David J. Green

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Cohomology of group number 1323 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_0, a nilpotent element of degree 1
2. b_1_1, an element of degree 1
3. b_1_2, 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_0, a nilpotent 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_0·b_1_2 + a_1_0²
2. b_1_1·b_1_2 + b_1_1² + a_1_0²
3. b_1_2·b_1_3 + a_1_0·b_1_3 + a_1_0·b_1_1 + a_1_0²
4. a_1_0³
5. a_1_0·b_1_1·b_1_3 + a_1_0²·b_1_3
6. b_1_2·a_3_0 + a_1_0·a_3_0
7. b_1_1·a_3_0 + a_1_0·b_3_11 + c_2_7·a_1_0·b_1_3 + c_2_7·a_1_0·b_1_1 + c_2_7·a_1_0²
8. b_1_2·b_3_11 + b_1_1·b_3_11 + b_1_2·a_3_0 + c_2_7·b_1_2² + c_2_7·b_1_1·b_1_3
      + c_2_7·b_1_1² + c_2_7·a_1_0·b_1_3 + c_2_7·a_1_0·b_1_1 + c_2_7·a_1_0²
9. b_1_3·b_3_12 + b_1_3·a_3_0 + b_1_2·a_3_0 + b_1_1·a_3_0
10. b_1_2·a_3_0 + a_1_0·b_3_12
11. b_1_2·b_3_11 + b_1_1·b_3_12 + b_1_1⁴ + c_2_7·b_1_2² + c_2_7·b_1_1²
       + c_2_7·a_1_0·b_1_3 + c_2_7·a_1_0·b_1_1
12. b_1_2·a_3_0 + a_1_0·b_3_13 + c_2_7·a_1_0·b_1_3
13. b_1_2·b_3_14 + b_1_2·b_3_12 + b_1_2·b_3_11 + b_1_1·b_3_13 + b_1_1·a_3_0 + a_1_0·b_3_14
       + c_2_7·b_1_2² + c_2_7·b_1_1·b_1_3 + c_2_7·b_1_1² + c_2_7·a_1_0·b_1_3
       + c_2_7·a_1_0²
14. b_1_3·b_3_13 + b_1_3·b_3_11 + b_1_1·b_3_14 + b_1_1·b_3_13 + b_1_1⁴ + b_1_3·a_3_0
       + b_1_2·a_3_0 + b_1_1·a_3_0 + c_2_7·b_1_1·b_1_3 + c_2_7·a_1_0·b_1_3 + c_2_7·a_1_0·b_1_1
       + c_2_7·a_1_0²
15. b_1_3·b_3_13 + b_1_2·b_3_15 + b_1_2·b_3_14 + b_1_2·b_3_13 + b_1_2·b_3_11 + b_1_2⁴
       + b_1_1·b_3_13 + b_1_1⁴ + b_1_2·a_3_0 + c_2_7·b_1_3² + c_2_7·b_1_1·b_1_3
       + c_2_7·b_1_1²
16. b_1_3·b_3_13 + b_1_2·b_3_14 + b_1_2·b_3_12 + b_1_2·b_3_11 + b_1_1·b_3_13 + b_1_2·a_3_0
       + a_1_0·b_3_15 + c_2_7·b_1_3² + c_2_7·b_1_2² + c_2_7·b_1_1·b_1_3 + c_2_7·b_1_1²
       + c_2_7·a_1_0·b_1_3 + c_2_7·a_1_0²
17. b_1_2·b_3_14 + b_1_2·b_3_12 + b_1_1·b_3_15 + b_1_1⁴ + b_1_3·a_3_0 + b_1_2·a_3_0
       + c_2_7·b_1_1·b_1_3 + c_2_7·b_1_1² + c_2_7·a_1_0·b_1_3
18. a_1_0·b_1_1·b_3_14 + a_1_0²·b_3_14
19. a_3_0·b_3_12 + a_3_0²
20. b_3_11·b_3_12 + b_3_11² + b_1_1³·b_3_11 + a_3_0² + c_2_7·b_1_2·b_3_12
       + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_1⁴ + c_2_7·b_1_3·a_3_0 + c_2_7·a_1_0·b_3_11
