_1² + c_4_16·b_1_0²
19. b_1_1·b_5_22 + b_1_0·b_5_24 + b_1_0²·b_1_1·b_3_10 + b_4_15·b_1_1·b_1_3
       + b_4_15·b_1_1² + b_1_1³·a_3_11 + c_4_16·b_1_1·b_1_3 + c_4_16·b_1_1²
       + c_4_16·b_1_0·b_1_1 + c_4_16·b_1_0²
20. b_4_15·b_3_10 + b_4_15·b_1_1²·b_1_3 + b_1_1·a_3_11·b_3_10 + b_1_1⁴·a_3_11
       + c_4_16·a_1_2·b_1_1²
21. b_1_1·a_3_11·b_3_10 + b_1_1⁴·a_3_11 + b_4_15·a_3_11 + a_1_2·b_1_3³·a_3_11
       + a_1_2²·b_1_3⁵ + a_1_2²·b_1_3²·a_3_11 + c_4_16·a_1_2·b_1_1²
       + c_4_16·a_1_2²·b_1_3
22. a_1_2·b_1_3·b_5_23 + a_1_2·b_1_3³·a_3_11 + a_1_2²·b_1_3²·a_3_11
       + a_1_2³·b_1_3·a_3_11 + c_4_16·a_1_2·b_1_3² + c_4_16·a_1_2²·b_1_3
23. b_1_3²·b_5_23 + b_1_1·b_1_3·b_5_23 + b_1_0·b_1_1·b_5_23 + b_1_0³·b_1_1·b_3_10
       + b_1_3⁴·a_3_11 + b_1_1⁴·a_3_11 + a_1_2·b_1_1·b_5_23 + b_4_15·a_1_2·b_1_1²
       + a_1_2·b_1_3³·a_3_11 + a_1_2²·b_5_24 + c_4_16·b_1_3³ + c_4_16·b_1_1²·b_1_3
       + c_4_16·b_1_0²·b_1_1 + c_4_16·a_1_2·b_1_3² + c_4_16·a_1_2³
24. b_4_15·b_1_1³·b_1_3 + b_4_15·b_1_1⁴ + b_4_15² + b_4_15·a_1_2·b_1_1³
       + a_1_2·b_1_3⁴·a_3_11 + a_1_2²·b_1_3⁶ + c_4_16·b_1_1³·b_1_3 + c_4_16·b_1_1⁴
       + c_4_16·b_1_0·b_1_1³ + c_4_16·a_1_2·b_1_1³ + c_4_16·a_1_2²·b_1_3²
25. a_3_11·b_5_22 + b_4_15·a_1_2·b_1_1³ + a_1_2²·b_1_3³·a_3_11 + c_4_16·b_1_3·a_3_11
       + c_4_16·b_1_1·a_3_11 + c_4_16·a_1_2·b_1_1³ + c_4_16·a_1_2³·b_1_3
26. b_3_10·b_5_24 + b_3_10·b_5_23 + b_1_1⁷·b_1_3 + b_1_0⁵·b_3_10 + b_4_15·b_1_1³·b_1_3
       + b_4_15·a_1_2·b_1_1³ + c_4_16·b_1_1·b_3_10 + c_4_16·b_1_0³·b_1_1 + c_4_16·b_1_0⁴
       + c_4_16·b_1_1·a_3_11 + c_4_16·a_1_2·b_1_1³
27. b_3_10·b_5_23 + b_1_1·b_7_40 + b_1_1³·b_5_23 + b_1_1⁷·b_1_3 + b_1_0·b_1_1²·b_5_23
       + b_1_0⁴·b_1_1·b_3_10 + b_1_0⁵·b_3_10 + b_4_15·b_1_1³·b_1_3 + b_4_15·b_1_1⁴
       + b_1_1⁵·a_3_11 + b_4_15·b_1_1·a_3_11 + b_4_15·a_1_2·b_1_1³ + c_4_16·b_1_1·b_3_10
       + c_4_16·b_1_0·b_3_10 + c_4_16·b_1_0⁴ + c_4_16·b_1_1·a_3_11
28. b_3_10·b_5_23 + b_1_3·b_7_40 + b_1_1²·b_1_3·b_5_23 + b_1_1⁷·b_1_3
       + b_1_0·b_1_1²·b_5_23 + b_1_0⁴·b_1_1·b_3_10 + b_1_0⁵·b_3_10 + a_3_11·b_5_23
       + a_1_2·b_1_1²·b_5_23 + b_4_15·b_1_1·a_3_11 + b_4_15·a_1_2·b_1_1³
       + a_1_2·b_1_3⁴·a_3_11 + a_1_2²·b_1_3³·a_3_11 + c_4_16·b_1_1·b_3_10
       + c_4_16·b_1_0·b_3_10 + c_4_16·b_1_0⁴ + c_4_16·b_1_3·a_3_11 + c_4_16·b_1_1·a_3_11
       + c_4_16·a_1_2·b_1_3³ + c_4_16·a_1_2·b_1_1³ + c_4_16·a_1_2·a_3_11
       + c_4_16·a_1_2²·b_1_3² + c_4_16·a_1_2³·b_1_3
29. b_3_10·b_5_22 + b_1_0·b_7_40 + b_1_0·b_1_1²·b_5_23 + b_1_0⁴·b_1_1·b_3_10
       + b_1_0⁷·b_1_1 + b_1_1⁵·a_3_11 + b_4_15·b_1_1·a_3_11 + c_4_16·b_1_0·b_3_10
       + c_4_16·b_1_1·a_3_11
30. a_1_2·b_7_40 + a_1_2·b_1_1²·b_5_23 + b_4_15·a_1_2·b_1_1³ + c_4_16·a_1_2²·b_1_3²
31. b_1_0·b_1_1³·b_5_23 + b_4_15·b_5_22 + b_4_15²·b_1_1 + b_1_1·a_3_11·b_5_23
