David J. Green

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Cohomology of group number 1311 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 4.
• It is non-abelian.
• It has p-Rank 4.
• Its center has rank 3.
• It has 2 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 4.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 4 and depth 3.
• The depth coincides with the Duflot bound.
• The Poincaré series is

  (t3  +  2·t  +  1) · (t3  +  t2  +  1)

  (t  +  1)2 · (t  −  1)4 · (t2  +  1)2

• The a-invariants are -∞,-∞,-∞,-5,-4. 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 15 minimal generators of maximal degree 5:

1. a_1_1, a nilpotent element of degree 1
2. a_1_2, a nilpotent element of degree 1
3. b_1_0, an element of degree 1
4. b_1_3, an element of degree 1
5. c_2_7, a Duflot regular element of degree 2
6. a_3_11, a nilpotent element of degree 3
7. a_3_10, a nilpotent element of degree 3
8. b_3_12, an element of degree 3
9. b_3_13, an element of degree 3
10. b_3_14, an element of degree 3
11. b_3_15, an element of degree 3
12. c_4_26, a Duflot regular element of degree 4
13. c_4_27, a Duflot regular element of degree 4
14. b_5_43, an element of degree 5
15. b_5_44, an element of degree 5

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 10:

1. a_1_2² + a_1_1·a_1_2 + a_1_1²
2. a_1_2·b_1_0
3. b_1_0·b_1_3 + a_1_1·b_1_0 + a_1_1²
4. a_1_1³
5. a_1_1²·b_1_3
6. a_1_2·a_3_11 + a_1_1·a_3_10 + c_2_7·a_1_1²
7. b_1_0·a_3_10 + c_2_7·a_1_1·b_1_0
8. a_1_2·a_3_10 + a_1_2·a_3_11 + a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2
9. b_1_0·a_3_11 + a_1_1·b_3_12 + a_1_2·a_3_11 + c_2_7·a_1_1·a_1_2 + c_2_7·a_1_1²
10. b_1_3·b_3_12 + b_1_3·a_3_10 + b_1_0·a_3_11 + a_1_1·a_3_11 + c_2_7·a_1_2·b_1_3
11. a_1_2·b_3_12 + a_1_2·a_3_11 + a_1_1·a_3_11 + c_2_7·a_1_1²
12. a_1_2·b_3_13 + a_1_2·a_3_11 + c_2_7·a_1_2·b_1_3
13. b_1_3·b_3_13 + a_1_1·b_3_14 + a_1_1·b_3_13 + c_2_7·b_1_3² + c_2_7·a_1_1·b_1_3
14. b_1_0·b_3_14 + a_1_1·b_3_13 + c_2_7·a_1_1·b_1_3
15. b_1_3·b_3_13 + b_1_3·a_3_10 + a_1_2·b_3_14 + a_1_1·b_3_15 + c_2_7·b_1_3²
       + c_2_7·a_1_1²
16. b_1_0·b_3_15 + b_1_0·b_3_13 + a_1_1·b_3_13 + c_2_7·a_1_1·b_1_3 + c_2_7·a_1_1·b_1_0
17. b_1_3·b_3_13 + b_1_3·a_3_10 + b_1_3·a_3_11 + a_1_2·b_3_15 + a_1_1·b_3_13 + a_1_2·a_3_11
       + c_2_7·b_1_3² + c_2_7·a_1_2·b_1_3 + c_2_7·a_1_1·a_1_2
18. a_1_1²·b_3_14 + a_1_1²·a_3_11
19. a_3_10² + a_3_11·a_3_10 + a_3_11² + c_2_7·a_1_1·a_3_11 + c_2_7²·a_1_1²
20. a_3_10·b_3_12 + a_3_11·a_3_10 + a_3_11² + c_2_7·a_1_1·b_3_12
21. b_3_12·b_3_15 + b_3_12·b_3_13 + a_3_10·b_3_15 + a_3_10·b_3_12 + a_3_11·b_3_13 + a_3_11²
       + c_2_7·a_1_1·b_3_14 + c_2_7·a_1_1·b_3_13 + c_2_7·a_1_1·a_3_10 + c_2_7·a_1_1·a_3_11
22. a_3_10·b_3_13 + a_3_11·a_3_10 + c_2_7·a_1_2·b_3_14 + c_2_7·a_1_1·b_3_15
       + c_2_7·a_1_1·b_3_14 + c_2_7·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3²
       + c_2_7²·a_1_1²
23. b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_13² + a_3_11·b_3_15 + a_3_11·b_3_14 + a_3_11·b_3_13
       + c_2_7·b_1_3·b_3_15 + c_2_7·b_1_3·b_3_14 + c_2_7·a_1_2·b_1_3³ + c_2_7·a_1_1·b_3_14
       + c_2_7·a_1_1·b_1_3³ + c_2_7·a_1_1·a_3_11 + c_2_7²·b_1_3²
24. b_3_12·b_3_14 + a_3_10·b_3_14 + a_3_10·b_3_13 + a_3_11·b_3_13 + a_3_11·a_3_10
       + c_2_7·a_1_2·b_3_15 + c_2_7·a_1_2·b_3_14 + c_2_7·a_1_1·b_3_14 + c_2_7·a_1_1·b_3_13
       + c_2_7·a_1_1·a_3_10 + c_2_7·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3²
       + c_2_7²·a_1_2·b_1_3 + c_2_7²·a_1_1·a_1_2 + c_2_7²·a_1_1²
25. a_3_11² + c_4_26·a_1_1² + c_2_7·a_1_1·a_1_2·b_1_3² + c_2_7²·a_1_1²
