David J. Green

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Cohomology of group number 1440 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 3 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_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. c_2_7, a Duflot regular element of degree 2
6. b_3_10, an element of degree 3
7. b_3_11, an 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_2·b_1_1
2. b_1_1·b_1_3 + b_1_0·b_1_1 + a_1_2·b_1_0
3. b_1_0·b_1_3 + a_1_2·b_1_0 + a_1_2²
4. a_1_2³
5. a_1_2²·b_1_3
6. b_1_3·b_3_11 + b_1_1·b_3_10 + a_1_2·b_3_10 + c_2_7·b_1_3² + c_2_7·b_1_0·b_1_1
      + c_2_7·a_1_2·b_1_3 + c_2_7·a_1_2·b_1_0
7. b_1_1·b_3_10 + b_1_0·b_3_11 + c_2_7·b_1_0·b_1_1 + c_2_7·a_1_2²
8. a_1_2·b_3_11 + c_2_7·a_1_2·b_1_3 + c_2_7·a_1_2²
9. b_1_1·b_3_12 + c_2_7·a_1_2·b_1_0
10. b_1_0·b_3_12 + a_1_2·b_3_10 + c_2_7·b_1_0² + c_2_7·a_1_2²
11. b_1_3·b_3_10 + a_1_2·b_3_12 + a_1_2·b_3_10 + c_2_7·a_1_2·b_1_3 + c_2_7·a_1_2·b_1_0
       + c_2_7·a_1_2²
12. b_1_3·b_3_14 + b_1_3·b_3_10 + b_1_1·b_3_13 + b_1_1·b_3_11 + a_1_2·b_3_13 + a_1_2·b_3_10
       + c_2_7·b_1_3² + c_2_7·b_1_0·b_1_1
13. b_1_1·b_3_13 + b_1_1·b_3_11 + b_1_0·b_3_14 + c_2_7·b_1_0·b_1_1 + c_2_7·b_1_0²
       + c_2_7·a_1_2²
14. a_1_2·b_3_14 + c_2_7·a_1_2·b_1_3 + c_2_7·a_1_2·b_1_0 + c_2_7·a_1_2²
15. b_1_1·b_3_15 + b_1_1·b_3_13 + a_1_2·b_3_10 + c_2_7·b_1_0·b_1_1
16. b_1_0·b_3_15 + b_1_0·b_3_13 + b_1_0·b_3_10 + a_1_2·b_3_13 + a_1_2·b_3_10 + c_2_7·b_1_0²
       + c_2_7·a_1_2·b_1_3 + c_2_7·a_1_2²
17. b_1_3·b_3_13 + b_1_3·b_3_10 + b_1_1·b_3_10 + a_1_2·b_3_15 + a_1_2·b_3_10 + c_2_7·b_1_3²
       + c_2_7·b_1_0·b_1_1 + c_2_7·a_1_2²
18. a_1_2²·b_3_15 + a_1_2²·b_3_12
19. b_3_11·b_3_12 + c_2_7·b_1_3·b_3_12 + c_2_7·a_1_2·b_3_12 + c_2_7·a_1_2·b_3_10
       + c_2_7²·a_1_2·b_1_0
20. b_3_12·b_3_14 + c_2_7·b_1_3·b_3_12 + c_2_7·a_1_2·b_3_13 + c_2_7·a_1_2·b_3_10
       + c_2_7·a_1_2·b_1_3³ + c_2_7²·b_1_0² + c_2_7²·a_1_2²
21. b_3_12·b_3_13 + b_3_11·b_3_13 + b_3_11·b_3_12 + b_3_11² + b_3_10·b_3_15 + b_3_10·b_3_14
       + b_3_10·b_3_13 + b_3_10·b_3_12 + b_3_10² + c_2_7·b_1_0·b_3_14 + c_2_7·b_1_0·b_3_13
       + c_2_7·b_1_0·b_3_10 + c_2_7²·b_1_0²
22. b_3_14·b_3_15 + b_3_13·b_3_14 + b_3_12·b_3_13 + b_3_12² + b_3_11·b_3_15 + b_3_11·b_3_12
       + b_3_11² + b_3_10·b_3_14 + b_3_10·b_3_12 + a_1_2·b_1_3²·b_3_12 + c_2_7·b_1_3⁴
       + c_2_7·b_1_0·b_3_13 + c_2_7·b_1_0·b_3_11 + c_2_7·b_1_0·b_3_10 + c_2_7·a_1_2·b_3_13
       + c_2_7·a_1_2·b_3_10 + c_2_7·a_1_2·b_1_3³ + c_2_7²·b_1_3² + c_2_7²·a_1_2·b_1_3
23. b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_10·b_3_12 + c_2_7·b_1_3·b_3_15 + c_2_7·b_1_0·b_3_10
       + c_2_7·a_1_2·b_3_13 + c_2_7·a_1_2·b_3_10 + c_2_7·a_1_2·b_1_3³ + c_2_7²·b_1_3²
       + c_2_7²·a_1_2²
24. b_3_11·b_3_13 + b_3_11² + b_3_10·b_3_14 + c_2_7·b_1_0·b_3_14 + c_2_7·b_1_0·b_3_11
       + c_2_7·b_1_0·b_3_10 + c_2_7·a_1_2·b_3_15 + c_2_7·a_1_2·b_3_13 + c_2_7·a_1_2·b_3_10
       + c_2_7²·b_1_0² + c_2_7²·a_1_2·b_1_0
25. b_3_11² + b_1_1³·b_3_11 + b_1_0·b_1_1²·b_3_14 + b_1_0·b_1_1²·b_3_11
       + c_4_26·b_1_1² + c_2_7²·b_1_3² + c_2_7²·a_1_2²
26. b_3_11·b_3_12 + b_3_10·b_3_11 + b_1_0·b_1_1²·b_3_11 + a_1_2·b_1_0²·b_3_10
       + c_4_26·b_1_0·b_1_1 + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_0·b_3_11 + c_2_7·a_1_2·b_3_10
       + c_2_7²·a_1_2·b_1_3
27. b_3_10² + b_1_0³·b_3_10 + a_1_2·b_1_0²·b_3_13 + a_1_2·b_1_0⁵ + c_4_26·b_1_0²
       + c_2_7²·b_1_0²
28. b_3_11·b_3_12 + b_3_10·b_3_12 + a_1_2·b_1_0²·b_3_10 + c_2_7·b_1_3·b_3_12
       + c_2_7·b_1_0·b_3_10 + c_4_26·a_1_2·b_1_0 + c_2_7·a_1_2·b_3_10 + c_2_7·a_1_2·b_1_3³
       + c_2_7²·a_1_2·b_1_3 + c_2_7²·a_1_2·b_1_0 + c_2_7²·a_1_2²
29. b_3_12² + a_1_2·b_1_3²·b_3_12 + c_2_7·b_1_3⁴ + c_2_7·a_1_2·b_1_3³
       + c_4_26·a_1_2² + c_2_7²·b_1_3² + c_2_7²·b_1_0²