       + a_1_2·b_1_1³·b_5_23 + b_4_15·b_1_1²·a_3_11 + b_4_15²·a_1_2 + b_4_15·c_4_16·b_1_3
       + b_4_15·c_4_16·b_1_1 + b_4_15·c_4_16·a_1_2 + c_4_16·a_1_2·b_1_3·a_3_11
32. b_1_0·b_1_1³·b_5_23 + b_4_15·b_5_24 + b_4_15·b_5_23 + b_4_15·b_5_22 + b_4_15·b_1_1⁵
       + b_4_15²·b_1_1 + b_1_3·a_3_11·b_5_24 + b_1_1⁶·a_3_11 + a_1_2·b_1_1³·b_5_23
       + b_4_15·b_1_1²·a_3_11 + b_4_15²·a_1_2 + a_1_2·b_1_3⁵·a_3_11
       + a_1_2²·b_1_3²·b_5_24 + a_1_2²·b_1_3⁷ + c_4_16·b_1_1⁴·b_1_3 + c_4_16·b_1_1⁵
       + b_4_15·c_4_16·b_1_1 + b_4_15·c_4_16·b_1_0 + b_4_15·c_4_16·a_1_2
       + c_4_16·a_1_2²·b_1_3³
33. b_1_1²·b_7_40 + b_1_1⁸·b_1_3 + b_1_0·b_1_1·b_7_40 + b_1_0·b_1_1³·b_5_23
       + b_8_47·b_1_1 + b_4_15·b_5_23 + b_4_15²·b_1_1 + b_1_3·a_3_11·b_5_23
       + a_1_2·b_1_1³·b_5_23 + b_4_15·b_1_1²·a_3_11 + a_1_2²·b_1_3⁴·a_3_11
       + c_4_16·b_1_1⁵ + c_4_16·b_1_0⁴·b_1_1 + b_4_15·c_4_16·b_1_3 + b_4_15·c_4_16·b_1_1
       + c_4_16·b_1_3²·a_3_11 + c_4_16·b_1_1²·a_3_11 + b_4_15·c_4_16·a_1_2
       + c_4_16·a_1_2·b_1_3·a_3_11
34. b_1_3⁴·b_5_24 + b_1_1³·b_1_3·b_5_23 + b_1_1⁸·b_1_3 + b_1_0·b_1_1·b_7_40
       + b_8_47·b_1_3 + b_1_3·a_3_11·b_5_23 + b_1_3⁶·a_3_11 + b_1_1⁶·a_3_11
       + a_1_2·b_1_1³·b_5_23 + a_1_2·a_3_11·b_5_24 + a_1_2·b_1_3⁵·a_3_11 + a_1_2²·b_1_3⁷
       + c_4_16·b_1_1⁴·b_1_3 + c_4_16·b_1_0⁴·b_1_1 + b_4_15·c_4_16·b_1_3
       + c_4_16·b_1_3²·a_3_11 + c_4_16·a_1_2·b_1_3⁴ + c_4_16·a_1_2·b_1_3·a_3_11
35. b_1_0·b_1_1·b_7_40 + b_1_0²·b_7_40 + b_1_0⁴·b_5_23 + b_1_0⁶·b_3_10 + b_1_0⁸·b_1_1
       + b_8_47·b_1_0 + b_4_15·b_5_22 + b_4_15²·b_1_1 + b_1_1⁶·a_3_11 + a_1_2²·b_1_3⁴·a_3_11
       + b_4_15·c_4_16·b_1_3 + b_4_15·c_4_16·b_1_1 + b_4_15·c_4_16·b_1_0
       + c_4_16·b_1_1²·a_3_11
36. b_1_0·b_1_1³·b_5_23 + b_4_15·b_5_22 + b_4_15²·b_1_1 + b_1_3·a_3_11·b_5_23
       + a_1_2·b_1_3³·b_5_24 + b_8_47·a_1_2 + b_4_15·b_1_1²·a_3_11 + b_4_15²·a_1_2
       + a_1_2²·b_1_3⁷ + a_1_2²·b_1_3⁴·a_3_11 + b_4_15·c_4_16·b_1_3 + b_4_15·c_4_16·b_1_1
       + c_4_16·b_1_3²·a_3_11 + c_4_16·b_1_1²·a_3_11 + b_4_15·c_4_16·a_1_2
       + c_4_16·a_1_2·b_1_3·a_3_11
37. b_4_15·b_1_0·b_5_23 + a_3_11·b_7_40 + b_1_1⁷·a_3_11 + a_1_2²·b_1_3⁵·a_3_11
       + c_4_16·a_3_11·b_3_10 + c_4_16·a_1_2·b_1_1⁵ + c_4_16·a_1_2·b_1_3²·a_3_11
       + c_4_16·a_1_2³·a_3_11
38. b_5_23² + b_1_1⁵·b_5_23 + b_1_1⁹·b_1_3 + b_1_0⁷·b_3_10 + b_4_15²·b_1_1²
       + b_4_15²·a_1_2·b_1_1 + a_1_2·b_1_3⁶·a_3_11 + a_1_2²·b_1_3⁸ + c_8_49·b_1_1²
       + c_4_16·b_1_1⁶ + c_4_16·b_1_0⁶ + b_4_15·c_4_16·b_1_1² + c_4_16·a_3_11·b_3_10
       + c_4_16·b_1_1³·a_3_11 + c_4_16·a_1_2·b_1_1⁵ + b_4_15·c_4_16·a_1_2·b_1_1
       + c_4_16·a_1_2²·b_1_3⁴ + c_4_16²·b_1_3² + c_4_16²·b_1_1² + c_4_16²·b_1_0²
       + c_4_16²·a_1_2²
39. b_5_22² + b_1_0⁶·b_1_1·b_3_10 + b_1_0⁹·b_1_1 + b_4_15²·b_1_1²
       + b_4_15·b_1_1³·a_3_11 + b_4_15²·a_1_2·b_1_1 + c_8_49·b_1_0²