26. b_3_12·b_3_15 + b_3_12·b_3_13 + a_3_10·b_3_14 + a_3_10·b_3_12 + a_3_11·b_3_15
       + a_3_11·a_3_10 + a_3_11² + a_1_1·a_1_2·b_1_3·b_3_15 + c_4_26·a_1_1·b_1_3
       + c_2_7·a_1_2·b_3_14 + c_2_7·a_1_2·b_1_3³ + c_2_7·a_1_1·b_3_14 + c_2_7·a_1_1·a_3_11
       + c_2_7²·a_1_1·b_1_3
27. a_3_10·b_3_14 + a_3_11·b_3_15 + a_3_11·b_3_14 + a_3_11·b_3_13 + a_1_1·a_1_2·b_1_3·b_3_15
       + c_4_26·a_1_2·b_1_3 + c_2_7·a_1_2·b_1_3³ + c_2_7·a_1_1·b_3_14 + c_2_7·a_1_1·b_1_3³
       + c_2_7·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3² + c_2_7²·a_1_2·b_1_3
28. a_3_11·b_3_12 + a_3_11·a_3_10 + c_4_26·a_1_1·b_1_0 + c_2_7·a_1_1·a_3_10
       + c_2_7²·a_1_1·b_1_0 + c_2_7²·a_1_1²
29. b_3_12² + a_1_1·b_1_0²·b_3_12 + a_1_1·b_1_0⁵ + a_3_11·a_3_10 + a_3_11²
       + c_4_26·b_1_0² + c_2_7·a_1_1·a_3_11 + c_2_7²·b_1_0² + c_2_7²·a_1_1·a_1_2
30. a_3_11·a_3_10 + c_4_26·a_1_1·a_1_2 + c_2_7·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3²
       + c_2_7²·a_1_1·a_1_2
31. b_3_14² + a_1_2·b_1_3²·b_3_14 + a_1_1·b_1_3²·b_3_15 + a_1_1·b_1_3²·b_3_14
       + a_3_11² + a_1_1·a_1_2·b_1_3·b_3_14 + c_4_26·b_1_3² + c_2_7·a_1_1·b_1_3³
       + c_4_27·a_1_1² + c_2_7·a_1_1·a_1_2·b_1_3² + c_2_7²·b_1_3² + c_2_7²·a_1_1²
32. b_3_13·b_3_14 + b_3_12·b_3_15 + b_3_12·b_3_13 + a_3_10·b_3_14 + a_3_10·b_3_12
       + a_3_11·b_3_15 + a_3_11·a_3_10 + a_1_1·a_1_2·b_1_3·b_3_15 + a_1_1·a_1_2·b_1_3·b_3_14
       + c_2_7·b_1_3·b_3_14 + c_4_27·a_1_1·b_1_0 + c_2_7·a_1_2·b_3_14 + c_2_7·a_1_2·b_1_3³
       + c_2_7·a_1_1·b_3_14 + c_2_7·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3²
       + c_2_7²·a_1_1·b_1_0
33. b_3_13² + a_1_1·b_1_0²·b_3_12 + a_1_1·b_1_0⁵ + a_3_11² + c_4_27·b_1_0²
       + c_2_7·a_1_1·a_1_2·b_1_3² + c_2_7²·b_1_3² + c_2_7²·b_1_0²
34. b_3_15² + b_3_13² + a_1_2·b_1_3²·b_3_15 + a_1_1·b_1_3²·b_3_15
       + a_1_1·b_1_3²·b_3_14 + a_3_11·a_3_10 + c_4_26·b_1_3² + c_2_7·b_1_3⁴
       + c_2_7·a_1_2·b_1_3³ + c_2_7·a_1_1·b_1_3³ + c_4_27·a_1_1·a_1_2 + c_2_7·a_1_1·a_3_11
       + c_2_7²·b_1_3² + c_2_7²·a_1_1·a_1_2 + c_2_7²·a_1_1²
35. b_3_15² + b_3_14² + b_3_13² + b_3_12·b_3_15 + b_3_12·b_3_14 + b_3_12·b_3_13
       + a_3_10·b_3_12 + a_3_11·b_3_15 + a_1_2·b_1_3²·b_3_15 + a_1_2·b_1_3²·b_3_14
       + a_1_1·b_5_43 + a_1_1·b_1_3²·b_3_15 + a_1_1·b_1_3²·b_3_14 + a_3_11·a_3_10 + a_3_11²
       + a_1_1·a_1_2·b_1_3·b_3_15 + a_1_1·a_1_2·b_1_3·b_3_14 + c_2_7·b_1_3⁴
       + c_2_7·a_1_1·b_3_14 + c_2_7·a_1_1·b_3_13 + c_2_7·a_1_1·b_1_3³ + c_2_7·a_1_1·a_3_10
       + c_2_7²·a_1_1·b_1_3 + c_2_7²·a_1_1·b_1_0
36. b_3_12·b_3_15 + b_3_12·b_3_13 + b_1_3·b_5_43 + b_1_3³·b_3_15 + b_1_3³·b_3_14
       + a_3_10·b_3_13 + a_3_10·b_3_12 + a_3_11² + a_1_1·a_1_2·b_1_3·b_3_15
       + a_1_1·a_1_2·b_1_3·b_3_14 + c_4_26·b_1_3² + c_2_7·b_1_3⁴ + c_4_27·a_1_2·b_1_3
       + c_4_27·a_1_1·b_1_3 + c_2_7·a_1_2·b_3_14 + c_2_7·a_1_2·b_1_3³ + c_2_7·a_1_1·b_3_14
       + c_2_7·a_1_1·b_1_3³ + c_2_7·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3²
       + c_2_7²·b_1_3² + c_2_7²·a_1_2·b_1_3 + c_2_7²·a_1_1·b_1_0 + c_2_7²·a_1_1²
37. b_3_13·b_3_14 + b_3_12·b_3_15 + b_1_0·b_5_43 + a_3_10·b_3_14 + a_3_10·b_3_13
       + a_3_10·b_3_12 + a_3_11·b_3_15 + a_1_1·b_1_0²·b_3_12 + a_3_11·a_3_10 + a_3_11²
       + a_1_1·a_1_2·b_1_3·b_3_15 + a_1_1·a_1_2·b_1_3·b_3_14 + c_2_7·b_1_3·b_3_14
       + c_2_7·b_1_0·b_3_13 + c_2_7·a_1_2·b_3_14 + c_2_7·a_1_2·b_1_3³ + c_2_7·a_1_1·b_3_14
       + c_2_7·a_1_1·b_1_0³ + c_2_7·a_1_1·a_3_10 + c_2_7²·b_1_0² + c_2_7²·a_1_2·b_1_3
       + c_2_7²·a_1_1·b_1_0
38. b_3_14² + a_3_10·b_3_14 + a_3_11·b_3_15 + a_3_11·b_3_14 + a_3_11·b_3_13 + a_1_2·b_5_43