       + c_2_7²·b_1_3² + c_2_7²·b_1_2² + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_1²
       + c_2_7²·a_1_0·b_1_3 + c_2_7²·a_1_0·b_1_1
21. a_3_0·b_3_13 + a_3_0² + c_2_7·b_1_3·a_3_0 + c_2_7·a_1_0²·b_1_3²
22. b_3_12·b_3_14 + b_3_12² + b_3_11·b_3_13 + b_3_11² + b_1_1³·b_3_13 + b_1_1³·b_3_11
       + a_3_0·b_3_14 + a_3_0·b_3_11 + a_3_0² + c_2_7·b_1_2·b_3_13 + c_2_7·b_1_1·b_3_14
       + c_2_7·b_1_1⁴ + c_2_7·a_1_0·b_3_11 + c_2_7·a_1_0·a_3_0 + c_2_7²·b_1_2²
       + c_2_7²·b_1_1² + c_2_7²·a_1_0·b_1_3 + c_2_7²·a_1_0·b_1_1 + c_2_7²·a_1_0²
23. b_3_12·b_3_15 + b_3_12·b_3_13 + b_3_12² + b_3_11·b_3_12 + b_3_11² + b_1_2³·b_3_12
       + b_1_1⁶ + a_3_0·b_3_15 + a_3_0² + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_1⁴
       + c_2_7·a_1_0·b_3_11 + c_2_7·a_1_0·a_3_0 + c_2_7²·b_1_3² + c_2_7²·b_1_2²
       + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_1² + c_2_7²·a_1_0·b_1_3 + c_2_7²·a_1_0·b_1_1
24. b_3_13·b_3_15 + b_3_13² + b_3_12·b_3_15 + b_3_12² + b_3_11·b_3_12 + b_3_11²
       + b_1_2³·b_3_13 + b_1_2³·b_3_12 + b_1_1³·b_3_13 + b_1_1⁶ + a_3_0²
       + c_2_7·b_1_3·b_3_15 + c_2_7·b_1_2·b_3_13 + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_1·b_1_3³
       + c_2_7·b_1_1⁴ + c_2_7·a_1_0·b_3_15 + c_2_7·a_1_0·b_3_14 + c_2_7·a_1_0·b_3_11
       + c_2_7·a_1_0·b_1_3³ + c_2_7·a_1_0²·b_1_3² + c_2_7²·b_1_2²
       + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_1² + c_2_7²·a_1_0²
25. b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_11·b_3_12 + a_3_0·b_3_14 + a_3_0·b_3_11
       + a_1_0·b_1_3²·b_3_15 + a_3_0² + a_1_0²·b_1_3·b_3_15 + a_1_0²·b_1_3·b_3_14
       + c_2_7·b_1_3·b_3_15 + c_2_7·b_1_2⁴ + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_1·b_1_3³
       + c_2_7·b_1_1⁴ + c_4_26·a_1_0·b_1_3 + c_2_7·a_1_0·b_3_11 + c_2_7·a_1_0·a_3_0
       + c_2_7·a_1_0²·b_1_3² + c_2_7²·b_1_3² + c_2_7²·b_1_2² + c_2_7²·b_1_1·b_1_3
       + c_2_7²·b_1_1²
26. b_3_13·b_3_15 + b_3_13² + b_3_12·b_3_14 + 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_1_2³·b_3_13 + b_1_1³·b_3_11 + a_3_0·b_3_14
       + b_1_3³·a_3_0 + a_1_0·b_1_3²·b_3_14 + a_3_0² + a_1_0²·b_1_3·b_3_15
       + a_1_0²·b_1_3·b_3_14 + c_4_26·b_1_1·b_1_3 + c_2_7·b_1_3·b_3_14 + c_2_7·b_1_2·b_3_13