       + c_4_16·b_1_0³·b_3_10 + c_4_16·b_1_0⁵·b_1_1 + c_4_16·b_1_0⁶ + c_4_16²·b_1_3²
       + c_4_16²·b_1_1²
40. b_5_23·b_5_24 + b_5_23² + b_5_22·b_5_24 + b_1_1⁵·b_5_23 + b_1_0⁶·b_1_1·b_3_10
       + b_1_0⁷·b_3_10 + b_8_47·b_1_1² + b_4_15·b_1_3·b_5_23 + b_4_15·b_1_1·b_5_23
       + b_4_15²·b_1_1² + b_1_3²·a_3_11·b_5_24 + b_1_1²·a_3_11·b_5_23
       + b_4_15·b_1_1³·a_3_11 + b_4_15²·a_1_2·b_1_1 + a_1_2²·a_3_11·b_5_24
       + a_1_2²·b_1_3⁵·a_3_11 + c_8_49·b_1_0·b_1_1 + c_4_16·b_1_1·b_5_23
       + c_4_16·b_1_0·b_5_23 + c_4_16·b_1_0·b_5_22 + c_4_16·b_1_0⁶
       + b_4_15·c_4_16·b_1_1·b_1_3 + c_8_49·a_1_2·b_1_1 + c_4_16·b_1_3³·a_3_11
       + c_4_16·a_1_2·b_5_24 + c_4_16·a_1_2·b_5_23 + c_4_16·a_1_2³·a_3_11 + c_4_16²·b_1_3²
       + c_4_16²·b_1_1·b_1_3 + c_4_16²·b_1_0² + c_4_16²·a_1_2·b_1_3
41. b_5_22·b_5_24 + b_8_47·b_1_0·b_1_1 + b_4_15·b_1_3·b_5_23 + b_4_15·b_1_1·b_5_23
       + b_4_15·b_1_0·b_5_23 + b_4_15²·b_1_1² + b_1_1⁷·a_3_11 + a_1_2·b_1_3·a_3_11·b_5_24
       + a_1_2·b_1_3⁶·a_3_11 + a_1_2²·b_1_3⁸ + a_1_2²·a_3_11·b_5_24 + c_8_49·b_1_0·b_1_1
       + c_4_16·b_1_3·b_5_24 + c_4_16·b_1_1·b_5_23 + c_4_16·b_1_1⁵·b_1_3
       + c_4_16·b_1_0·b_5_23 + c_4_16·b_1_0·b_5_22 + c_4_16·b_1_0²·b_1_1·b_3_10
       + c_4_16·b_1_0³·b_3_10 + c_4_16·b_1_0⁵·b_1_1 + b_4_15·c_4_16·b_1_1·b_1_3
       + b_4_15·c_4_16·b_1_1² + c_4_16·b_1_3³·a_3_11 + c_4_16·b_1_1³·a_3_11
       + c_4_16·a_1_2·b_5_23 + c_4_16²·b_1_1·b_1_3 + c_4_16²·b_1_0² + c_4_16²·a_1_2·b_1_3
       + c_4_16²·a_1_2·b_1_1 + c_4_16²·a_1_2²
42. b_5_22·b_5_23 + b_3_10·b_7_40 + b_1_1⁹·b_1_3 + b_1_0⁵·b_5_23 + b_1_0⁷·b_3_10
       + b_1_0⁹·b_1_1 + b_4_15·b_1_1·b_5_23 + b_4_15·b_1_1⁶ + b_4_15·b_1_0·b_5_23
       + b_4_15²·b_1_1² + b_1_1²·a_3_11·b_5_23 + b_1_1⁷·a_3_11 + b_8_47·a_1_2·b_1_1
       + b_4_15·b_1_1³·a_3_11 + b_4_15²·a_1_2·b_1_1 + a_1_2²·b_1_3⁵·a_3_11
       + c_8_49·b_1_0·b_1_1 + c_4_16·b_1_3·b_5_23 + c_4_16·b_1_1·b_5_23 + c_4_16·b_1_1⁶
       + c_4_16·b_1_0²·b_1_1·b_3_10 + c_4_16·b_1_0³·b_3_10 + c_4_16·b_1_0⁶
       + c_4_16·a_3_11·b_3_10 + c_4_16·a_1_2·b_5_23 + c_4_16·a_1_2·b_1_1⁵
       + c_4_16²·b_1_0² + c_4_16²·a_1_2·b_1_3 + c_4_16²·a_1_2·b_1_1 + c_4_16²·a_1_2²
43. b_5_24² + b_5_23² + b_1_1⁹·b_1_3 + b_1_0⁷·b_3_10 + b_4_15²·b_1_1²
       + b_1_3⁷·a_3_11 + b_8_47·a_1_2·b_1_3 + a_1_2·b_1_3⁶·a_3_11 + a_1_2²·a_3_11·b_5_24
       + a_1_2²·b_1_3⁵·a_3_11 + c_4_16·b_1_3⁶ + c_4_16·b_1_1⁵·b_1_3 + c_4_16·b_1_0⁶
       + c_4_16·a_3_11·b_3_10 + c_8_49·a_1_2² + c_4_16·a_1_2·b_1_3²·a_3_11
       + c_4_16·a_1_2²·b_1_3⁴ + c_4_16·a_1_2²·b_1_3·a_3_11 + c_4_16²·b_1_3²
44. b_5_22·b_5_24 + b_5_22·b_5_23 + b_1_0⁶·b_1_1·b_3_10 + b_1_0⁹·b_1_1 + b_8_47·b_1_0²
       + b_4_15·b_1_0·b_5_23 + b_4_15²·b_1_1² + b_1_1²·a_3_11·b_5_23
       + b_4_15·b_1_1³·a_3_11 + b_4_15²·a_1_2·b_1_1 + a_1_2·b_1_3·a_3_11·b_5_24