       + a_1_2·b_1_3²·b_3_15 + a_1_1·b_1_3²·b_3_15 + a_1_1·b_1_3²·b_3_14 + a_3_11·a_3_10
       + a_1_1·a_1_2·b_1_3·b_3_15 + a_1_1·a_1_2·b_1_3·b_3_14 + c_4_26·b_1_3²
       + c_2_7·a_1_1·b_3_14 + c_2_7·a_1_1·a_3_10 + c_2_7·a_1_1·a_3_11
       + c_2_7·a_1_1·a_1_2·b_1_3² + c_2_7²·b_1_3² + c_2_7²·a_1_1²
39. b_3_13·b_3_14 + a_3_11·b_3_15 + a_3_11·b_3_14 + a_3_11·b_3_13 + a_1_1·b_5_44
       + a_1_1·b_1_3²·b_3_15 + a_1_1·b_1_0²·b_3_12 + a_3_11·a_3_10 + a_3_11²
       + a_1_1·a_1_2·b_1_3·b_3_15 + a_1_1·a_1_2·b_1_3·b_3_14 + c_2_7·b_1_3·b_3_14
       + c_2_7·a_1_2·b_1_3³ + c_2_7·a_1_1·b_3_13 + c_2_7·a_1_1·b_1_3³ + c_2_7·a_1_1·a_3_10
       + c_2_7·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3² + c_2_7²·a_1_1·b_1_3
40. b_3_15² + b_3_14·b_3_15 + b_3_13² + b_3_12·b_3_15 + b_3_12·b_3_14 + b_3_12·b_3_13
       + b_1_3·b_5_44 + b_1_3³·b_3_15 + a_3_10·b_3_14 + a_3_10·b_3_13 + a_3_10·b_3_12
       + a_3_11·b_3_14 + a_1_2·b_1_3²·b_3_14 + a_1_1·b_1_0²·b_3_12 + a_3_11²
       + c_4_26·b_1_3² + c_2_7·b_1_3·b_3_14 + c_2_7·b_1_3⁴ + c_2_7·a_1_1·a_3_11
       + c_2_7²·b_1_3² + c_2_7²·a_1_1²
41. b_3_13² + b_1_0·b_5_44 + b_1_0³·b_3_12 + a_3_10·b_3_12 + a_3_11·b_3_12 + a_1_1·b_1_0⁵
       + a_3_11² + c_2_7·b_1_0·b_3_13 + c_2_7²·b_1_3² + c_2_7²·a_1_1·a_1_2
42. b_3_12·b_3_15 + b_3_12·b_3_13 + a_3_10·b_3_12 + a_3_11·b_3_15 + a_3_11·b_3_14
       + a_1_2·b_5_44 + a_1_2·b_1_3²·b_3_15 + a_1_1·a_1_2·b_1_3·b_3_15
       + a_1_1·a_1_2·b_1_3·b_3_14 + c_2_7·a_1_2·b_3_14 + c_2_7·a_1_2·b_1_3³
       + c_2_7·a_1_1·a_3_10 + c_2_7·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3²
       + c_2_7²·a_1_1·a_1_2 + c_2_7²·a_1_1²
43. b_3_12·b_5_43 + a_3_10·b_5_43 + a_1_1·b_1_0²·b_5_43 + a_1_1·b_1_0⁴·b_3_13
       + c_4_26·b_1_0·b_3_13 + c_2_7·b_1_0·b_5_43 + c_4_27·a_1_1·b_3_12
       + c_4_26·a_1_1·b_1_0³ + c_2_7·a_1_2·b_1_3²·b_3_15 + c_2_7·a_1_2·b_1_3²·b_3_14
       + c_2_7·a_1_1·b_1_0²·b_3_13 + c_4_27·a_1_1·a_3_10 + c_4_26·a_1_1·a_3_11
       + c_2_7·a_1_1·a_1_2·b_1_3⁴ + c_2_7²·b_1_0·b_3_12 + c_2_7·c_4_27·a_1_1·b_1_0
       + c_2_7·c_4_26·a_1_2·b_1_3 + c_2_7²·a_1_2·b_1_3³ + c_2_7²·a_1_1·b_1_0³
       + c_2_7·c_4_27·a_1_1·a_1_2 + c_2_7·c_4_27·a_1_1² + c_2_7·c_4_26·a_1_1·a_1_2
       + c_2_7·c_4_26·a_1_1² + c_2_7²·a_1_1·a_3_10 + c_2_7²·a_1_1·a_1_2·b_1_3²
       + c_2_7³·b_1_0² + c_2_7³·a_1_2·b_1_3 + c_2_7³·a_1_1·b_1_0 + c_2_7³·a_1_1·a_1_2
44. b_3_15·b_5_43 + b_3_13·b_5_43 + b_1_3³·b_5_44 + b_1_3⁵·b_3_15 + a_1_2·b_1_3⁴·b_3_14
       + a_1_1·b_1_3²·b_5_44 + a_1_1·b_1_3⁴·b_3_15 + a_1_1·a_1_2·b_1_3³·b_3_15
       + c_4_26·b_1_3·b_3_15 + c_4_26·b_1_3⁴ + c_2_7·b_1_3⁶ + c_4_27·a_1_2·b_3_15
       + c_4_27·a_1_1·b_3_15 + c_4_27·a_1_1·b_3_13 + c_4_27·a_1_1·b_3_12 + c_4_26·a_1_2·b_3_14
       + c_4_26·a_1_2·b_1_3³ + c_4_26·a_1_1·b_3_15 + c_2_7·a_1_2·b_1_3²·b_3_14
       + c_2_7·a_1_1·b_5_43 + c_2_7·a_1_1·b_1_3²·b_3_15 + c_2_7·a_1_1·b_1_3²·b_3_14
       + c_2_7·a_1_1·b_1_3⁵ + c_4_26·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3·b_3_15
       + c_2_7·a_1_1·a_1_2·b_1_3⁴ + c_2_7·c_4_26·b_1_3² + c_2_7²·b_1_3·b_3_15
       + c_2_7²·b_1_3⁴ + c_2_7·c_4_27·a_1_2·b_1_3 + c_2_7·c_4_27·a_1_1·b_1_0
       + c_2_7·c_4_26·a_1_2·b_1_3 + c_2_7²·a_1_2·b_3_15 + c_2_7²·a_1_2·b_3_14
       + c_2_7²·a_1_1·b_3_12 + c_2_7²·a_1_1·a_3_11 + c_2_7²·a_1_1·a_1_2·b_1_3²
       + c_2_7³·b_1_3² + c_2_7³·a_1_1·b_1_3 + c_2_7³·a_1_1·b_1_0
45. a_3_10·b_5_43 + a_1_2·b_1_3²·b_5_44 + a_1_2·b_1_3⁴·b_3_15
       + a_1_1·a_1_2·b_1_3³·b_3_14 + c_4_26·a_1_2·b_3_14 + c_4_26·a_1_2·b_1_3³
       + c_4_26·a_1_1·b_3_15 + c_4_26·a_1_1·b_3_14 + c_4_26·a_1_1·b_3_13 + c_2_7·a_1_1·b_5_43
       + c_2_7·a_1_1·b_1_3⁵ + c_4_27·a_1_1·a_3_11 + c_4_26·a_1_1·a_3_10