30. b_3_14² + b_1_1³·b_3_11 + b_1_0·b_1_1²·b_3_14 + c_4_27·b_1_1² + c_2_7²·b_1_3²
       + c_2_7²·b_1_1² + c_2_7²·b_1_0² + c_2_7²·a_1_2²
31. b_3_13·b_3_14 + b_3_11·b_3_14 + b_3_11·b_3_13 + b_3_11·b_3_12 + b_3_11² + b_3_10·b_3_14
       + b_1_0·b_1_1²·b_3_11 + a_1_2·b_1_0²·b_3_10 + c_4_27·b_1_0·b_1_1 + c_2_7·b_1_3·b_3_12
       + c_2_7·b_1_0·b_3_13 + c_2_7·b_1_0·b_3_10 + c_2_7·a_1_2·b_3_10 + c_2_7·a_1_2·b_1_0³
       + c_2_7²·b_1_0·b_1_1 + c_2_7²·a_1_2·b_1_3
32. b_3_13² + b_3_12² + b_3_11² + b_1_0³·b_3_10 + a_1_2·b_1_3²·b_3_12
       + a_1_2·b_1_0²·b_3_10 + c_4_27·b_1_0² + c_2_7·b_1_3⁴ + c_2_7·b_1_0⁴
       + c_2_7·a_1_2·b_1_3³ + c_2_7·a_1_2·b_1_0³ + c_2_7²·b_1_3² + c_2_7²·b_1_0²
       + c_2_7²·a_1_2²
33. b_3_13·b_3_15 + b_3_13² + b_3_12·b_3_13 + b_3_12² + b_3_11·b_3_15 + b_3_11²
       + b_3_10·b_3_14 + b_3_10·b_3_13 + b_3_10·b_3_11 + a_1_2·b_1_3²·b_3_15
       + a_1_2·b_1_3²·b_3_12 + a_1_2·b_1_0²·b_3_10 + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_3⁴
       + c_2_7·b_1_0·b_3_14 + c_2_7·b_1_0·b_3_11 + c_2_7·b_1_0·b_3_10 + c_4_27·a_1_2·b_1_0
       + c_4_26·a_1_2·b_1_3 + c_2_7·a_1_2·b_3_10 + c_2_7·a_1_2·b_1_0³ + c_2_7²·b_1_3²
34. b_3_15² + b_3_13² + b_3_10² + b_1_3³·b_3_15 + c_4_26·b_1_3² + c_4_27·a_1_2²
       + c_2_7²·b_1_3² + c_2_7²·b_1_0²
35. b_3_14² + b_3_13·b_3_15 + b_3_13² + b_3_12·b_3_13 + b_3_12² + b_3_11·b_3_15
       + b_3_11² + b_3_10·b_3_13 + b_3_10·b_3_12 + b_3_10·b_3_11 + b_1_1·b_5_43 + b_1_1³·b_3_11
       + a_1_2·b_1_3²·b_3_15 + a_1_2·b_1_3²·b_3_12 + a_1_2·b_1_0²·b_3_13
       + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_3⁴ + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_0·b_3_11
       + c_2_7·b_1_0·b_3_10 + c_4_26·a_1_2·b_1_3 + c_2_7·a_1_2·b_3_10 + c_2_7·a_1_2·b_1_3³
36. b_3_15² + b_3_13·b_3_14 + b_3_13² + b_3_12·b_3_15 + b_3_11·b_3_15 + b_3_11·b_3_14
       + b_3_11² + b_3_10·b_3_14 + b_3_10·b_3_12 + b_3_10² + b_1_3·b_5_43 + b_1_3³·b_3_12
       + b_1_0·b_1_1²·b_3_11 + a_1_2·b_1_0²·b_3_13 + c_4_27·b_1_3² + c_2_7·b_1_3⁴
       + c_2_7·b_1_0·b_3_11 + c_2_7·b_1_0·b_3_10 + c_4_26·a_1_2·b_1_3 + c_2_7·a_1_2·b_1_3³
       + c_2_7²·a_1_2·b_1_3
37. b_3_15² + b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_13² + b_3_12·b_3_13 + b_3_12²
       + b_3_11·b_3_15 + b_3_11·b_3_14 + b_3_11·b_3_13 + b_3_11·b_3_12 + b_3_11²
       + b_1_3³·b_3_15 + b_1_0·b_5_43 + b_1_0·b_1_1²·b_3_11 + b_1_0³·b_3_13
       + a_1_2·b_1_3²·b_3_15 + a_1_2·b_1_3²·b_3_12 + a_1_2·b_1_0⁵ + c_4_26·b_1_3²
       + c_2_7·b_1_3⁴ + c_2_7·b_1_0·b_3_14 + c_2_7·b_1_0·b_3_11 + c_2_7·b_1_0·b_3_10
       + c_4_26·a_1_2·b_1_3 + c_2_7·a_1_2·b_3_10 + c_2_7·a_1_2·b_1_0³ + c_2_7²·a_1_2·b_1_3
       + c_2_7²·a_1_2·b_1_0
38. b_3_13·b_3_15 + b_3_13² + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_10·b_3_13 + b_3_10·b_3_12
       + b_3_10·b_3_11 + a_1_2·b_5_43 + a_1_2·b_1_3²·b_3_12 + a_1_2·b_1_0²·b_3_13
       + c_2_7·b_1_0·b_3_13 + c_2_7·b_1_0·b_3_11 + c_2_7·b_1_0·b_3_10 + c_4_27·a_1_2·b_1_3
       + c_2_7·a_1_2·b_3_13 + c_2_7·a_1_2·b_3_10 + c_2_7²·a_1_2·b_1_0 + c_2_7²·a_1_2²
39. b_3_13·b_3_15 + b_3_13² + b_3_12·b_3_13 + b_3_12² + b_3_11·b_3_15 + b_3_11·b_3_14
       + b_3_10·b_3_13 + b_3_10·b_3_11 + b_1_1·b_5_44 + a_1_2·b_1_3²·b_3_15
       + a_1_2·b_1_3²·b_3_12 + a_1_2·b_1_0²·b_3_13 + a_1_2·b_1_0²·b_3_10
       + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_3⁴ + c_2_7·b_1_1·b_3_14 + c_2_7·b_1_0·b_3_14
       + c_2_7·b_1_0·b_1_1³ + c_4_26·a_1_2·b_1_3 + c_2_7·a_1_2·b_3_13 + c_2_7²·b_1_3²
       + c_2_7²·b_1_1² + c_2_7²·a_1_2·b_1_3 + c_2_7²·a_1_2·b_1_0 + c_2_7²·a_1_2²
40. b_3_15² + b_3_13·b_3_15 + b_3_12·b_3_15 + b_3_12² + b_3_10·b_3_14 + b_3_10·b_3_13
       + b_3_10·b_3_12 + b_3_10² + b_1_3·b_5_44 + a_1_2·b_1_0²·b_3_13 + a_1_2·b_1_0²·b_3_10