       + a_1_2²·b_1_3⁵·a_3_11 + c_4_16·b_1_3·b_5_24 + c_4_16·b_1_3·b_5_23
       + c_4_16·b_1_1⁵·b_1_3 + c_4_16·b_1_0·b_5_23 + c_4_16·b_1_0⁵·b_1_1 + c_4_16·b_1_0⁶
       + b_4_15·c_4_16·b_1_1·b_1_3 + b_4_15·c_4_16·b_1_1² + c_4_16·a_3_11·b_3_10
       + c_4_16·a_1_2·b_1_3²·a_3_11 + c_4_16·a_1_2²·b_1_3·a_3_11 + c_4_16²·b_1_1·b_1_3
       + c_4_16²·b_1_0² + c_4_16²·a_1_2·b_1_1
45. b_4_15·b_7_40 + b_4_15·b_1_1·b_1_3·b_5_23 + b_4_15·b_1_1²·b_5_23 + b_4_15·b_1_1⁷
       + a_1_2²·b_1_3⁶·a_3_11 + c_4_16·b_1_1⁶·b_1_3 + c_4_16·b_1_1⁷
       + b_4_15·c_4_16·b_1_1²·b_1_3 + c_4_16·b_1_1⁴·a_3_11 + c_4_16·a_1_2·b_1_1·b_5_23
       + c_4_16·a_1_2·b_1_1⁶ + c_4_16·a_1_2·b_1_3³·a_3_11 + c_4_16·a_1_2³·b_1_3·a_3_11
46. b_1_0⁶·b_5_23 + b_1_0⁷·b_1_1·b_3_10 + b_1_0⁸·b_3_10 + b_8_47·b_3_10
       + b_8_47·b_1_0²·b_1_1 + b_8_47·b_1_0³ + b_4_15·b_1_1⁴·a_3_11
       + b_4_15²·a_1_2·b_1_1² + c_4_16·b_1_0²·b_5_23 + c_4_16·b_1_0²·b_5_22
       + c_4_16·b_1_0³·b_1_1·b_3_10 + c_4_16·b_1_0⁶·b_1_1 + b_4_15·c_4_16·b_1_1²·b_1_3
       + c_4_16·a_1_2·b_1_1·b_5_23 + b_4_15·c_4_16·a_3_11 + c_4_16·a_1_2·b_1_3³·a_3_11
       + c_4_16·a_1_2²·b_1_3⁵ + c_4_16·a_1_2²·b_1_3²·a_3_11 + c_4_16²·b_1_0²·b_1_1
       + c_4_16²·a_1_2²·b_1_3
47. b_1_3³·a_3_11·b_5_24 + b_1_1³·a_3_11·b_5_23 + b_1_1⁸·a_3_11 + b_8_47·a_3_11
       + b_4_15·a_1_2·b_1_1·b_5_23 + b_4_15²·a_1_2·b_1_1² + a_1_2·b_1_3⁷·a_3_11
       + a_1_2²·b_1_3⁹ + a_1_2²·b_1_3·a_3_11·b_5_24 + c_4_16·b_1_1⁴·a_3_11
       + c_4_16·a_1_2·b_1_1·b_5_23 + c_4_16·a_1_2·b_1_1⁶ + b_4_15·c_4_16·a_3_11
       + b_4_15·c_4_16·a_1_2·b_1_1² + c_4_16·a_1_2·b_1_3³·a_3_11
       + c_4_16·a_1_2²·b_1_3⁵ + c_4_16·a_1_2²·b_1_3²·a_3_11
48. b_5_24·b_7_40 + b_5_23·b_7_40 + b_5_22·b_7_40 + b_1_1¹¹·b_1_3 + b_1_0⁸·b_1_1·b_3_10
       + b_1_0¹¹·b_1_1 + b_8_47·b_1_0⁴ + b_4_15·b_1_1²·b_1_3·b_5_23
       + b_1_1⁴·a_3_11·b_5_23 + b_1_1⁹·a_3_11 + b_4_15·a_3_11·b_5_23
       + b_4_15²·a_1_2·b_1_1³ + b_8_47·a_1_2²·b_1_3² + c_8_49·b_1_0·b_3_10
       + c_8_49·b_1_0·b_1_1³ + c_4_16·b_1_1·b_7_40 + c_4_16·b_1_1⁷·b_1_3
       + c_4_16·b_1_0·b_7_40 + c_4_16·b_1_0·b_1_1²·b_5_23 + c_4_16·b_1_0³·b_5_23
       + c_4_16·b_1_0³·b_5_22 + c_4_16·b_1_0⁴·b_1_1·b_3_10 + c_4_16·b_1_0⁵·b_3_10
       + c_4_16·b_1_0⁸ + b_4_15·c_4_16·b_1_1⁴ + b_4_15²·c_4_16 + c_8_49·a_1_2·b_1_1³
       + c_4_16·b_1_1⁵·a_3_11 + c_4_16·a_1_2·b_1_3²·b_5_24 + c_4_16·a_1_2·b_1_1²·b_5_23
       + c_4_16·a_1_2·b_1_1⁷ + b_4_15·c_4_16·a_1_2·b_1_1³ + c_4_16·a_1_2·b_1_3⁴·a_3_11
       + c_4_16·a_1_2²·b_1_3³·a_3_11 + c_4_16²·b_1_1³·b_1_3 + c_4_16²·b_1_1⁴
       + c_4_16²·b_1_0·b_3_10 + c_4_16²·b_1_0·b_1_1³ + c_4_16²·b_1_0³·b_1_1
       + c_4_16²·b_1_0⁴ + c_4_16²·a_1_2·b_1_1³ + c_4_16²·a_1_2²·b_1_3²
       + c_4_16²·a_1_2³·b_1_3