       + c_4_26·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3⁴ + c_2_7²·a_1_2·b_3_14
       + c_2_7²·a_1_2·b_1_3³ + c_2_7²·a_1_1·b_3_15 + c_2_7²·a_1_1·b_3_14
       + c_2_7²·a_1_1·b_3_13 + c_2_7·c_4_26·a_1_1·a_1_2 + c_2_7·c_4_26·a_1_1²
       + c_2_7²·a_1_1·a_3_10 + c_2_7³·a_1_1·a_1_2 + c_2_7³·a_1_1²
46. a_3_11·b_5_43 + a_1_1·b_1_3²·b_5_44 + a_1_1·b_1_3⁴·b_3_15 + a_1_1·a_1_2·b_1_3·b_5_44
       + c_4_26·a_1_2·b_3_15 + c_4_26·a_1_2·b_3_14 + c_4_26·a_1_1·b_3_15
       + c_4_26·a_1_1·b_1_3³ + c_2_7·a_1_2·b_1_3⁵ + c_2_7·a_1_1·b_5_43
       + c_2_7·a_1_1·b_1_3²·b_3_15 + c_2_7·a_1_1·b_1_3²·b_3_14 + c_2_7·a_1_1·b_1_3⁵
       + c_4_27·a_1_1·a_3_10 + c_4_27·a_1_1·a_3_11 + c_4_26·a_1_1·a_3_11
       + c_2_7·a_1_1·a_1_2·b_1_3·b_3_14 + c_2_7·a_1_1·a_1_2·b_1_3⁴
       + c_2_7·c_4_26·a_1_2·b_1_3 + c_2_7²·a_1_2·b_3_15 + c_2_7²·a_1_2·b_3_14
       + c_2_7²·a_1_1·b_3_15 + c_2_7²·a_1_1·b_3_13 + c_2_7²·a_1_1·b_3_12
       + c_2_7·c_4_27·a_1_1·a_1_2 + c_2_7·c_4_26·a_1_1·a_1_2 + c_2_7·c_4_26·a_1_1²
       + c_2_7²·a_1_1·a_3_10 + c_2_7²·a_1_1·a_3_11 + c_2_7²·a_1_1·a_1_2·b_1_3²
       + c_2_7³·a_1_2·b_1_3 + c_2_7³·a_1_1·b_1_3 + c_2_7³·a_1_1·b_1_0 + c_2_7³·a_1_1·a_1_2
47. b_3_13·b_5_43 + b_3_12·b_5_44 + b_3_12·b_5_43 + a_3_11·b_5_43 + a_1_1·b_1_3²·b_5_44
       + a_1_1·b_1_3⁴·b_3_15 + a_1_1·b_1_0⁴·b_3_13 + a_1_1·b_1_0⁷ + c_4_26·b_1_0·b_3_13
       + c_4_26·b_1_0⁴ + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_3³·b_3_14 + c_4_27·a_1_1·b_3_13
       + c_4_27·a_1_1·b_3_12 + c_4_26·a_1_2·b_1_3³ + c_4_26·a_1_1·b_3_15
       + c_4_26·a_1_1·b_3_14 + c_4_26·a_1_1·b_3_12 + c_4_26·a_1_1·b_1_3³
       + c_4_26·a_1_1·b_1_0³ + c_2_7·a_1_2·b_1_3⁵ + c_2_7·a_1_1·b_1_3²·b_3_15
       + c_2_7·a_1_1·b_1_3²·b_3_14 + c_2_7·a_1_1·b_1_3⁵ + c_2_7·a_1_1·b_1_0²·b_3_13
       + c_2_7·a_1_1·b_1_0⁵ + c_4_27·a_1_1·a_3_10 + c_4_26·a_1_1·a_3_10
       + c_2_7·a_1_1·a_1_2·b_1_3·b_3_15 + c_2_7·c_4_27·b_1_0² + c_2_7·c_4_26·b_1_3²
       + c_2_7²·b_1_3⁴ + c_2_7²·b_1_0·b_3_12 + c_2_7²·b_1_0⁴ + c_2_7·c_4_27·a_1_2·b_1_3
       + c_2_7·c_4_27·a_1_1·b_1_0 + c_2_7·c_4_26·a_1_2·b_1_3 + c_2_7·c_4_26·a_1_1·b_1_3
       + c_2_7·c_4_26·a_1_1·b_1_0 + c_2_7²·a_1_2·b_3_15 + c_2_7²·a_1_2·b_1_3³
       + c_2_7²·a_1_1·b_3_15 + c_2_7²·a_1_1·b_3_14 + c_2_7²·a_1_1·b_1_3³
       + c_2_7²·a_1_1·b_1_0³ + c_2_7·c_4_26·a_1_1·a_1_2 + c_2_7·c_4_26·a_1_1²
       + c_2_7³·b_1_3² + c_2_7³·b_1_0² + c_2_7³·a_1_2·b_1_3 + c_2_7³·a_1_1·a_1_2
48. b_3_14·b_5_44 + b_3_14·b_5_43 + a_1_2·b_1_3⁴·b_3_14 + a_1_1·b_1_3⁴·b_3_15
       + a_1_1·b_1_3⁴·b_3_14 + a_1_1·b_1_0²·b_5_43 + c_4_26·b_1_3·b_3_15
       + c_4_26·b_1_3·b_3_14 + c_4_26·b_1_3⁴ + c_2_7·b_1_3³·b_3_14 + c_4_27·a_1_2·b_3_14
       + c_4_27·a_1_1·b_3_14 + c_4_27·a_1_1·b_3_13 + c_4_27·a_1_1·b_3_12 + c_4_26·a_1_2·b_3_15
       + c_4_26·a_1_2·b_3_14 + c_4_26·a_1_2·b_1_3³ + c_4_26·a_1_1·b_3_15
       + c_2_7·a_1_2·b_1_3²·b_3_14 + c_2_7·a_1_1·b_1_3²·b_3_14
       + c_2_7·a_1_1·b_1_0²·b_3_13 + c_4_26·a_1_1·a_3_11 + c_2_7·a_1_1·a_1_2·b_1_3⁴
       + c_2_7·c_4_26·b_1_3² + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3·b_3_14
       + c_2_7²·b_1_3⁴ + c_2_7·c_4_27·a_1_1·b_1_3 + c_2_7·c_4_26·a_1_2·b_1_3
       + c_2_7²·a_1_2·b_3_15 + c_2_7²·a_1_2·b_1_3³ + c_2_7²·a_1_1·b_3_15
       + c_2_7²·a_1_1·b_3_12 + c_2_7²·a_1_1·b_1_0³ + c_2_7·c_4_27·a_1_1·a_1_2
       + c_2_7·c_4_27·a_1_1² + c_2_7·c_4_26·a_1_1·a_1_2 + c_2_7·c_4_26·a_1_1²
       + c_2_7²·a_1_1·a_3_11 + c_2_7³·b_1_3² + c_2_7³·a_1_2·b_1_3
49. b_3_15·b_5_44 + b_3_15·b_5_43 + b_3_14·b_5_43 + b_3_13·b_5_44 + a_3_11·b_5_43