       + c_4_27·b_1_3² + c_4_26·b_1_3² + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_3⁴
       + c_2_7·b_1_0·b_3_10 + c_4_27·a_1_2·b_1_3 + c_2_7·a_1_2·b_3_10 + c_2_7²·b_1_0·b_1_1
       + c_2_7²·b_1_0²
41. b_3_15² + b_3_12² + b_3_11·b_3_12 + b_3_11² + b_3_10·b_3_14 + b_3_10·b_3_13
       + b_3_10·b_3_12 + b_3_10² + b_1_3³·b_3_15 + b_1_0·b_5_44 + b_1_0³·b_3_13
       + b_1_0³·b_3_10 + a_1_2·b_1_3²·b_3_12 + a_1_2·b_1_0⁵ + c_4_26·b_1_3²
       + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_3⁴ + c_2_7·b_1_0·b_3_13 + c_2_7·a_1_2·b_3_10
       + c_2_7·a_1_2·b_1_0³ + c_2_7²·b_1_0·b_1_1 + c_2_7²·a_1_2·b_1_3
       + c_2_7²·a_1_2·b_1_0 + c_2_7²·a_1_2²
42. b_3_15² + b_3_13·b_3_15 + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_10·b_3_13 + b_3_10·b_3_11
       + b_3_10² + b_1_3³·b_3_15 + a_1_2·b_5_44 + a_1_2·b_1_0²·b_3_13 + a_1_2·b_1_0²·b_3_10
       + c_4_26·b_1_3² + c_2_7·b_1_0·b_3_13 + c_2_7·b_1_0·b_3_11 + c_4_27·a_1_2·b_1_3
       + c_4_26·a_1_2·b_1_3 + c_2_7·a_1_2·b_3_13 + c_2_7²·b_1_3² + c_2_7²·b_1_0²
43. b_3_15·b_5_43 + b_3_13·b_5_43 + b_3_11·b_5_43 + b_1_3⁵·b_3_15 + a_1_2·b_1_3²·b_5_43
       + a_1_2·b_1_3⁴·b_3_12 + a_1_2·b_1_0²·b_5_43 + a_1_2·b_1_0⁴·b_3_10
       + c_4_27·b_1_3·b_3_15 + c_4_27·b_1_1·b_3_11 + c_4_27·b_1_0·b_3_11 + c_4_27·b_1_0·b_3_10
       + c_4_26·b_1_3·b_3_15 + c_4_26·b_1_3·b_3_12 + c_4_26·b_1_3⁴ + c_4_26·b_1_0·b_3_14
       + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_10 + c_2_7·b_1_1³·b_3_11
       + c_2_7·b_1_0·b_1_1²·b_3_14 + c_2_7·b_1_0·b_1_1²·b_3_11 + c_2_7·b_1_0³·b_3_13
       + c_4_27·a_1_2·b_3_15 + c_4_27·a_1_2·b_3_13 + c_4_27·a_1_2·b_3_12
       + c_4_27·a_1_2·b_1_3³ + c_4_27·a_1_2·b_1_0³ + c_4_26·a_1_2·b_3_13
       + c_2_7·a_1_2·b_1_3²·b_3_12 + c_2_7·a_1_2·b_1_0²·b_3_13
       + c_2_7·a_1_2·b_1_0²·b_3_10 + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_27·b_1_0²
       + c_2_7·c_4_26·b_1_3² + c_2_7·c_4_26·b_1_1² + c_2_7·c_4_26·b_1_0²
       + c_2_7²·b_1_1·b_3_11 + c_2_7²·b_1_0·b_3_11 + c_2_7²·b_1_0·b_3_10 + 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_2·b_1_0 + c_2_7·c_4_26·a_1_2·b_1_0
       + c_2_7²·a_1_2·b_3_13 + c_2_7²·a_1_2·b_3_10 + c_2_7²·a_1_2·b_1_3³
       + c_2_7²·a_1_2·b_1_0³ + c_2_7·c_4_27·a_1_2² + c_2_7³·b_1_0·b_1_1
       + c_2_7³·b_1_0² + c_2_7³·a_1_2·b_1_3 + c_2_7³·a_1_2·b_1_0 + c_2_7³·a_1_2²
44. b_3_12·b_5_43 + b_3_10·b_5_43 + b_1_3³·b_5_43 + b_1_3⁵·b_3_15 + b_1_3⁵·b_3_12
       + a_1_2·b_1_3⁴·b_3_12 + a_1_2·b_1_0²·b_5_43 + a_1_2·b_1_0⁴·b_3_10
       + c_4_27·b_1_3·b_3_12 + c_4_27·b_1_3⁴ + c_4_27·b_1_0·b_3_11 + c_4_27·b_1_0·b_3_10
       + c_4_26·b_1_3·b_3_12 + c_4_26·b_1_3⁴ + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_11
       + c_4_26·b_1_0·b_3_10 + c_2_7·b_1_3·b_5_43 + c_2_7·b_1_3³·b_3_15
       + c_2_7·b_1_0·b_1_1²·b_3_11 + c_2_7·b_1_0³·b_3_13 + c_4_27·a_1_2·b_3_12
       + c_4_26·a_1_2·b_3_13 + c_4_26·a_1_2·b_3_10 + c_4_26·a_1_2·b_1_3³
       + c_4_26·a_1_2·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_12
       + c_2_7·a_1_2·b_1_0²·b_3_10 + c_2_7·a_1_2·b_1_0⁵ + c_2_7·c_4_27·b_1_3²
       + c_2_7·c_4_27·b_1_0² + c_2_7·c_4_26·b_1_3² + c_2_7·c_4_26·b_1_0·b_1_1
       + c_2_7²·b_1_0·b_3_11 + c_2_7²·b_1_0·b_3_10 + c_2_7²·b_1_0⁴
       + 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_10
       + c_2_7²·a_1_2·b_1_0³ + c_2_7·c_4_26·a_1_2² + c_2_7³·b_1_0²
       + c_2_7³·a_1_2·b_1_0 + c_2_7³·a_1_2²
45. b_3_10·b_5_43 + a_1_2·b_1_3²·b_5_43 + a_1_2·b_1_3⁴·b_3_15 + a_1_2·b_1_3⁴·b_3_12
       + a_1_2·b_1_0²·b_5_43 + a_1_2·b_1_0⁴·b_3_10 + c_4_27·b_1_0·b_3_11
       + c_4_27·b_1_0·b_3_10 + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_10
       + c_2_7·b_1_0·b_5_43 + c_2_7·b_1_0·b_1_1²·b_3_11 + c_2_7·b_1_0³·b_3_13