49. b_5_24·b_7_40 + b_1_1⁷·b_5_23 + b_1_1¹¹·b_1_3 + b_8_47·b_1_0³·b_1_1 + b_4_15·b_1_1⁸
       + b_4_15³ + b_1_1⁹·a_3_11 + b_4_15·a_3_11·b_5_23 + b_8_47·a_1_2²·b_1_3²
       + a_1_2²·b_1_3⁷·a_3_11 + c_8_49·b_1_1·b_3_10 + c_8_49·b_1_1⁴
       + c_8_49·b_1_0·b_1_1³ + c_4_16·b_1_1²·b_1_3·b_5_23 + c_4_16·b_1_0·b_7_40
       + c_4_16·b_1_0³·b_5_23 + c_4_16·b_1_0⁵·b_3_10 + c_8_49·a_1_2·b_1_1³
       + c_4_16·b_1_1⁵·a_3_11 + c_4_16·a_1_2·b_1_3²·b_5_24 + c_4_16·a_1_2·b_1_1²·b_5_23
       + c_4_16·a_1_2·b_1_1⁷ + b_4_15·c_4_16·a_1_2·b_1_1³ + c_4_16·a_1_2·b_1_3⁴·a_3_11
       + c_4_16·a_1_2²·b_1_3⁶ + c_4_16²·b_1_1·b_3_10 + c_4_16²·b_1_1³·b_1_3
       + c_4_16²·b_1_1⁴ + c_4_16²·b_1_0·b_1_1³ + c_4_16²·b_1_0⁴
       + c_4_16²·a_1_2²·b_1_3² + c_4_16²·a_1_2³·b_1_3
50. b_5_24·b_7_40 + b_5_23·b_7_40 + b_1_1¹¹·b_1_3 + b_8_47·b_1_0·b_3_10
       + b_4_15·b_1_1³·b_5_23 + b_4_15³ + b_1_1⁹·a_3_11 + b_8_47·a_1_2·b_1_1³
       + b_4_15·b_1_1⁵·a_3_11 + b_4_15²·a_1_2·b_1_1³ + b_8_47·a_1_2²·b_1_3²
       + c_4_16·b_1_1·b_7_40 + c_4_16·b_1_1²·b_1_3·b_5_23 + c_4_16·b_1_1³·b_5_23
       + c_4_16·b_1_1⁷·b_1_3 + c_4_16·b_1_0⁴·b_1_1·b_3_10 + c_4_16·b_1_0⁵·b_3_10
       + b_4_15·c_4_16·b_1_1⁴ + b_4_15²·c_4_16 + c_8_49·a_1_2·b_1_1³
       + c_4_16·a_3_11·b_5_23 + c_4_16·b_1_1⁵·a_3_11 + c_4_16·a_1_2·b_1_3²·b_5_24
       + c_4_16·a_1_2·b_1_1²·b_5_23 + b_4_15·c_4_16·a_1_2·b_1_1³
       + c_4_16·a_1_2·b_1_3⁴·a_3_11 + c_4_16·a_1_2²·b_1_3⁶
       + c_4_16·a_1_2²·b_1_3³·a_3_11 + c_4_16²·b_1_1³·b_1_3 + c_4_16²·b_1_1⁴
       + c_4_16²·b_1_0·b_1_1³ + c_4_16²·b_1_3·a_3_11 + c_4_16²·a_1_2·b_1_3³
       + c_4_16²·a_1_2·b_1_1³ + c_4_16²·a_1_2·a_3_11 + c_4_16²·a_1_2²·b_1_3²
       + c_4_16²·a_1_2³·b_1_3
51. b_4_15·b_8_47 + b_8_47·b_1_3·a_3_11 + b_8_47·a_1_2²·b_1_3²
       + a_1_2²·b_1_3²·a_3_11·b_5_24 + c_4_16·b_1_1²·b_1_3·b_5_23 + c_4_16·b_1_1³·b_5_23
       + c_4_16·b_1_0·b_1_1²·b_5_23 + b_4_15²·c_4_16 + b_4_15·c_4_16·b_1_1·a_3_11
       + b_4_15·c_4_16·a_1_2·b_1_1³ + c_4_16·a_1_2·b_1_3⁴·a_3_11
       + c_4_16·a_1_2²·b_1_3⁶ + c_4_16²·a_1_2·b_1_1³ + c_4_16²·a_1_2²·b_1_3²
52. b_1_0⁹·b_1_1·b_3_10 + b_1_0¹²·b_1_1 + b_8_47·b_5_22 + b_8_47·b_1_0²·b_3_10
       + b_8_47·b_1_0⁵ + b_8_47·a_1_2·b_1_1⁴ + b_8_47·a_1_2·b_1_3·a_3_11
       + c_8_49·b_1_0·b_1_1·b_3_10 + c_8_49·b_1_0²·b_3_10 + c_8_49·b_1_0⁴·b_1_1
       + c_4_16·b_1_1³·b_1_3·b_5_23 + c_4_16·b_1_1⁴·b_5_23 + c_4_16·b_1_0⁵·b_1_1·b_3_10
       + c_4_16·b_1_0⁶·b_3_10 + c_4_16·b_1_0⁹ + c_4_16·b_8_47·b_1_3 + c_4_16·b_8_47·b_1_1
       + c_4_16·b_8_47·b_1_0 + b_4_15²·c_4_16·b_1_1 + c_8_49·b_1_1²·a_3_11
       + c_8_49·a_1_2·b_1_1⁴ + c_4_16·b_1_1·a_3_11·b_5_23 + c_4_16·a_1_2·b_1_1³·b_5_23
       + c_4_16·a_1_2·b_1_1⁸ + b_4_15·c_4_16·b_1_1²·a_3_11 + c_4_16²·b_1_0·b_1_1·b_3_10
       + c_4_16²·b_1_0²·b_3_10 + c_4_16²·b_1_0⁵ + b_4_15·c_4_16²·b_1_0