       + a_1_2·b_1_3⁴·b_3_14 + a_1_1·b_1_3⁴·b_3_15 + a_1_1·b_1_3⁴·b_3_14
       + a_1_1·b_1_0⁴·b_3_12 + a_1_1·a_1_2·b_1_3³·b_3_15 + c_4_27·b_1_0·b_3_12
       + c_4_26·b_1_3·b_3_15 + c_4_26·b_1_3⁴ + c_4_27·a_1_2·b_3_15 + c_4_27·a_1_2·b_3_14
       + c_4_27·a_1_1·b_3_15 + c_4_27·a_1_1·b_3_14 + c_4_27·a_1_1·b_3_13 + c_4_26·a_1_2·b_3_15
       + c_4_26·a_1_2·b_1_3³ + c_4_26·a_1_1·b_3_15 + c_4_26·a_1_1·b_3_13
       + c_4_26·a_1_1·b_1_3³ + c_4_26·a_1_1·b_1_0³ + c_2_7·a_1_2·b_1_3²·b_3_15
       + c_2_7·a_1_1·b_1_3²·b_3_15 + c_2_7·a_1_1·b_1_3⁵ + c_2_7·a_1_1·b_1_0²·b_3_13
       + c_2_7·a_1_1·b_1_0⁵ + c_4_27·a_1_1·a_3_10 + c_4_26·a_1_1·a_3_10
       + c_4_26·a_1_1·a_3_11 + c_4_26·a_1_1·a_1_2·b_1_3² + c_2_7·c_4_27·b_1_0²
       + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3⁴ + c_2_7²·b_1_0·b_3_13 + c_2_7²·b_1_0·b_3_12
       + c_2_7·c_4_27·a_1_1·b_1_3 + c_2_7·c_4_27·a_1_1·b_1_0 + c_2_7·c_4_26·a_1_2·b_1_3
       + c_2_7·c_4_26·a_1_1·b_1_3 + c_2_7²·a_1_2·b_3_15 + c_2_7²·a_1_2·b_3_14
       + c_2_7²·a_1_2·b_1_3³ + c_2_7²·a_1_1·b_3_15 + c_2_7²·a_1_1·b_3_14
       + c_2_7²·a_1_1·b_3_12 + c_2_7²·a_1_1·b_1_0³ + c_2_7·c_4_27·a_1_1²
       + c_2_7·c_4_26·a_1_1·a_1_2 + c_2_7²·a_1_1·a_3_11 + c_2_7²·a_1_1·a_1_2·b_1_3²
       + c_2_7³·b_1_0² + c_2_7³·a_1_1·b_1_3 + c_2_7³·a_1_1·a_1_2
50. a_3_10·b_5_43 + a_3_11·b_5_44 + a_3_11·b_5_43 + a_1_1·b_1_3²·b_5_44
       + a_1_1·b_1_3⁴·b_3_15 + c_4_27·a_1_1·b_3_12 + c_4_26·a_1_2·b_3_14
       + c_4_26·a_1_1·b_3_13 + c_4_26·a_1_1·b_1_0³ + c_2_7·a_1_2·b_1_3²·b_3_15
       + c_2_7·a_1_1·b_5_43 + c_2_7·a_1_1·b_1_3²·b_3_15 + c_2_7·a_1_1·b_1_3²·b_3_14
       + c_2_7·a_1_1·b_1_3⁵ + c_4_26·a_1_1·a_3_10 + c_4_26·a_1_1·a_1_2·b_1_3²
       + c_2_7·a_1_1·a_1_2·b_1_3·b_3_15 + c_2_7·c_4_26·a_1_1·b_1_3 + c_2_7²·a_1_2·b_3_14
       + c_2_7²·a_1_2·b_1_3³ + c_2_7²·a_1_1·b_3_13 + c_2_7²·a_1_1·b_1_3³
       + c_2_7²·a_1_1·b_1_0³ + c_2_7·c_4_27·a_1_1·a_1_2 + c_2_7·c_4_27·a_1_1²
       + c_2_7·c_4_26·a_1_1·a_1_2 + c_2_7²·a_1_1·a_3_11 + c_2_7³·a_1_1·b_1_3
       + c_2_7³·a_1_1·a_1_2 + c_2_7³·a_1_1²
51. b_3_15·b_5_43 + b_3_14·b_5_43 + a_3_10·b_5_44 + a_3_10·b_5_43 + a_3_11·b_5_43
       + a_1_2·b_1_3⁴·b_3_15 + a_1_2·b_1_3⁴·b_3_14 + a_1_1·b_1_0²·b_5_43
       + a_1_1·b_1_0⁴·b_3_12 + a_1_1·a_1_2·b_1_3³·b_3_15 + a_1_1·a_1_2·b_1_3³·b_3_14
       + c_4_27·b_1_0·b_3_12 + c_4_26·b_1_3·b_3_15 + c_4_26·b_1_3·b_3_14
       + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_3³·b_3_14 + c_2_7·b_1_3⁶ + c_4_27·a_1_2·b_3_15
       + c_4_27·a_1_2·b_3_14 + c_4_27·a_1_1·b_3_15 + c_4_27·a_1_1·b_3_14 + c_4_26·a_1_2·b_3_15
       + c_4_26·a_1_2·b_3_14 + c_4_26·a_1_2·b_1_3³ + c_4_26·a_1_1·b_3_15
       + c_4_26·a_1_1·b_3_13 + c_4_26·a_1_1·b_1_0³ + c_2_7·a_1_2·b_1_3²·b_3_15
       + c_2_7·a_1_2·b_1_3²·b_3_14 + c_2_7·a_1_1·b_5_43 + c_2_7·a_1_1·b_1_3²·b_3_14
       + c_2_7·a_1_1·b_1_3⁵ + c_2_7·a_1_1·b_1_0⁵ + c_4_27·a_1_1·a_3_10
       + c_4_27·a_1_1·a_1_2·b_1_3² + c_4_26·a_1_1·a_3_10 + c_2_7·a_1_1·a_1_2·b_1_3·b_3_15
       + c_2_7·a_1_1·a_1_2·b_1_3·b_3_14 + c_2_7·a_1_1·a_1_2·b_1_3⁴ + c_2_7·c_4_27·b_1_0²
       + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3·b_3_14 + c_2_7²·b_1_3⁴ + c_2_7²·b_1_0·b_3_13
       + c_2_7²·b_1_0·b_3_12 + c_2_7·c_4_26·a_1_1·b_1_3 + c_2_7²·a_1_2·b_3_15
       + c_2_7²·a_1_1·b_3_14 + c_2_7²·a_1_1·b_3_12 + c_2_7²·a_1_1·b_1_3³
       + c_2_7·c_4_27·a_1_1² + c_2_7·c_4_26·a_1_1·a_1_2 + c_2_7·c_4_26·a_1_1²
       + c_2_7²·a_1_1·a_3_10 + c_2_7³·b_1_0² + c_2_7³·a_1_2·b_1_3 + c_2_7³·a_1_1·b_1_0
       + c_2_7³·a_1_1·a_1_2 + c_2_7³·a_1_1²
52. b_3_15·b_5_43 + b_3_14·b_5_43 + a_3_11·b_5_43 + a_1_2·b_1_3⁴·b_3_15