       + c_4_27·a_1_2·b_3_12 + c_4_27·a_1_2·b_3_10 + c_4_27·a_1_2·b_1_3³
       + c_4_26·a_1_2·b_3_12 + c_4_26·a_1_2·b_1_3³ + c_4_26·a_1_2·b_1_0³
       + c_2_7·a_1_2·b_1_3²·b_3_15 + c_2_7·a_1_2·b_1_0²·b_3_13
       + c_2_7·a_1_2·b_1_0²·b_3_10 + c_2_7·a_1_2·b_1_0⁵ + c_2_7·c_4_27·b_1_0²
       + c_2_7·c_4_26·b_1_0·b_1_1 + c_2_7²·b_1_0·b_3_11 + c_2_7²·b_1_0·b_3_10
       + c_2_7²·b_1_0⁴ + 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_7·c_4_27·a_1_2² + c_2_7³·b_1_0² + c_2_7³·a_1_2²
46. b_3_12·b_5_43 + b_3_11·b_5_43 + b_3_10·b_5_43 + b_1_3³·b_5_43 + b_1_3⁵·b_3_15
       + b_1_3⁵·b_3_12 + a_1_2·b_1_3⁴·b_3_12 + a_1_2·b_1_0²·b_5_43 + a_1_2·b_1_0⁴·b_3_10
       + c_4_27·b_1_3·b_3_12 + c_4_27·b_1_3⁴ + c_4_27·b_1_1·b_3_11 + c_4_27·b_1_0·b_3_11
       + c_4_27·b_1_0·b_3_10 + c_4_26·b_1_3·b_3_12 + c_4_26·b_1_3⁴ + c_4_26·b_1_0·b_3_14
       + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_10
       + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_1³·b_3_11 + c_2_7·b_1_0·b_1_1²·b_3_14
       + c_2_7·b_1_0³·b_3_13 + c_4_27·a_1_2·b_3_12 + c_4_27·a_1_2·b_3_10
       + c_4_26·a_1_2·b_3_13 + c_4_26·a_1_2·b_1_3³ + c_4_26·a_1_2·b_1_0³
       + c_2_7·a_1_2·b_5_43 + c_2_7·a_1_2·b_1_3²·b_3_15 + c_2_7·a_1_2·b_1_3²·b_3_12
       + c_2_7·a_1_2·b_1_0²·b_3_13 + c_2_7·a_1_2·b_1_0²·b_3_10 + c_2_7·a_1_2·b_1_0⁵
       + c_2_7·c_4_27·b_1_3² + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7·c_4_27·b_1_0²
       + c_2_7·c_4_26·b_1_3² + c_2_7·c_4_26·b_1_1² + c_2_7·c_4_26·b_1_0·b_1_1
       + c_2_7·c_4_26·b_1_0² + c_2_7²·b_1_1·b_3_11 + c_2_7²·b_1_0·b_3_10
       + c_2_7²·b_1_0⁴ + 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_7·c_4_26·a_1_2·b_1_0 + c_2_7²·a_1_2·b_3_10 + c_2_7³·b_1_0·b_1_1
       + c_2_7³·b_1_0²
47. b_3_14·b_5_43 + b_3_13·b_5_43 + b_3_11·b_5_44 + b_3_11·b_5_43 + b_1_1³·b_5_44
       + a_1_2·b_1_3⁴·b_3_15 + a_1_2·b_1_0⁴·b_3_13 + a_1_2·b_1_0⁴·b_3_10 + a_1_2·b_1_0⁷
       + c_4_27·b_1_1·b_3_14 + c_4_27·b_1_0·b_3_14 + c_4_27·b_1_0·b_3_13 + c_4_27·b_1_0·b_3_10
       + c_4_27·b_1_0⁴ + c_4_26·b_1_1·b_3_14 + c_4_26·b_1_1·b_3_11 + c_4_26·b_1_0·b_3_14
       + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0⁴ + c_2_7·b_1_3³·b_3_12
       + c_2_7·b_1_1³·b_3_14 + c_2_7·b_1_0·b_1_1²·b_3_14 + c_2_7·b_1_0·b_1_1²·b_3_11
       + c_2_7·b_1_0·b_1_1⁵ + c_2_7·b_1_0⁶ + c_4_27·a_1_2·b_3_15 + c_4_27·a_1_2·b_3_13
       + c_4_26·a_1_2·b_3_15 + c_4_26·a_1_2·b_3_12 + c_4_26·a_1_2·b_3_10
       + c_4_26·a_1_2·b_1_3³ + c_2_7·a_1_2·b_1_3²·b_3_12 + c_2_7·a_1_2·b_1_0²·b_3_13
       + c_2_7·a_1_2·b_1_0²·b_3_10 + c_2_7·a_1_2·b_1_0⁵ + c_2_7·c_4_27·b_1_0·b_1_1
       + c_2_7·c_4_27·b_1_0² + c_2_7·c_4_26·b_1_3² + c_2_7·c_4_26·b_1_0·b_1_1
       + c_2_7²·b_1_3·b_3_12 + c_2_7²·b_1_3⁴ + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_1·b_3_11
       + c_2_7²·b_1_1⁴ + c_2_7²·b_1_0·b_3_14 + c_2_7²·b_1_0·b_3_13 + c_2_7²·b_1_0·b_3_11
       + c_2_7²·b_1_0·b_3_10 + c_2_7²·b_1_0⁴ + 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_13 + c_2_7²·a_1_2·b_3_12
       + c_2_7²·a_1_2·b_3_10 + c_2_7²·a_1_2·b_1_0³ + c_2_7·c_4_26·a_1_2²
       + c_2_7³·b_1_3² + c_2_7³·b_1_0·b_1_1 + c_2_7³·b_1_0² + c_2_7³·a_1_2²
48. b_3_12·b_5_44 + b_3_11·b_5_43 + b_3_10·b_5_43 + b_1_3³·b_5_43 + b_1_3⁵·b_3_15
       + b_1_3⁵·b_3_12 + a_1_2·b_1_3²·b_5_43 + a_1_2·b_1_3⁴·b_3_15 + a_1_2·b_1_3⁴·b_3_12
       + a_1_2·b_1_0²·b_5_43 + a_1_2·b_1_0⁴·b_3_10 + c_4_27·b_1_3·b_3_12 + c_4_27·b_1_3⁴
       + c_4_27·b_1_1·b_3_11 + c_4_27·b_1_0·b_3_11 + c_4_27·b_1_0·b_3_10 + c_4_26·b_1_3⁴
       + c_4_26·b_1_0·b_3_14 + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_10
       + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_3³·b_3_12 + c_2_7·b_1_3⁶ + c_2_7·b_1_1³·b_3_11
       + c_2_7·b_1_0·b_1_1²·b_3_14 + c_2_7·b_1_0³·b_3_13 + c_4_27·a_1_2·b_3_10