       + c_2_7·b_1_2⁴ + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_1·b_1_3³ + c_2_7·b_1_1⁴
       + c_2_7·b_1_3·a_3_0 + c_2_7·a_1_0·b_3_14 + c_2_7·a_1_0·b_3_11 + c_2_7·a_1_0·b_1_3³
       + c_2_7·a_1_0·a_3_0 + c_2_7²·b_1_2² + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_1²
27. b_3_12² + b_1_2³·b_3_13 + b_1_2⁶ + b_1_1³·b_3_11 + b_1_1⁶ + a_1_0²·b_1_3·b_3_15
       + c_4_26·b_1_2² + c_2_7·b_1_2⁴ + c_2_7·a_1_0²·b_1_3² + c_2_7²·b_1_2²
28. a_3_0² + a_1_0²·b_1_3·b_3_15 + c_4_26·a_1_0² + c_2_7·a_1_0²·b_1_3²
       + c_2_7²·a_1_0²
29. a_3_0·b_3_11 + a_1_0²·b_1_3·b_3_15 + c_4_26·a_1_0·b_1_1 + c_2_7·b_1_3·a_3_0
       + c_2_7·a_1_0·b_3_11 + c_2_7·a_1_0·a_3_0 + c_2_7²·a_1_0·b_1_3 + c_2_7²·a_1_0²
30. b_3_11² + b_1_1³·b_3_13 + b_1_1³·b_3_11 + b_1_1⁶ + c_4_26·b_1_1² + c_2_7·b_1_1⁴
       + c_2_7·a_1_0²·b_1_3² + c_2_7²·b_1_3² + c_2_7²·b_1_2²
31. b_3_15² + b_3_12² + b_1_2³·b_3_13 + b_1_1³·b_3_13 + b_1_1⁶ + a_1_0·b_1_3²·b_3_15
       + a_3_0² + a_1_0²·b_1_3·b_3_15 + c_4_27·b_1_2² + c_2_7·b_1_3⁴ + c_2_7·b_1_2⁴
       + c_2_7·b_1_1⁴ + c_2_7·a_1_0·b_1_3³ + c_2_7²·b_1_3² + c_2_7²·b_1_2²
       + c_2_7²·a_1_0²
32. b_3_15² + b_3_13² + b_3_12² + b_1_2⁶ + b_1_1⁶ + a_1_0·b_1_3²·b_3_15
       + a_1_0²·b_1_3·b_3_15 + c_2_7·b_1_3⁴ + c_2_7·a_1_0·b_1_3³ + c_4_27·a_1_0²
       + c_2_7·a_1_0²·b_1_3² + c_2_7²·b_1_2² + c_2_7²·a_1_0²
33. b_3_15² + b_3_14² + b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_12·b_3_14 + b_3_12²
       + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_11·b_3_12 + b_1_3³·b_3_15 + b_1_2³·b_3_13
       + b_1_2⁶ + b_1_1³·b_3_11 + b_1_1⁶ + b_1_3³·a_3_0 + a_1_0·b_1_3²·b_3_15
       + a_1_0²·b_1_3·b_3_15 + c_4_26·b_1_3² + c_2_7·b_1_3·b_3_14 + c_2_7·b_1_2·b_3_13
       + c_2_7·b_1_2⁴ + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_1·b_1_3³ + c_2_7·b_1_1⁴
       + c_4_27·a_1_0·b_1_1 + c_2_7·b_1_3·a_3_0 + c_2_7·a_1_0·b_3_11 + c_2_7·a_1_0·b_1_3³
       + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_1² + c_2_7²·a_1_0·b_1_1
34. b_3_14² + b_3_12² + b_3_11² + b_1_3³·b_3_15 + b_1_1⁶ + b_1_3³·a_3_0
       + a_1_0²·b_1_3·b_3_15 + c_4_27·b_1_1² + c_4_26·b_1_3² + c_2_7·b_1_3⁴
       + c_2_7·a_1_0²·b_1_3² + c_2_7²·b_1_3² + c_2_7²·b_1_2² + c_2_7²·b_1_1²