       + c_4_16²·b_1_1²·a_3_11 + c_4_16²·a_1_2·b_1_1⁴ + b_4_15·c_4_16²·a_1_2
       + c_4_16²·a_1_2·b_1_3·a_3_11
53. b_1_0⁹·b_1_1·b_3_10 + b_1_0¹²·b_1_1 + b_8_47·b_5_23 + b_8_47·b_5_22 + b_8_47·b_1_1⁵
       + b_8_47·b_1_0⁴·b_1_1 + b_8_47·b_1_0⁵ + b_8_47·b_1_3²·a_3_11
       + b_8_47·a_1_2·b_1_1⁴ + b_4_15·b_1_1·a_3_11·b_5_23 + b_4_15·b_1_1⁶·a_3_11
       + b_4_15·a_1_2·b_1_1³·b_5_23 + b_4_15³·a_1_2 + a_1_2²·b_1_3⁸·a_3_11
       + b_8_47·a_1_2²·a_3_11 + c_8_49·b_1_1⁴·b_1_3 + c_8_49·b_1_1⁵
       + c_8_49·b_1_0²·b_3_10 + c_8_49·b_1_0⁴·b_1_1 + c_4_16·b_1_1³·b_1_3·b_5_23
       + c_4_16·b_1_1⁴·b_5_23 + c_4_16·b_1_1⁸·b_1_3 + c_4_16·b_1_1⁹
       + c_4_16·b_1_0⁴·b_5_23 + c_4_16·b_1_0⁵·b_1_1·b_3_10 + c_4_16·b_1_0⁸·b_1_1
       + c_4_16·b_1_0⁹ + c_4_16·b_8_47·b_1_1 + b_4_15·c_8_49·b_1_3 + b_4_15·c_8_49·b_1_1
       + b_4_15·c_4_16·b_5_23 + b_4_15·c_4_16·b_1_1⁵ + b_4_15²·c_4_16·b_1_1
       + c_8_49·b_1_3²·a_3_11 + c_8_49·a_1_2·b_1_1⁴ + c_4_16·b_1_1·a_3_11·b_5_23
       + c_4_16·b_1_1⁶·a_3_11 + c_4_16·b_8_47·a_1_2 + b_4_15²·c_4_16·a_1_2
       + c_8_49·a_1_2²·b_1_3³ + c_4_16·a_1_2·b_1_3⁵·a_3_11 + c_8_49·a_1_2²·a_3_11
       + c_4_16·a_1_2²·b_1_3⁴·a_3_11 + c_4_16²·b_1_0²·b_3_10 + b_4_15·c_4_16²·b_1_1
       + b_4_15·c_4_16²·b_1_0 + c_4_16²·b_1_3²·a_3_11 + c_4_16²·b_1_1²·a_3_11
       + c_4_16²·a_1_2·b_1_3·a_3_11 + c_4_16²·a_1_2²·a_3_11
54. b_8_47·b_5_24 + b_8_47·b_1_1⁵ + b_8_47·b_1_0⁴·b_1_1 + b_1_3¹⁰·a_3_11
       + b_1_1¹⁰·a_3_11 + b_8_47·b_1_3²·a_3_11 + b_8_47·a_1_2·b_1_3⁴
       + b_8_47·a_1_2·b_1_1⁴ + b_4_15·b_1_1·a_3_11·b_5_23 + b_4_15·a_1_2·b_1_1³·b_5_23
       + b_4_15³·a_1_2 + a_1_2·b_1_3⁹·a_3_11 + c_8_49·b_1_1⁴·b_1_3 + c_8_49·b_1_1⁵
       + c_8_49·b_1_0·b_1_1·b_3_10 + c_4_16·b_1_3⁹ + c_4_16·b_1_1³·b_1_3·b_5_23
       + c_4_16·b_1_1⁴·b_5_23 + c_4_16·b_1_1⁹ + c_4_16·b_1_0⁵·b_1_1·b_3_10
       + c_4_16·b_1_0⁸·b_1_1 + c_4_16·b_8_47·b_1_0 + b_4_15·c_8_49·b_1_3
       + b_4_15·c_8_49·b_1_1 + b_4_15·c_4_16·b_5_23 + b_4_15·c_4_16·b_5_22
       + b_4_15²·c_4_16·b_1_1 + c_8_49·b_1_3²·a_3_11 + c_8_49·b_1_1²·a_3_11
       + c_8_49·a_1_2·b_1_1⁴ + c_4_16·b_1_3·a_3_11·b_5_24 + c_4_16·a_1_2·b_1_3³·b_5_24
       + c_4_16·a_1_2·b_1_1⁸ + b_4_15·c_8_49·a_1_2 + b_4_15²·c_4_16·a_1_2
       + c_8_49·a_1_2·b_1_3·a_3_11 + c_4_16·a_1_2·b_1_3⁵·a_3_11 + c_4_16·a_1_2²·b_1_3⁷
       + c_8_49·a_1_2²·a_3_11 + c_4_16²·b_1_1⁴·b_1_3 + c_4_16²·b_1_1⁵
       + c_4_16²·b_1_0·b_1_1·b_3_10 + c_4_16²·b_1_0⁴·b_1_1 + b_4_15·c_4_16²·b_1_3
       + b_4_15·c_4_16²·b_1_0 + c_4_16²·b_1_3²·a_3_11 + c_4_16²·a_1_2·b_1_3·a_3_11
       + c_4_16²·a_1_2²·a_3_11
55. b_7_40² + b_1_1¹³·b_1_3 + b_8_47·b_1_1⁶ + b_4_15²·b_1_1·b_5_23 + b_1_1¹¹·a_3_11
       + b_4_15·b_1_1⁷·a_3_11 + b_4_15³·a_1_2·b_1_1 + c_8_49·b_1_1⁵·b_1_3 + c_8_49·b_1_1⁶
       + c_8_49·b_1_0³·b_3_10 + c_4_16·b_1_1⁹·b_1_3 + c_4_16·b_1_1¹⁰