       + c_4_27·a_1_2·b_1_3³ + c_4_26·a_1_2·b_3_13 + c_4_26·a_1_2·b_3_10
       + c_4_26·a_1_2·b_1_0³ + c_2_7·a_1_2·b_1_3²·b_3_12 + c_2_7·a_1_2·b_1_3⁵
       + c_2_7·a_1_2·b_1_0²·b_3_13 + c_2_7·c_4_27·b_1_3² + c_2_7·c_4_27·b_1_0·b_1_1
       + c_2_7·c_4_27·b_1_0² + c_2_7·c_4_26·b_1_3² + c_2_7·c_4_26·b_1_1²
       + c_2_7·c_4_26·b_1_0·b_1_1 + c_2_7²·b_1_3·b_3_12 + c_2_7²·b_1_1·b_3_11
       + c_2_7²·b_1_0⁴ + c_2_7²·a_1_2·b_3_13 + c_2_7²·a_1_2·b_3_10
       + c_2_7²·a_1_2·b_1_3³ + c_2_7²·a_1_2·b_1_0³ + c_2_7³·b_1_3²
       + c_2_7³·b_1_0·b_1_1 + c_2_7³·b_1_0² + c_2_7³·a_1_2·b_1_3
49. b_3_13·b_5_44 + b_3_13·b_5_43 + b_3_12·b_5_43 + b_3_11·b_5_44 + b_1_3³·b_5_43
       + b_1_3⁵·b_3_15 + b_1_3⁵·b_3_12 + b_1_0·b_1_1²·b_5_44 + a_1_2·b_1_3⁴·b_3_12
       + a_1_2·b_1_0⁴·b_3_13 + c_4_27·b_1_3·b_3_12 + c_4_27·b_1_3⁴ + c_4_27·b_1_1·b_3_11
       + c_4_27·b_1_0·b_3_14 + c_4_27·b_1_0·b_3_11 + c_4_26·b_1_3·b_3_12 + c_4_26·b_1_3⁴
       + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_11 + c_2_7·b_1_3³·b_3_15
       + c_2_7·b_1_1³·b_3_11 + c_2_7·b_1_0·b_1_1²·b_3_11 + c_2_7·b_1_0³·b_3_13
       + c_4_27·a_1_2·b_3_13 + c_4_27·a_1_2·b_1_0³ + c_4_26·a_1_2·b_3_15
       + c_4_26·a_1_2·b_3_13 + c_4_26·a_1_2·b_3_10 + c_4_26·a_1_2·b_1_3³
       + c_4_26·a_1_2·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_12
       + c_2_7·a_1_2·b_1_0⁵ + c_2_7·c_4_27·b_1_3² + c_2_7·c_4_26·b_1_3²
       + c_2_7·c_4_26·b_1_1² + c_2_7·c_4_26·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_0²
       + c_2_7²·b_1_1·b_3_11 + c_2_7²·b_1_0·b_3_14 + c_2_7²·b_1_0·b_3_13
       + c_2_7²·b_1_0·b_3_11 + c_2_7²·b_1_0·b_3_10 + c_2_7²·b_1_0·b_1_1³
       + c_2_7²·b_1_0⁴ + c_2_7·c_4_26·a_1_2·b_1_3 + c_2_7²·a_1_2·b_3_12
       + c_2_7²·a_1_2·b_3_10 + c_2_7²·a_1_2·b_1_3³ + c_2_7·c_4_27·a_1_2²
       + c_2_7·c_4_26·a_1_2² + c_2_7³·b_1_0·b_1_1 + c_2_7³·b_1_0² + c_2_7³·a_1_2·b_1_3
       + c_2_7³·a_1_2²
50. b_3_10·b_5_44 + b_3_10·b_5_43 + b_1_0·b_1_1²·b_5_44 + a_1_2·b_1_0⁴·b_3_10
       + c_4_27·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_14 + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_10
       + c_2_7·b_1_0·b_1_1²·b_3_14 + c_2_7·b_1_0³·b_3_10 + c_4_27·a_1_2·b_3_10
       + c_4_26·a_1_2·b_3_12 + c_4_26·a_1_2·b_3_10 + c_2_7·a_1_2·b_1_3⁵
       + c_2_7·a_1_2·b_1_0²·b_3_13 + c_2_7·a_1_2·b_1_0²·b_3_10 + c_2_7·a_1_2·b_1_0⁵
       + c_2_7·c_4_27·b_1_0·b_1_1 + c_2_7²·b_1_0·b_3_14 + c_2_7²·b_1_0·b_3_11
       + c_2_7²·b_1_0·b_1_1³ + c_2_7·c_4_26·a_1_2·b_1_3 + c_2_7²·a_1_2·b_3_10
       + c_2_7²·a_1_2·b_1_3³ + c_2_7·c_4_27·a_1_2² + c_2_7·c_4_26·a_1_2²
       + c_2_7³·a_1_2·b_1_0
51. b_3_14·b_5_44 + b_3_14·b_5_43 + b_3_11·b_5_44 + b_3_11·b_5_43 + b_1_0·b_1_1²·b_5_44
       + b_1_0·b_1_1⁴·b_3_11 + c_4_27·b_1_1·b_3_14 + c_4_27·b_1_0·b_1_1³
       + c_4_26·b_1_1·b_3_11 + c_4_26·a_1_2·b_3_13 + c_4_26·a_1_2·b_3_12 + c_4_26·a_1_2·b_3_10
       + c_2_7·a_1_2·b_1_3⁵ + c_2_7·a_1_2·b_1_0²·b_3_13 + c_2_7·a_1_2·b_1_0²·b_3_10
       + c_2_7·a_1_2·b_1_0⁵ + c_2_7·c_4_27·b_1_1² + c_2_7·c_4_27·b_1_0·b_1_1
       + c_2_7·c_4_26·b_1_1² + c_2_7·c_4_26·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_0²
       + c_2_7²·b_1_1·b_3_11 + c_2_7²·b_1_0·b_3_10 + c_2_7·c_4_26·a_1_2·b_1_0
       + c_2_7²·a_1_2·b_3_10 + c_2_7²·a_1_2·b_1_3³ + c_2_7·c_4_26·a_1_2²
       + c_2_7³·b_1_1² + c_2_7³·b_1_0·b_1_1
52. b_3_15·b_5_44 + b_3_12·b_5_43 + b_3_11·b_5_44 + b_3_11·b_5_43 + b_3_10·b_5_43
       + b_1_3⁵·b_3_15 + b_1_0·b_1_1²·b_5_44 + a_1_2·b_1_3⁴·b_3_15 + a_1_2·b_1_3⁴·b_3_12
       + a_1_2·b_1_0⁷ + c_4_27·b_1_3·b_3_15 + c_4_27·b_1_3·b_3_12 + c_4_27·b_1_1·b_3_11
       + c_4_27·b_1_0·b_3_13 + c_4_27·b_1_0·b_3_10 + c_4_27·b_1_0⁴ + c_4_26·b_1_3⁴
       + c_4_26·b_1_0·b_3_10 + c_4_26·b_1_0⁴ + c_2_7·b_1_3⁶ + c_2_7·b_1_1³·b_3_11