35. b_3_11·b_3_15 + b_3_11·b_3_14 + b_3_11² + b_1_3·b_5_43 + b_1_3³·b_3_15 + a_3_0·b_3_14
       + a_1_0·b_1_3²·b_3_15 + a_1_0·b_1_3²·b_3_14 + a_3_0² + a_1_0²·b_1_3·b_3_15
       + a_1_0²·b_1_3·b_3_14 + c_4_27·b_1_3² + c_2_7·b_1_3·b_3_14 + c_2_7·b_1_3⁴
       + c_2_7·b_1_2·b_3_13 + c_2_7·b_1_2⁴ + c_2_7·b_1_1·b_3_13 + c_2_7·b_1_1·b_3_11
       + c_2_7·b_1_1·b_1_3³ + c_2_7·b_1_1⁴ + c_4_27·a_1_0·b_1_3 + c_2_7·b_1_3·a_3_0
       + c_2_7·a_1_0·b_3_14 + c_2_7·a_1_0·b_3_11 + c_2_7·a_1_0·b_1_3³
       + c_2_7·a_1_0²·b_1_3² + c_2_7²·b_1_1·b_1_3
36. b_3_15² + b_3_14² + b_3_13·b_3_14 + b_3_13² + b_3_12·b_3_15 + b_3_12·b_3_14
       + b_3_12·b_3_13 + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_11·b_3_12 + b_3_11²
       + b_1_3³·b_3_15 + b_1_2·b_5_43 + b_1_2³·b_3_12 + b_1_2⁶ + b_1_1³·b_3_11 + b_1_1⁶
       + b_1_3³·a_3_0 + a_3_0² + a_1_0²·b_1_3·b_3_14 + c_4_26·b_1_3² + c_2_7·b_1_3·b_3_15
       + c_2_7·b_1_3·b_3_14 + c_2_7·b_1_2·b_3_13 + c_4_27·a_1_0·b_1_3 + c_2_7·b_1_3·a_3_0
       + c_2_7·a_1_0·b_3_14 + c_2_7·a_1_0·b_1_3³ + c_2_7·a_1_0²·b_1_3² + c_2_7²·b_1_2²
       + c_2_7²·b_1_1²
37. b_3_15² + b_3_13·b_3_15 + b_3_12·b_3_15 + b_3_11·b_3_12 + b_3_11² + b_1_2³·b_3_13
       + b_1_2³·b_3_12 + b_1_2⁶ + b_1_1³·b_3_13 + a_3_0·b_3_11 + a_1_0·b_5_43
       + a_1_0²·b_1_3·b_3_14 + c_2_7·b_1_3·b_3_15 + c_2_7·b_1_3⁴ + c_2_7·b_1_2·b_3_13
       + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_1·b_1_3³ + c_2_7·b_1_1⁴ + c_4_27·a_1_0·b_1_3
       + c_2_7·b_1_3·a_3_0 + c_2_7·a_1_0·b_3_14 + c_2_7·a_1_0·b_3_11 + c_2_7·a_1_0·b_1_3³
       + c_2_7·a_1_0·a_3_0 + c_2_7·a_1_0²·b_1_3² + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_1²
       + c_2_7²·a_1_0·b_1_3 + c_2_7²·a_1_0·b_1_1 + c_2_7²·a_1_0²
38. b_3_15² + b_3_14² + b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_11·b_3_15 + b_3_11·b_3_13
       + b_3_11·b_3_12 + b_1_3³·b_3_15 + b_1_2³·b_3_13 + b_1_2⁶ + b_1_1·b_5_43
       + b_1_1³·b_3_13 + b_1_1³·b_3_11 + a_3_0·b_3_14 + a_3_0·b_3_11 + a_1_0·b_1_3²·b_3_15
       + a_1_0·b_1_3²·b_3_14 + a_3_0² + a_1_0²·b_1_3·b_3_14 + c_4_27·b_1_1·b_1_3
       + c_4_26·b_1_3² + c_2_7·b_1_3·b_3_14 + c_2_7·b_1_2·b_3_13 + c_2_7·b_1_2⁴
       + c_2_7·b_1_1·b_3_13 + c_2_7·b_1_1·b_3_11 + c_2_7·b_1_1·b_1_3³ + c_2_7·b_1_3·a_3_0