       + c_4_16·b_8_47·b_1_1² + b_4_15·c_4_16·b_1_3·b_5_23 + b_4_15·c_4_16·b_1_1·b_5_23
       + b_4_15·c_4_16·b_1_1⁶ + b_4_15²·c_4_16·b_1_1² + c_8_49·b_1_1³·a_3_11
       + c_4_16·a_3_11·b_7_40 + b_4_15·c_8_49·a_1_2·b_1_1 + b_4_15²·c_4_16·a_1_2·b_1_1
       + c_4_16·a_1_2·b_1_3⁶·a_3_11 + c_4_16·a_1_2²·b_1_3⁸
       + c_4_16·a_1_2²·a_3_11·b_5_24 + c_4_16·a_1_2²·b_1_3⁵·a_3_11
       + c_4_16·c_8_49·b_1_0² + c_4_16²·b_1_1⁵·b_1_3 + c_4_16²·b_1_0⁵·b_1_1
       + b_4_15·c_4_16²·b_1_1² + c_4_16²·a_3_11·b_3_10 + c_4_16²·b_1_3³·a_3_11
       + c_4_16²·a_1_2²·b_1_3⁴ + c_4_16²·a_1_2²·b_1_3·a_3_11 + c_4_16³·b_1_0²
56. b_8_47·b_7_40 + b_8_47·b_1_1⁷ + b_8_47·a_1_2·b_1_1⁶ + b_8_47·a_1_2²·b_1_3⁵
       + c_8_49·b_1_1⁶·b_1_3 + c_8_49·b_1_1⁷ + c_8_49·b_1_0⁴·b_3_10
       + c_4_16·b_1_1¹⁰·b_1_3 + c_4_16·b_1_1¹¹ + c_4_16·b_1_0⁷·b_1_1·b_3_10
       + c_4_16·b_1_0¹⁰·b_1_1 + c_4_16·b_8_47·b_3_10 + c_4_16·b_8_47·b_1_1³
       + c_4_16·b_8_47·b_1_0²·b_1_1 + b_4_15·c_8_49·b_1_1²·b_1_3 + b_4_15·c_8_49·b_1_1³
       + c_8_49·b_1_1⁴·a_3_11 + c_8_49·a_1_2·b_1_1⁶ + c_4_16·b_1_1·a_3_11·b_7_40
       + c_4_16·b_8_47·a_1_2·b_1_3² + b_4_15·c_8_49·a_1_2·b_1_1²
       + b_4_15·c_4_16·a_1_2·b_1_1·b_5_23 + b_4_15²·c_4_16·a_1_2·b_1_1²
       + c_4_16·a_1_2²·b_1_3⁶·a_3_11 + c_4_16·c_8_49·b_1_0²·b_1_1
       + c_4_16·c_8_49·b_1_0³ + c_4_16²·b_1_1⁶·b_1_3 + c_4_16²·b_1_1⁷
       + c_4_16²·b_1_0²·b_5_23 + c_4_16²·b_1_0²·b_5_22 + c_4_16²·b_1_0⁶·b_1_1
       + b_4_15·c_4_16²·b_1_1²·b_1_3 + c_4_16·c_8_49·a_1_2·b_1_1²
       + b_4_15·c_4_16²·a_3_11 + c_4_16²·a_1_2·b_1_3³·a_3_11 + c_4_16²·a_1_2²·b_1_3⁵
       + c_4_16²·a_1_2²·b_1_3²·a_3_11 + c_4_16²·a_1_2³·b_1_3·a_3_11 + c_4_16³·b_1_0³
       + c_4_16³·a_1_2·b_1_1² + c_4_16³·a_1_2²·b_1_3
57. b_8_47·b_1_1⁸ + b_8_47² + b_1_3¹³·a_3_11 + b_1_1¹³·a_3_11 + b_8_47·a_1_2·b_1_3⁷
       + b_4_15·b_1_1⁹·a_3_11 + a_1_2·b_1_3¹²·a_3_11 + a_1_2²·b_1_3¹¹·a_3_11
       + b_8_47·a_1_2²·b_1_3³·a_3_11 + c_8_49·b_1_1⁷·b_1_3 + c_8_49·b_1_1⁸
       + c_8_49·b_1_0⁵·b_3_10 + c_4_16·b_1_3¹² + c_4_16·b_1_1¹² + c_4_16·b_8_47·b_1_1⁴
       + b_4_15·c_4_16·b_1_1²·b_1_3·b_5_23 + b_4_15·c_4_16·b_1_1³·b_5_23
       + b_4_15·c_4_16·b_1_1⁸ + b_4_15²·c_8_49 + b_4_15³·c_4_16 + c_8_49·b_1_1⁵·a_3_11
       + b_4_15·c_8_49·a_1_2·b_1_1³ + b_4_15·c_4_16·a_3_11·b_5_23
       + b_4_15·c_4_16·b_1_1⁵·a_3_11 + b_4_15²·c_4_16·a_1_2·b_1_1³
       + c_8_49·a_1_2·b_1_3⁴·a_3_11 + c_4_16·a_1_2·b_1_3⁸·a_3_11
       + c_4_16·a_1_2²·b_1_3¹⁰ + c_4_16·a_1_2²·b_1_3⁷·a_3_11 + c_4_16·c_8_49·b_1_0⁴
       + c_4_16²·b_1_1⁷·b_1_3 + c_4_16²·b_1_1⁸ + c_4_16²·b_1_0⁷·b_1_1
       + c_4_16²·b_1_0⁸ + b_4_15·c_4_16²·b_1_1⁴ + c_4_16²·b_1_1⁵·a_3_11
       + c_4_16²·a_1_2·b_1_1²·b_5_23 + b_4_15·c_4_16²·a_1_2·b_1_1³
       + c_4_16·c_8_49·a_1_2²·b_1_3² + c_4_16³·b_1_0⁴ + c_4_16³·a_1_2³·b_1_3