       + c_2_7·b_1_0·b_1_1²·b_3_11 + c_2_7·b_1_0³·b_3_13 + c_2_7·b_1_0³·b_3_10
       + c_2_7·b_1_0⁶ + c_4_27·a_1_2·b_3_15 + c_4_27·a_1_2·b_3_13 + c_4_27·a_1_2·b_3_12
       + c_4_27·a_1_2·b_1_0³ + c_4_26·a_1_2·b_3_15 + c_4_26·a_1_2·b_3_13
       + c_4_26·a_1_2·b_3_12 + c_4_26·a_1_2·b_3_10 + c_4_26·a_1_2·b_1_3³
       + c_4_26·a_1_2·b_1_0³ + c_2_7·a_1_2·b_1_3²·b_3_15 + c_2_7·a_1_2·b_1_0²·b_3_13
       + c_2_7·c_4_27·b_1_0² + c_2_7·c_4_26·b_1_1² + c_2_7·c_4_26·b_1_0·b_1_1
       + c_2_7²·b_1_3·b_3_12 + c_2_7²·b_1_1·b_3_11 + c_2_7²·b_1_0·b_3_14
       + c_2_7²·b_1_0·b_3_11 + c_2_7²·b_1_0·b_3_10 + c_2_7²·b_1_0·b_1_1³
       + c_2_7·c_4_27·a_1_2·b_1_3 + c_2_7·c_4_27·a_1_2·b_1_0 + c_2_7·c_4_26·a_1_2·b_1_0
       + c_2_7²·a_1_2·b_3_13 + c_2_7²·a_1_2·b_3_10 + c_2_7²·a_1_2·b_1_0³
       + c_2_7·c_4_26·a_1_2² + c_2_7³·b_1_3² + c_2_7³·a_1_2·b_1_3 + c_2_7³·a_1_2²
53. b_3_14·b_5_43 + b_3_13·b_5_43 + b_3_12·b_5_43 + b_3_11·b_5_43 + b_3_10·b_5_43
       + b_1_3³·b_5_43 + b_1_3⁵·b_3_15 + b_1_3⁵·b_3_12 + a_1_2·b_1_3⁴·b_3_15
       + a_1_2·b_1_3⁴·b_3_12 + a_1_2·b_1_0²·b_5_43 + a_1_2·b_1_0⁴·b_3_13 + a_1_2·b_1_0⁷
       + c_4_27·b_1_3·b_3_12 + c_4_27·b_1_3⁴ + c_4_27·b_1_1·b_3_14 + c_4_27·b_1_0·b_3_14
       + c_4_27·b_1_0·b_3_13 + c_4_27·b_1_0·b_3_11 + c_4_27·b_1_0·b_1_1³ + c_4_27·b_1_0⁴
       + c_4_26·b_1_3·b_3_12 + c_4_26·b_1_3⁴ + c_4_26·b_1_0·b_3_10 + c_4_26·b_1_0·b_1_1³
       + c_4_26·b_1_0⁴ + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_1·b_5_44 + c_2_7·b_1_1³·b_3_11
       + c_2_7·b_1_0·b_1_1²·b_3_14 + c_2_7·b_1_0³·b_3_13 + c_2_7·b_1_0⁶
       + c_4_27·a_1_2·b_3_15 + c_4_27·a_1_2·b_3_13 + c_4_27·a_1_2·b_3_12 + c_4_27·a_1_2·b_3_10
       + c_4_26·a_1_2·b_3_15 + c_4_26·a_1_2·b_3_13 + c_4_26·a_1_2·b_3_12
       + c_4_26·a_1_2·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_12
       + c_2_7·a_1_2·b_1_0²·b_3_10 + c_2_7·c_4_27·b_1_3² + c_2_7·c_4_26·b_1_3²
       + c_2_7·c_4_26·b_1_1² + c_2_7·c_4_26·b_1_0·b_1_1 + c_2_7·c_4_26·b_1_0²
       + c_2_7²·b_1_0·b_3_13 + c_2_7²·a_1_2·b_3_10 + c_2_7²·a_1_2·b_1_0³
       + c_2_7·c_4_27·a_1_2² + c_2_7³·b_1_1² + c_2_7³·b_1_0² + c_2_7³·a_1_2²
54. b_3_13·b_5_43 + b_3_12·b_5_43 + b_3_10·b_5_43 + b_1_3³·b_5_43 + b_1_3⁵·b_3_15
       + b_1_3⁵·b_3_12 + a_1_2·b_1_3²·b_5_43 + a_1_2·b_1_0²·b_5_43 + a_1_2·b_1_0⁴·b_3_13
       + a_1_2·b_1_0⁷ + c_4_27·b_1_3·b_3_12 + c_4_27·b_1_3⁴ + c_4_27·b_1_1·b_3_11
       + c_4_27·b_1_0·b_3_14 + c_4_27·b_1_0·b_3_13 + c_4_27·b_1_0⁴ + c_4_26·b_1_3·b_3_12
       + c_4_26·b_1_3⁴ + c_4_26·b_1_0·b_3_14 + c_4_26·b_1_0·b_3_10 + c_4_26·b_1_0⁴
       + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_1³·b_3_11 + c_2_7·b_1_0·b_5_44
       + c_2_7·b_1_0·b_1_1²·b_3_14 + c_2_7·b_1_0·b_1_1²·b_3_11 + c_2_7·b_1_0³·b_3_13
       + c_2_7·b_1_0⁶ + c_4_27·a_1_2·b_3_15 + c_4_27·a_1_2·b_1_3³ + c_4_27·a_1_2·b_1_0³
       + c_4_26·a_1_2·b_3_15 + c_4_26·a_1_2·b_3_10 + c_4_26·a_1_2·b_1_3³
       + c_2_7·a_1_2·b_1_3²·b_3_12 + c_2_7·a_1_2·b_1_0²·b_3_13
       + c_2_7·a_1_2·b_1_0²·b_3_10 + c_2_7·c_4_27·b_1_3² + c_2_7·c_4_26·b_1_3²
       + c_2_7·c_4_26·b_1_1² + c_2_7·c_4_26·b_1_0² + c_2_7²·b_1_1·b_3_11
       + c_2_7²·b_1_0·b_3_13 + c_2_7²·b_1_0·b_3_10 + c_2_7·c_4_27·a_1_2·b_1_0
       + c_2_7³·b_1_0·b_1_1 + c_2_7³·b_1_0² + c_2_7³·a_1_2²
55. b_5_43² + b_1_3⁷·b_3_15 + a_1_2·b_1_3⁴·b_5_43 + a_1_2·b_1_3⁶·b_3_15
       + a_1_2·b_1_0⁴·b_5_43 + a_1_2·b_1_0⁶·b_3_10 + a_1_2·b_1_0⁹ + c_4_27·b_1_0³·b_3_10
       + c_4_27·b_1_0⁶ + c_4_26·b_1_3⁶ + c_4_26·b_1_0³·b_3_10 + c_4_26·b_1_0⁶
       + c_2_7·b_1_3⁵·b_3_15 + c_2_7·b_1_3⁸ + c_2_7·b_1_0⁵·b_3_10 + c_2_7·b_1_0⁸
       + c_4_27·a_1_2·b_1_3⁵ + c_4_27·a_1_2·b_1_0²·b_3_13 + c_4_26·a_1_2·b_1_3²·b_3_12
       + c_4_26·a_1_2·b_1_3⁵ + c_4_26·a_1_2·b_1_0²·b_3_10 + c_2_7·a_1_2·b_1_0⁷