       + c_2_7·a_1_0·b_3_14 + c_2_7·a_1_0²·b_1_3² + c_2_7²·a_1_0·b_1_1 + c_2_7²·a_1_0²
39. b_3_15² + b_3_14·b_3_15 + b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_12·b_3_14 + b_3_12·b_3_13
       + b_3_12² + b_3_11·b_3_14 + b_3_11·b_3_13 + b_1_3·b_5_44 + b_1_2³·b_3_13
       + b_1_2³·b_3_12 + b_1_2⁶ + b_1_1·b_1_3²·b_3_14 + b_1_1³·b_3_13 + a_3_0·b_3_14
       + a_1_0·b_1_3²·b_3_15 + c_4_27·b_1_3² + c_4_27·b_1_1·b_1_3 + c_2_7·b_1_3⁴
       + c_2_7·b_1_1⁴ + c_2_7·a_1_0·b_3_14 + c_2_7·a_1_0·a_3_0 + c_2_7·a_1_0²·b_1_3²
       + c_2_7²·b_1_3² + c_2_7²·b_1_2² + c_2_7²·b_1_1·b_1_3 + c_2_7²·a_1_0·b_1_1
40. b_3_15² + b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_13² + b_3_12·b_3_15 + b_3_12·b_3_14
       + b_3_12² + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_11² + b_1_2·b_5_44 + b_1_1³·b_3_11
       + b_1_1⁶ + a_1_0·b_1_3²·b_3_15 + a_3_0² + a_1_0²·b_1_3·b_3_15
       + a_1_0²·b_1_3·b_3_14 + c_2_7·b_1_3·b_3_14 + c_2_7·b_1_3⁴ + c_2_7·b_1_2·b_3_13
       + c_2_7·b_1_1·b_3_13 + c_4_27·a_1_0·b_1_3 + c_2_7·b_1_3·a_3_0 + c_2_7·a_1_0·b_3_14
       + c_2_7·a_1_0·b_1_3³ + c_2_7·a_1_0·a_3_0 + c_2_7·a_1_0²·b_1_3²
       + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_1² + c_2_7²·a_1_0·b_1_3 + c_2_7²·a_1_0·b_1_1
41. b_3_15² + b_3_14² + b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_12·b_3_15 + b_3_12·b_3_14
       + b_3_12·b_3_13 + b_3_11·b_3_15 + b_3_11·b_3_13 + b_3_11² + b_1_3³·b_3_15
       + b_1_2³·b_3_13 + b_1_2³·b_3_12 + b_1_2⁶ + b_1_1³·b_3_11 + a_3_0·b_3_11
       + b_1_3³·a_3_0 + a_1_0·b_5_44 + a_1_0·b_1_3²·b_3_15 + a_1_0²·b_1_3·b_3_14
       + c_4_26·b_1_3² + c_2_7·b_1_3·b_3_14 + c_2_7·b_1_2·b_3_13 + c_2_7·b_1_2⁴
       + c_4_27·a_1_0·b_1_3 + c_2_7·b_1_3·a_3_0 + c_2_7·a_1_0·b_3_14 + c_2_7·a_1_0·b_1_3³
       + c_2_7²·b_1_3² + c_2_7²·b_1_2² + c_2_7²·a_1_0·b_1_3 + c_2_7²·a_1_0·b_1_1
       + c_2_7²·a_1_0²
42. b_3_14² + b_3_13·b_3_15 + b_3_13·b_3_14 + b_3_13² + b_3_12·b_3_14 + b_3_11·b_3_13
       + b_3_11² + b_1_3³·b_3_15 + b_1_2³·b_3_13 + b_1_1·b_5_44 + b_1_1⁶ + b_1_3³·a_3_0
       + c_4_27·b_1_1·b_1_3 + c_4_26·b_1_3² + c_2_7·b_1_3·b_3_15 + c_2_7·b_1_3·b_3_14
       + c_2_7·b_1_3⁴ + c_2_7·b_1_1⁴ + c_2_7·a_1_0·b_3_11 + c_2_7·a_1_0·b_1_3³