       + a_1_2·b_1_3⁴·b_3_14 + a_1_1·b_1_3²·b_5_44 + a_1_1·b_1_3⁴·b_3_15
       + a_1_1·b_1_0²·b_5_43 + a_1_1·b_1_0⁴·b_3_12 + a_1_1·a_1_2·b_1_3³·b_3_15
       + a_1_1·a_1_2·b_1_3³·b_3_14 + c_4_27·b_1_0·b_3_12 + c_4_26·b_1_3·b_3_15
       + c_4_26·b_1_3·b_3_14 + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_3³·b_3_14 + c_2_7·b_1_3⁶
       + c_4_27·a_1_2·b_3_15 + c_4_27·a_1_2·b_3_14 + c_4_27·a_1_1·b_3_15 + c_4_27·a_1_1·b_3_14
       + c_4_26·a_1_1·b_3_15 + c_4_26·a_1_1·b_3_13 + c_4_26·a_1_1·b_1_3³
       + c_4_26·a_1_1·b_1_0³ + c_2_7·a_1_2·b_1_3²·b_3_15 + c_2_7·a_1_1·b_5_44
       + c_2_7·a_1_1·b_1_3²·b_3_15 + c_2_7·a_1_1·b_1_3²·b_3_14 + c_2_7·a_1_1·b_1_3⁵
       + c_2_7·a_1_1·b_1_0⁵ + c_4_27·a_1_1·a_3_10 + c_4_27·a_1_1·a_3_11
       + c_4_27·a_1_1·a_1_2·b_1_3² + c_2_7·a_1_1·a_1_2·b_1_3·b_3_15
       + c_2_7·a_1_1·a_1_2·b_1_3·b_3_14 + c_2_7·a_1_1·a_1_2·b_1_3⁴ + c_2_7·c_4_27·b_1_0²
       + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3·b_3_14 + c_2_7²·b_1_3⁴ + c_2_7²·b_1_0·b_3_13
       + c_2_7²·b_1_0·b_3_12 + c_2_7·c_4_26·a_1_2·b_1_3 + c_2_7·c_4_26·a_1_1·b_1_3
       + c_2_7²·a_1_2·b_3_14 + c_2_7²·a_1_2·b_1_3³ + c_2_7²·a_1_1·b_3_14
       + c_2_7²·a_1_1·b_3_12 + c_2_7²·a_1_1·b_1_3³ + c_2_7·c_4_27·a_1_1²
       + c_2_7²·a_1_1·a_3_10 + c_2_7²·a_1_1·a_3_11 + c_2_7³·b_1_0² + c_2_7³·a_1_1·b_1_0
       + c_2_7³·a_1_1²
53. b_3_13·b_5_44 + b_1_0³·b_5_43 + a_1_1·b_1_3²·b_5_44 + a_1_1·b_1_3⁴·b_3_15
       + a_1_1·b_1_0²·b_5_43 + a_1_1·b_1_0⁴·b_3_12 + a_1_1·a_1_2·b_1_3³·b_3_15
       + a_1_1·a_1_2·b_1_3³·b_3_14 + c_4_27·b_1_0·b_3_13 + c_2_7·b_1_3·b_5_44
       + c_2_7·b_1_0³·b_3_13 + c_4_27·a_1_1·b_1_0³ + c_4_26·a_1_1·b_3_15
       + c_2_7·a_1_1·b_5_43 + c_2_7·a_1_1·b_1_3²·b_3_15 + c_4_26·a_1_1·a_3_10
       + c_2_7·a_1_1·a_1_2·b_1_3·b_3_15 + c_2_7·a_1_1·a_1_2·b_1_3⁴ + c_2_7·c_4_27·b_1_0²
       + c_2_7²·b_1_0·b_3_13 + c_2_7²·b_1_0⁴ + c_2_7·c_4_27·a_1_1·b_1_0
       + c_2_7²·a_1_1·b_3_15 + c_2_7²·a_1_1·b_1_3³ + c_2_7²·a_1_1·b_1_0³
       + c_2_7·c_4_27·a_1_1·a_1_2 + c_2_7²·a_1_1·a_3_11 + c_2_7³·b_1_0²
       + c_2_7³·a_1_1·a_1_2 + c_2_7³·a_1_1²
54. b_3_15·b_5_43 + b_3_14·b_5_43 + b_3_13·b_5_43 + a_3_11·b_5_43 + a_1_2·b_1_3⁴·b_3_15
       + a_1_2·b_1_3⁴·b_3_14 + a_1_1·a_1_2·b_1_3³·b_3_14 + c_4_26·b_1_3·b_3_15
       + c_4_26·b_1_3·b_3_14 + c_2_7·b_1_3⁶ + c_4_27·a_1_2·b_3_15 + c_4_27·a_1_2·b_3_14
       + c_4_27·a_1_1·b_3_15 + c_4_27·a_1_1·b_3_14 + c_4_27·a_1_1·b_3_13 + c_4_26·a_1_1·b_3_15
       + c_4_26·a_1_1·b_3_14 + c_4_26·a_1_1·b_3_13 + c_2_7·a_1_2·b_5_44
       + c_2_7·a_1_1·b_1_3²·b_3_14 + c_2_7·a_1_1·b_1_3⁵ + c_4_27·a_1_1·a_3_11
       + c_4_27·a_1_1·a_1_2·b_1_3² + c_4_26·a_1_1·a_3_10 + c_4_26·a_1_1·a_3_11
       + c_4_26·a_1_1·a_1_2·b_1_3² + c_2_7·a_1_1·a_1_2·b_1_3·b_3_15
       + c_2_7·c_4_26·b_1_3² + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3·b_3_14
       + c_2_7·c_4_27·a_1_2·b_1_3 + c_2_7·c_4_26·a_1_2·b_1_3 + c_2_7²·a_1_2·b_3_15
       + c_2_7²·a_1_2·b_3_14 + c_2_7²·a_1_1·b_3_13 + c_2_7²·a_1_1·b_3_12
       + c_2_7·c_4_26·a_1_1·a_1_2 + c_2_7·c_4_26·a_1_1² + c_2_7³·b_1_3²
       + c_2_7³·a_1_1·b_1_3 + c_2_7³·a_1_1·b_1_0 + c_2_7³·a_1_1·a_1_2 + c_2_7³·a_1_1²
55. b_5_43² + a_1_2·b_1_3⁶·b_3_15 + a_1_2·b_1_3⁶·b_3_14 + a_1_1·a_1_2·b_1_3⁵·b_3_14
       + c_2_7·b_1_3⁸ + c_4_27·a_1_1·b_1_0²·b_3_12 + c_4_27·a_1_1·b_1_0⁵
       + c_4_26·a_1_1·b_1_0²·b_3_12 + c_4_26·a_1_1·b_1_0⁵ + c_2_7·a_1_2·b_1_3⁷
       + c_4_27·a_1_1·a_1_2·b_1_3⁴ + c_4_26·a_1_1·a_1_2·b_1_3⁴
       + c_2_7·a_1_1·a_1_2·b_1_3⁶ + c_4_26·c_4_27·b_1_0² + c_4_26²·b_1_3²
       + c_2_7²·a_1_1·b_1_0²·b_3_12 + c_2_7²·a_1_1·b_1_0⁵ + c_4_27²·a_1_1·a_1_2