       + c_4_27²·b_1_3² + c_4_27²·b_1_1² + c_4_27²·b_1_0² + c_4_26·c_4_27·b_1_0²
       + c_4_26²·b_1_3² + c_4_26²·b_1_0² + c_2_7·c_4_26·b_1_3⁴ + c_2_7·c_4_26·b_1_0⁴
       + c_2_7²·b_1_1³·b_3_11 + c_2_7²·b_1_0·b_1_1²·b_3_14
       + c_2_7²·b_1_0·b_1_1²·b_3_11 + c_2_7²·b_1_0³·b_3_10 + c_2_7·c_4_26·a_1_2·b_1_3³
       + c_2_7·c_4_26·a_1_2·b_1_0³ + c_2_7²·a_1_2·b_1_0²·b_3_13
       + c_2_7²·c_4_26·b_1_1² + c_2_7²·c_4_26·b_1_0² + c_2_7⁴·b_1_1²
       + c_2_7⁴·b_1_0²
56. b_5_44² + b_5_43² + b_1_0·b_1_1⁶·b_3_11 + a_1_2·b_1_3⁶·b_3_12
       + c_4_27·b_1_1³·b_3_11 + c_4_27·b_1_0·b_1_1²·b_3_14 + c_4_27·b_1_0·b_1_1²·b_3_11
       + c_4_26·b_1_1³·b_3_11 + c_4_26·b_1_0·b_1_1²·b_3_14 + c_4_26·b_1_0·b_1_1⁵
       + c_2_7·b_1_3⁸ + c_2_7·a_1_2·b_1_3⁷ + c_4_27²·b_1_1² + c_4_26·c_4_27·b_1_1²
       + c_4_26²·b_1_3² + c_4_26²·b_1_1² + c_4_26²·b_1_0² + c_2_7²·b_1_1³·b_3_11
       + c_2_7²·b_1_0·b_1_1²·b_3_14 + c_2_7²·b_1_0³·b_3_10
       + c_2_7²·a_1_2·b_1_3²·b_3_12 + c_2_7²·a_1_2·b_1_0²·b_3_13
       + c_2_7²·a_1_2·b_1_0⁵ + c_4_27²·a_1_2² + c_2_7²·c_4_27·b_1_1²
       + c_2_7²·c_4_26·b_1_0² + c_2_7³·b_1_3⁴ + c_2_7³·a_1_2·b_1_3³
       + c_2_7²·c_4_26·a_1_2² + c_2_7⁴·b_1_1² + c_2_7⁴·b_1_0²
57. b_5_43·b_5_44 + b_1_3⁵·b_5_43 + b_1_3⁷·b_3_12 + a_1_2·b_1_3⁶·b_3_15
       + a_1_2·b_1_0⁶·b_3_10 + a_1_2·b_1_0⁹ + c_4_27·b_1_3³·b_3_12 + c_4_27·b_1_3⁶
       + c_4_27·b_1_1·b_5_44 + c_4_27·b_1_0³·b_3_10 + c_4_27·b_1_0⁶ + c_4_26·b_1_3·b_5_43
       + c_4_26·b_1_3³·b_3_12 + c_4_26·b_1_0·b_5_44 + c_4_26·b_1_0³·b_3_10 + c_4_26·b_1_0⁶
       + c_2_7·b_1_3³·b_5_43 + c_2_7·b_1_3⁵·b_3_15 + c_2_7·b_1_3⁵·b_3_12 + c_2_7·b_1_3⁸
       + c_2_7·b_1_1³·b_5_44 + c_2_7·b_1_0⁵·b_3_10 + c_2_7·b_1_0⁸
       + c_4_27·a_1_2·b_1_0²·b_3_13 + c_4_27·a_1_2·b_1_0²·b_3_10 + c_4_27·a_1_2·b_1_0⁵
       + c_4_26·a_1_2·b_5_43 + c_2_7·a_1_2·b_1_3⁴·b_3_12 + c_2_7·a_1_2·b_1_3⁷
       + c_4_27²·b_1_3² + c_4_27²·b_1_0² + c_4_26·c_4_27·b_1_0² + c_4_26²·b_1_3²
       + c_4_26²·b_1_0·b_1_1 + c_2_7·c_4_27·b_1_3·b_3_12 + c_2_7·c_4_27·b_1_0·b_3_11
       + c_2_7·c_4_27·b_1_0·b_3_10 + c_2_7·c_4_26·b_1_3·b_3_12 + c_2_7·c_4_26·b_1_3⁴
       + c_2_7·c_4_26·b_1_1·b_3_14 + c_2_7·c_4_26·b_1_1·b_3_11 + c_2_7·c_4_26·b_1_0·b_3_13
       + c_2_7·c_4_26·b_1_0⁴ + c_2_7²·b_1_3³·b_3_15 + c_2_7²·b_1_1³·b_3_14
       + c_2_7²·b_1_1³·b_3_11 + c_2_7²·b_1_0·b_5_44 + c_2_7²·b_1_0·b_1_1²·b_3_14
       + c_2_7²·b_1_0·b_1_1²·b_3_11 + c_2_7²·b_1_0·b_1_1⁵ + c_2_7²·b_1_0³·b_3_13
       + c_2_7²·b_1_0³·b_3_10 + c_4_27²·a_1_2·b_1_3 + c_4_27²·a_1_2·b_1_0
       + c_4_26·c_4_27·a_1_2·b_1_0 + c_4_26²·a_1_2·b_1_3 + c_4_26²·a_1_2·b_1_0
       + c_2_7·c_4_27·a_1_2·b_3_13 + c_2_7·c_4_27·a_1_2·b_3_10 + c_2_7·c_4_27·a_1_2·b_1_3³
       + c_2_7·c_4_27·a_1_2·b_1_0³ + c_2_7·c_4_26·a_1_2·b_3_12 + c_2_7·c_4_26·a_1_2·b_3_10
       + c_2_7·c_4_26·a_1_2·b_1_3³ + c_2_7·c_4_26·a_1_2·b_1_0³
       + c_2_7²·a_1_2·b_1_3²·b_3_12 + c_2_7²·a_1_2·b_1_0⁵ + c_4_26²·a_1_2²
       + c_2_7²·c_4_27·b_1_3² + c_2_7²·c_4_27·b_1_0² + c_2_7²·c_4_26·b_1_3²
       + c_2_7²·c_4_26·b_1_1² + c_2_7²·c_4_26·b_1_0·b_1_1 + c_2_7³·b_1_1·b_3_14
       + c_2_7³·b_1_1·b_3_11 + c_2_7³·b_1_1⁴ + c_2_7³·b_1_0·b_1_1³ + c_2_7³·b_1_0⁴
       + c_2_7²·c_4_27·a_1_2·b_1_3 + c_2_7²·c_4_27·a_1_2·b_1_0
       + c_2_7²·c_4_26·a_1_2·b_1_3 + c_2_7²·c_4_26·a_1_2² + c_2_7⁴·b_1_1²
       + c_2_7⁴·b_1_0·b_1_1

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_1² + 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_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. c_2_7 → c_1_2², an element of degree 2
6. b_3_10 → 0, an element of degree 3
7. b_3_11 → 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_1⁴ + c_1_0⁴, an element of degree 4
13. c_4_27 → c_1_2⁴ + 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_2 → 0, an element of degree 1