       + c_2_7²·b_1_3² + c_2_7²·b_1_2² + c_2_7²·b_1_1² + c_2_7²·a_1_0²
43. b_3_15·b_5_43 + b_3_13·b_5_43 + b_3_12·b_5_43 + b_3_11·b_5_43 + b_1_2³·b_5_43
       + b_1_1³·b_5_43 + b_1_1⁵·b_3_13 + b_1_1⁸ + a_3_0·b_5_43 + b_1_3²·a_3_0·b_3_14
       + a_1_0²·b_1_3³·b_3_14 + c_4_27·b_1_3·b_3_15 + c_4_27·b_1_1·b_3_14
       + c_4_27·b_1_1·b_3_13 + c_4_26·b_1_1·b_3_13 + c_4_26·b_1_1·b_3_11
       + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_3⁶ + c_2_7·b_1_1·b_1_3²·b_3_14
       + c_4_27·b_1_3·a_3_0 + c_4_27·a_1_0·b_3_15 + c_4_27·a_1_0·b_3_11 + c_4_26·b_1_3·a_3_0
       + c_4_26·a_1_0·b_3_15 + c_4_26·a_1_0·b_3_14 + c_4_26·a_1_0·b_1_3³
       + c_2_7·a_3_0·b_3_14 + c_2_7·b_1_3³·a_3_0 + c_2_7·a_1_0·b_1_3²·b_3_15
       + c_4_27·a_1_0·a_3_0 + c_4_27·a_1_0²·b_1_3² + c_2_7·a_1_0²·b_1_3·b_3_14
       + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_1²
       + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_1·b_3_13
       + c_2_7²·b_1_1·b_1_3³ + c_2_7²·b_1_1⁴ + c_2_7·c_4_27·a_1_0·b_1_1
       + c_2_7·c_4_26·a_1_0·b_1_1 + c_2_7²·b_1_3·a_3_0 + c_2_7²·a_1_0·b_3_11
       + c_2_7²·a_1_0·b_1_3³ + c_2_7³·b_1_3² + c_2_7³·a_1_0·b_1_1
44. b_3_12·b_5_43 + b_1_2⁸ + b_1_1³·b_5_43 + b_1_1⁵·b_3_13 + a_3_0·b_5_43
       + c_4_27·b_1_2⁴ + c_4_26·b_1_2·b_3_13 + c_4_26·b_1_1·b_3_11 + c_2_7·b_1_2·b_5_43
       + c_2_7·b_1_2³·b_3_12 + c_2_7·b_1_1³·b_3_11 + c_2_7·b_1_1⁶ + c_4_27·a_1_0·b_3_11
       + c_4_26·a_1_0·b_3_11 + c_2_7·a_1_0·b_1_3²·b_3_15 + c_4_27·a_1_0·a_3_0
       + c_2_7·a_1_0²·b_1_3·b_3_15 + c_2_7·a_1_0²·b_1_3·b_3_14 + c_2_7·a_1_0²·b_1_3⁴
       + c_2_7·c_4_26·b_1_2² + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7²·b_1_2·b_3_12
       + c_2_7²·b_1_1·b_3_11 + c_2_7²·b_1_1⁴ + c_2_7·c_4_26·a_1_0·b_1_1
       + c_2_7²·a_1_0·b_3_15 + c_2_7²·a_1_0·b_1_3³ + c_2_7·c_4_27·a_1_0²
       + c_2_7·c_4_26·a_1_0² + c_2_7²·a_1_0²·b_1_3² + c_2_7³·b_1_2²
       + c_2_7³·b_1_1·b_1_3 + c_2_7³·b_1_1² + c_2_7³·a_1_0·b_1_3 + c_2_7³·a_1_0·b_1_1
       + c_2_7³·a_1_0²
45. 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_3³·b_5_44
       + b_1_2³·b_5_43 + b_1_2⁵·b_3_12 + b_1_2⁸ + b_1_1·b_1_3⁴·b_3_14 + b_1_1⁵·b_3_11