About the group

Ring generators

Ring relations

Completion information

Restriction maps

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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_4_16, a Duflot regular element of degree 4
  2. c_8_49, a Duflot regular element of degree 8
  3. b_1_3² + b_1_1·b_1_3 + b_1_1² + b_1_0², an element of degree 2
• 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

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Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 2

1. a_1_2 → 0, an element of degree 1
2. b_1_0 → 0, an element of degree 1
3. b_1_1 → 0, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. a_3_11 → 0, an element of degree 3
6. b_3_10 → 0, an element of degree 3
7. b_4_15 → 0, an element of degree 4
8. c_4_16 → c_1_0⁴, an element of degree 4
9. b_5_22 → 0, an element of degree 5
10. b_5_23 → 0, an element of degree 5
11. b_5_24 → 0, an element of degree 5
12. b_7_40 → 0, an element of degree 7
13. b_8_47 → 0, an element of degree 8
14. c_8_49 → c_1_1⁸ + c_1_0⁸, an element of degree 8

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

1. a_1_2 → 0, an element of degree 1
2. b_1_0 → c_1_2, an element of degree 1
3. b_1_1 → 0, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. a_3_11 → 0, an element of degree 3
6. b_3_10 → c_1_0·c_1_2² + c_1_0²·c_1_2, an element of degree 3
7. b_4_15 → 0, an element of degree 4
8. c_4_16 → c_1_0·c_1_2³ + c_1_0⁴, an element of degree 4
9. b_5_22 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2 + c_1_0²·c_1_2³ + c_1_0⁴·c_1_2, an element of degree 5
10. b_5_23 → c_1_0²·c_1_2³ + c_1_0⁴·c_1_2, an element of degree 5
11. b_5_24 → c_1_0·c_1_2⁴ + c_1_0⁴·c_1_2, an element of degree 5
12. b_7_40 → c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2² + c_1_0²·c_1_2⁵
       + c_1_0²·c_1_1²·c_1_2³ + c_1_0²·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_2³, an element of degree 7
13. b_8_47 → c_1_0·c_1_2⁷ + c_1_0·c_1_1²·c_1_2⁵ + 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, an element of degree 8
14. c_8_49 → c_1_1⁴·c_1_2⁴ + c_1_1⁸ + c_1_0·c_1_2⁷ + c_1_0²·c_1_2⁶ + c_1_0³·c_1_2⁵
       + c_1_0⁵·c_1_2³ + c_1_0⁶·c_1_2² + c_1_0⁸, an element of degree 8

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

1. a_1_2 → 0, an element of degree 1
2. b_1_0 → 0, an element of degree 1
3. b_1_1 → c_1_2, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. a_3_11 → 0, an element of degree 3
6. b_3_10 → 0, an element of degree 3
7. b_4_15 → c_1_0·c_1_2³ + c_1_0²·c_1_2², an element of degree 4
8. c_4_16 → c_1_0·c_1_2³ + c_1_0⁴, an element of degree 4
9. b_5_22 → c_1_0²·c_1_2³ + c_1_0⁴·c_1_2, an element of degree 5
10. b_5_23 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2 + c_1_0·c_1_2⁴ + c_1_0²·c_1_2³, an element of degree 5
11. b_5_24 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2, an element of degree 5
12. b_7_40 → c_1_1²·c_1_2⁵ + c_1_1⁴·c_1_2³, an element of degree 7
13. b_8_47 → c_1_1²·c_1_2⁶ + c_1_1⁴·c_1_2⁴ + c_1_0·c_1_2⁷ + c_1_0·c_1_1²·c_1_2⁵
       + 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_0³·c_1_2⁵ + c_1_0⁴·c_1_2⁴ + c_1_0⁵·c_1_2³
       + c_1_0⁶·c_1_2², an element of degree 8
14. c_8_49 → c_1_1²·c_1_2⁶ + c_1_1⁸ + c_1_0²·c_1_2⁶ + c_1_0³·c_1_2⁵ + c_1_0⁴·c_1_2⁴
       + c_1_0⁵·c_1_2³ + c_1_0⁶·c_1_2² + c_1_0⁸, an element of degree 8

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

1. a_1_2 → 0, an element of degree 1
2. b_1_0 → 0, an element of degree 1
3. b_1_1 → 0, an element of degree 1
4. b_1_3 → c_1_2, an element of degree 1
5. a_3_11 → 0, an element of degree 3
6. b_3_10 → 0, an element of degree 3
7. b_4_15 → 0, an element of degree 4
8. c_4_16 → c_1_0²·c_1_2² + c_1_0⁴, an element of degree 4
9. b_5_22 → c_1_0²·c_1_2³ + c_1_0⁴·c_1_2, an element of degree 5
10. b_5_23 → c_1_0²·c_1_2³ + c_1_0⁴·c_1_2, an element of degree 5
11. b_5_24 → c_1_0·c_1_2⁴ + c_1_0²·c_1_2³, an element of degree 5
12. b_7_40 → 0, an element of degree 7
13. b_8_47 → c_1_0·c_1_2⁷ + c_1_0²·c_1_2⁶, an element of degree 8
14. c_8_49 → c_1_1⁴·c_1_2⁴ + c_1_1⁸ + c_1_0⁴·c_1_2⁴ + c_1_0⁸, an element of degree 8

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

1. a_1_2 → 0, an element of degree 1
2. b_1_0 → 0, an element of degree 1
3. b_1_1 → c_1_2, an element of degree 1
4. b_1_3 → c_1_2, an element of degree 1
5. a_3_11 → 0, an element of degree 3
6. b_3_10 → c_1_2³, an element of degree 3
7. b_4_15 → 0, an element of degree 4
8. c_4_16 → c_1_2⁴ + c_1_0²·c_1_2² + c_1_0⁴, an element of degree 4
9. b_5_22 → 0, an element of degree 5
10. b_5_23 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2 + c_1_0²·c_1_2³ + c_1_0⁴·c_1_2, an element of degree 5
11. b_5_24 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2, an element of degree 5
12. b_7_40 → c_1_0²·c_1_2⁵ + c_1_0⁴·c_1_2³, an element of degree 7
13. b_8_47 → 0, an element of degree 8
14. c_8_49 → c_1_1²·c_1_2⁶ + c_1_1⁸ + c_1_0⁴·c_1_2⁴ + c_1_0⁸, an element of degree 8

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128