       + c_4_26²·a_1_1·a_1_2 + c_4_26²·a_1_1² + c_2_7·c_4_26·a_1_1·a_1_2·b_1_3²
       + c_2_7²·a_1_1·a_1_2·b_1_3⁴ + c_2_7²·c_4_26·b_1_0² + c_2_7²·c_4_26·a_1_1·a_1_2
       + c_2_7²·c_4_26·a_1_1² + c_2_7⁴·b_1_3² + c_2_7⁴·b_1_0² + c_2_7⁴·a_1_1·a_1_2
56. b_5_44² + a_1_2·b_1_3⁶·b_3_15 + a_1_1·b_1_3⁶·b_3_15 + a_1_1·b_1_3⁶·b_3_14
       + a_1_1·b_1_0⁶·b_3_12 + a_1_1·b_1_0⁹ + a_1_1·a_1_2·b_1_3³·b_5_44
       + a_1_1·a_1_2·b_1_3⁵·b_3_15 + c_4_26·b_1_3⁶ + c_4_26·b_1_0⁶ + c_2_7·b_1_3⁸
       + c_4_26·a_1_2·b_1_3²·b_3_15 + c_4_26·a_1_2·b_1_3²·b_3_14
       + c_2_7·a_1_2·b_1_3⁴·b_3_14 + c_2_7·a_1_2·b_1_3⁷ + c_2_7·a_1_1·b_1_3⁴·b_3_15
       + c_2_7·a_1_1·b_1_3⁴·b_3_14 + c_2_7·a_1_1·b_1_3⁷ + c_4_27·a_1_1·a_1_2·b_1_3⁴
       + c_4_26·a_1_1·a_1_2·b_1_3·b_3_14 + c_4_26·a_1_1·a_1_2·b_1_3⁴
       + c_2_7·a_1_1·a_1_2·b_1_3³·b_3_14 + c_2_7·a_1_1·a_1_2·b_1_3⁶ + c_4_27²·b_1_0²
       + c_4_26²·b_1_3² + c_2_7·c_4_26·b_1_3⁴ + c_2_7²·b_1_0⁶
       + c_2_7·c_4_26·a_1_2·b_1_3³ + c_2_7²·a_1_2·b_1_3²·b_3_15
       + c_2_7²·a_1_2·b_1_3²·b_3_14 + c_2_7²·a_1_1·b_1_3⁵
       + c_2_7²·a_1_1·b_1_0²·b_3_12 + c_2_7²·a_1_1·b_1_0⁵ + c_4_26·c_4_27·a_1_1·a_1_2
       + c_4_26·c_4_27·a_1_1² + c_2_7·c_4_26·a_1_1·a_1_2·b_1_3²
       + c_2_7²·a_1_1·a_1_2·b_1_3·b_3_14 + c_2_7²·c_4_27·b_1_0² + c_2_7³·b_1_3⁴
       + c_2_7³·a_1_2·b_1_3³ + c_2_7²·c_4_27·a_1_1·a_1_2 + c_2_7²·c_4_27·a_1_1²
       + c_2_7⁴·b_1_3² + c_2_7⁴·a_1_1²
57. b_5_44² + b_5_43·b_5_44 + b_1_3⁵·b_5_44 + b_1_3⁷·b_3_15 + a_1_2·b_1_3⁶·b_3_15
       + a_1_2·b_1_3⁶·b_3_14 + a_1_1·b_1_3⁶·b_3_15 + a_1_1·b_1_3⁶·b_3_14
       + a_1_1·b_1_0⁴·b_5_43 + a_1_1·b_1_0⁶·b_3_13 + a_1_1·b_1_0⁶·b_3_12 + a_1_1·b_1_0⁹
       + a_1_1·a_1_2·b_1_3⁵·b_3_15 + a_1_1·a_1_2·b_1_3⁵·b_3_14 + c_4_27·b_1_0·b_5_43
       + c_4_26·b_1_3·b_5_44 + c_4_26·b_1_3³·b_3_15 + c_4_26·b_1_3³·b_3_14
       + c_4_26·b_1_0³·b_3_13 + c_4_26·b_1_0⁶ + c_2_7·b_1_3⁵·b_3_15 + c_2_7·b_1_0³·b_5_43
       + c_4_27·a_1_2·b_5_44 + c_4_27·a_1_1·b_5_44 + c_4_26·a_1_2·b_1_3²·b_3_14
       + c_4_26·a_1_2·b_1_3⁵ + c_4_26·a_1_1·b_5_44 + c_4_26·a_1_1·b_5_43
       + c_4_26·a_1_1·b_1_3²·b_3_14 + c_4_26·a_1_1·b_1_3⁵ + c_4_26·a_1_1·b_1_0²·b_3_13
       + c_4_26·a_1_1·b_1_0⁵ + c_2_7·a_1_2·b_1_3²·b_5_44 + c_2_7·a_1_2·b_1_3⁴·b_3_15
       + c_2_7·a_1_1·b_1_0²·b_5_43 + c_2_7·a_1_1·b_1_0⁴·b_3_13
       + c_2_7·a_1_1·b_1_0⁴·b_3_12 + c_4_27·a_1_1·a_1_2·b_1_3·b_3_15
       + c_4_27·a_1_1·a_1_2·b_1_3⁴ + c_4_26·a_1_1·a_1_2·b_1_3·b_3_15
       + c_4_26·a_1_1·a_1_2·b_1_3·b_3_14 + c_2_7·a_1_1·a_1_2·b_1_3·b_5_44
       + c_2_7·a_1_1·a_1_2·b_1_3³·b_3_15 + c_2_7·a_1_1·a_1_2·b_1_3³·b_3_14
       + c_4_27²·b_1_0² + c_4_26²·b_1_3² + c_2_7·c_4_27·b_1_0·b_3_12
       + c_2_7²·b_1_3·b_5_44 + c_2_7²·b_1_3³·b_3_15 + c_2_7²·b_1_3³·b_3_14
       + c_2_7²·b_1_0·b_5_43 + c_2_7²·b_1_0³·b_3_12 + c_2_7²·b_1_0⁶
       + c_4_27²·a_1_1·b_1_0 + c_4_26²·a_1_2·b_1_3 + c_2_7·c_4_27·a_1_1·b_1_0³
       + c_2_7·c_4_26·a_1_2·b_3_14 + c_2_7·c_4_26·a_1_2·b_1_3³ + c_2_7·c_4_26·a_1_1·b_3_13
       + c_2_7·c_4_26·a_1_1·b_1_0³ + c_2_7²·a_1_2·b_5_44 + c_2_7²·a_1_2·b_1_3²·b_3_15
       + c_2_7²·a_1_1·b_1_3²·b_3_14 + c_2_7²·a_1_1·b_1_0⁵ + c_4_26·c_4_27·a_1_1²
       + c_4_26²·a_1_1·a_1_2 + c_2_7·c_4_27·a_1_1·a_1_2·b_1_3²
       + c_2_7²·a_1_1·a_1_2·b_1_3·b_3_15 + c_2_7³·b_1_0·b_3_13 + c_2_7³·b_1_0·b_3_12
       + c_2_7³·b_1_0⁴ + c_2_7²·c_4_27·a_1_1·b_1_0 + c_2_7³·a_1_2·b_3_14
       + c_2_7³·a_1_1·b_3_13 + c_2_7³·a_1_1·b_3_12 + c_2_7²·c_4_27·a_1_1·a_1_2
       + c_2_7²·c_4_26·a_1_1² + c_2_7³·a_1_1·a_3_10 + c_2_7⁴·b_1_3² + c_2_7⁴·b_1_0²
       + c_2_7⁴·a_1_2·b_1_3 + c_2_7⁴·a_1_1·b_1_0 + c_2_7⁴·a_1_1·a_1_2