2. b_1_0 → c_1_3, 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. c_2_7 → c_1_2², an element of degree 2
6. b_3_10 → c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_1·c_1_3² + c_1_1²·c_1_3 + c_1_0·c_1_3²
      + c_1_0²·c_1_3, an element of degree 3
7. b_3_11 → 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_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 → c_1_2²·c_1_3, an element of degree 3
11. b_3_15 → c_1_2·c_1_3² + 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_2·c_1_3³ + c_1_1·c_1_3³ + c_1_1⁴ + c_1_0·c_1_3³ + c_1_0⁴, an element of degree 4
13. c_4_27 → c_1_2·c_1_3³ + c_1_2⁴ + c_1_1·c_1_3³ + c_1_1²·c_1_3² + c_1_0·c_1_3³ + c_1_0⁴, an element of degree 4
14. b_5_43 → c_1_1²·c_1_3³ + c_1_1⁴·c_1_3 + c_1_0·c_1_3⁴ + c_1_0·c_1_2·c_1_3³
       + c_1_0·c_1_1·c_1_3³ + c_1_0·c_1_1²·c_1_3² + c_1_0²·c_1_2·c_1_3²
       + 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
15. b_5_44 → c_1_2·c_1_3⁴ + c_1_2³·c_1_3² + 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 + c_1_1²·c_1_2²·c_1_3
       + c_1_0·c_1_2·c_1_3³ + 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_2·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

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

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_3, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. c_2_7 → c_1_2·c_1_3 + c_1_2², an element of degree 2
6. b_3_10 → 0, an element of degree 3
7. b_3_11 → c_1_1·c_1_3² + c_1_1²·c_1_3 + c_1_0·c_1_3² + c_1_0²·c_1_3, an element of degree 3
8. b_3_12 → 0, an element of degree 3
9. b_3_13 → c_1_1·c_1_3² + c_1_1²·c_1_3 + c_1_0·c_1_3² + c_1_0²·c_1_3, an element of degree 3
10. b_3_14 → c_1_1·c_1_3² + c_1_0·c_1_3² + c_1_0²·c_1_3, an element of degree 3
11. b_3_15 → c_1_1·c_1_3² + c_1_1²·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_1·c_1_3³ + c_1_1⁴ + c_1_0·c_1_3³ + c_1_0⁴, an element of degree 4
13. c_4_27 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_3³ + c_1_0·c_1_3³ + c_1_0⁴, an element of degree 4
14. b_5_43 → c_1_1·c_1_3⁴ + 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_3⁴
       + c_1_0·c_1_2·c_1_3³ + c_1_0·c_1_2²·c_1_3² + c_1_0²·c_1_2·c_1_3²
       + c_1_0²·c_1_2²·c_1_3 + c_1_0⁴·c_1_3, 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_2·c_1_3³ + c_1_1·c_1_2²·c_1_3²
       + c_1_1³·c_1_3² + c_1_1⁴·c_1_3 + c_1_0·c_1_2·c_1_3³ + c_1_0·c_1_2²·c_1_3²
       + c_1_0·c_1_1²·c_1_3² + c_1_0²·c_1_2·c_1_3² + c_1_0²·c_1_2²·c_1_3
       + c_1_0²·c_1_1²·c_1_3, an element of degree 5

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

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_3, an element of degree 1
5. c_2_7 → c_1_2², an element of degree 2
6. b_3_10 → 0, an element of degree 3
7. b_3_11 → c_1_2²·c_1_3, an element of degree 3
8. b_3_12 → c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
9. b_3_13 → c_1_2²·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_1·c_1_3² + c_1_1²·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_1·c_1_3³ + c_1_1⁴ + c_1_0·c_1_3³ + c_1_0⁴, an element of degree 4
13. c_4_27 → c_1_2⁴ + c_1_1·c_1_3³ + c_1_1²·c_1_3² + c_1_0·c_1_3³ + c_1_0⁴, an element of degree 4
14. b_5_43 → c_1_2·c_1_3⁴ + c_1_2⁴·c_1_3 + c_1_1·c_1_3⁴ + c_1_1·c_1_2·c_1_3³
       + c_1_1²·c_1_2·c_1_3² + c_1_1⁴·c_1_3 + c_1_0·c_1_3⁴ + c_1_0·c_1_2·c_1_3³
       + c_1_0²·c_1_3³ + c_1_0²·c_1_2·c_1_3², an element of degree 5
15. b_5_44 → c_1_2³·c_1_3² + c_1_2⁴·c_1_3 + c_1_1·c_1_2·c_1_3³ + c_1_1²·c_1_2·c_1_3²
       + c_1_0·c_1_2·c_1_3³ + c_1_0²·c_1_3³ + c_1_0²·c_1_2·c_1_3² + c_1_0⁴·c_1_3, an element of degree 5

About the group

Ring generators

Ring relations

Completion information

Restriction maps

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