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 10.
• 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_7, a Duflot regular element of degree 2
  2. c_4_26, a Duflot regular element of degree 4
  3. c_4_27, a Duflot regular element of degree 4
  4. b_1_3² + b_1_0², an element of degree 2
• The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 5, 8].
• The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

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 3

1. a_1_1 → 0, an element of degree 1
2. a_1_2 → 0, an element of degree 1
3. b_1_0 → 0, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. c_2_7 → c_1_1², an element of degree 2
6. a_3_11 → 0, an element of degree 3
7. a_3_10 → 0, an element of degree 3
8. b_3_12 → 0, an element of degree 3
9. b_3_13 → 0, an element of degree 3
10. b_3_14 → 0, an element of degree 3
11. b_3_15 → 0, an element of degree 3
12. c_4_26 → c_1_2⁴ + c_1_1⁴, an element of degree 4
13. c_4_27 → c_1_2⁴ + c_1_1⁴ + c_1_0⁴, an element of degree 4
14. b_5_43 → 0, an element of degree 5
15. b_5_44 → 0, an element of degree 5

Restriction map to a maximal el. ab. subgp. of rank 4

1. a_1_1 → 0, an element of degree 1
2. a_1_2 → 0, an element of degree 1
3. b_1_0 → c_1_3, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. c_2_7 → c_1_1·c_1_3 + c_1_1², an element of degree 2
6. a_3_11 → 0, an element of degree 3
7. a_3_10 → 0, an element of degree 3
8. b_3_12 → c_1_2²·c_1_3, an element of degree 3
9. b_3_13 → c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_0·c_1_3² + c_1_0²·c_1_3, an element of degree 3
10. b_3_14 → 0, an element of degree 3
11. b_3_15 → c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_0·c_1_3² + c_1_0²·c_1_3, an element of degree 3
12. c_4_26 → c_1_2⁴ + c_1_1²·c_1_3² + c_1_1⁴, an element of degree 4
13. c_4_27 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1²·c_1_3² + c_1_1⁴ + c_1_0²·c_1_3² + c_1_0⁴, an element of degree 4
14. b_5_43 → c_1_2³·c_1_3² + c_1_2⁴·c_1_3 + c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2²·c_1_3²
       + c_1_1²·c_1_3³ + c_1_1²·c_1_2·c_1_3² + c_1_1²·c_1_2²·c_1_3 + c_1_1⁴·c_1_3
       + c_1_0·c_1_2²·c_1_3² + c_1_0·c_1_1·c_1_3³ + c_1_0·c_1_1²·c_1_3²
       + c_1_0²·c_1_2²·c_1_3 + c_1_0²·c_1_1·c_1_3² + c_1_0²·c_1_1²·c_1_3, an element of degree 5
15. b_5_44 → c_1_2⁴·c_1_3 + c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2²·c_1_3² + c_1_1²·c_1_2·c_1_3²
       + c_1_1²·c_1_2²·c_1_3 + c_1_0·c_1_1·c_1_3³ + c_1_0·c_1_1²·c_1_3²
       + c_1_0²·c_1_3³ + c_1_0²·c_1_1·c_1_3² + c_1_0²·c_1_1²·c_1_3 + c_1_0⁴·c_1_3, an element of degree 5

Restriction map to a maximal el. ab. subgp. of rank 4

1. a_1_1 → 0, an element of degree 1
2. a_1_2 → 0, an element of degree 1
3. b_1_0 → 0, an element of degree 1
4. b_1_3 → c_1_3, an element of degree 1
5. c_2_7 → c_1_1², an element of degree 2
6. a_3_11 → 0, an element of degree 3
7. a_3_10 → 0, an element of degree 3
8. b_3_12 → 0, an element of degree 3
9. b_3_13 → c_1_1²·c_1_3, an element of degree 3
10. b_3_14 → c_1_2²·c_1_3, an element of degree 3
11. b_3_15 → c_1_2²·c_1_3 + c_1_1·c_1_3² + c_1_1²·c_1_3, an element of degree 3
12. c_4_26 → c_1_2⁴ + c_1_1⁴, an element of degree 4
13. c_4_27 → c_1_2⁴ + c_1_1⁴ + c_1_0²·c_1_3² + c_1_0⁴, an element of degree 4
14. b_5_43 → c_1_2⁴·c_1_3 + c_1_1·c_1_3⁴, an element of degree 5
15. b_5_44 → c_1_2²·c_1_3³ + c_1_2⁴·c_1_3 + c_1_1·c_1_3⁴ + c_1_1·c_1_2²·c_1_3²
       + c_1_1²·c_1_3³, an element of degree 5

About the group

Ring generators

Ring relations

Completion information

Restriction maps

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