       + b_1_3²·a_3_0·b_3_14 + b_1_3⁵·a_3_0 + a_1_0·b_1_3⁴·b_3_15 + a_1_0·b_1_3⁴·b_3_14
       + c_4_27·b_1_3·b_3_14 + c_4_27·b_1_3⁴ + c_4_27·b_1_2·b_3_12 + c_4_27·b_1_2⁴
       + c_4_27·b_1_1·b_3_11 + c_4_27·b_1_1·b_1_3³ + c_4_26·b_1_2·b_3_13
       + c_4_26·b_1_1·b_3_14 + c_4_26·b_1_1·b_1_3³ + c_4_26·b_1_1⁴ + c_2_7·b_1_3³·b_3_15
       + c_2_7·b_1_3³·b_3_14 + c_2_7·b_1_2³·b_3_13 + c_2_7·b_1_1·b_1_3²·b_3_14
       + c_2_7·b_1_1·b_1_3⁵ + c_2_7·b_1_1³·b_3_13 + c_4_27·a_1_0·b_3_15
       + c_4_26·a_1_0·b_3_15 + c_4_26·a_1_0·b_3_14 + c_4_26·a_1_0·b_3_11
       + c_4_26·a_1_0·b_1_3³ + c_2_7·b_1_3³·a_3_0 + c_2_7·a_1_0·b_1_3²·b_3_15
       + c_2_7·a_1_0·b_1_3⁵ + c_4_27·a_1_0·a_3_0 + c_4_27·a_1_0²·b_1_3²
       + c_4_26·a_1_0²·b_1_3² + c_2_7·a_1_0²·b_1_3·b_3_14 + c_2_7·a_1_0²·b_1_3⁴
       + c_2_7·c_4_27·b_1_3² + c_2_7·c_4_26·b_1_2² + c_2_7·c_4_26·b_1_1·b_1_3
       + c_2_7·c_4_26·b_1_1² + 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_2·b_3_12 + c_2_7²·b_1_2⁴ + c_2_7²·b_1_1·b_1_3³
       + c_2_7·c_4_27·a_1_0·b_1_1 + c_2_7·c_4_26·a_1_0·b_1_1 + c_2_7²·a_1_0·b_3_15
       + c_2_7²·a_1_0·b_3_14 + c_2_7²·a_1_0·b_1_3³ + c_2_7·c_4_26·a_1_0²
       + c_2_7³·b_1_3² + c_2_7³·b_1_1·b_1_3 + c_2_7³·a_1_0·b_1_3 + c_2_7³·a_1_0·b_1_1
46. b_3_13·b_5_43 + b_3_12·b_5_43 + b_1_2³·b_5_43 + b_1_2⁵·b_3_12 + b_1_2⁸
       + b_1_1⁵·b_3_13 + a_3_0·b_5_43 + a_1_0·b_1_3²·b_5_44 + a_1_0²·b_1_3³·b_3_14
       + c_4_27·b_1_2·b_3_12 + c_4_27·b_1_2⁴ + c_4_26·b_1_2·b_3_13 + c_4_26·b_1_1·b_3_13
       + c_4_26·b_1_1·b_3_11 + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_2³·b_3_13
       + c_2_7·b_1_2³·b_3_12 + c_2_7·b_1_1·b_5_43 + c_2_7·b_1_1³·b_3_13
       + c_2_7·b_1_1³·b_3_11 + c_4_27·a_1_0·b_3_15 + c_4_27·a_1_0·b_3_14
       + c_4_27·a_1_0·b_1_3³ + c_4_26·a_1_0·b_3_11 + c_2_7·a_3_0·b_3_14
       + c_2_7·a_1_0·b_1_3²·b_3_15 + c_2_7·a_1_0·b_1_3⁵ + c_4_27·a_1_0²·b_1_3²
       + c_4_26·a_1_0·a_3_0 + c_4_26·a_1_0²·b_1_3² + c_2_7·a_1_0²·b_1_3·b_3_15
       + c_2_7·a_1_0²·b_1_3⁴ + c_2_7·c_4_27·b_1_3² + c_2_7·c_4_27·b_1_2²
       + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_2² + c_2_7·c_4_26·b_1_1·b_1_3
       + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3⁴ + c_2_7²·b_1_2·b_3_13 + c_2_7²·b_1_1·b_3_14
       + c_2_7²·b_1_1⁴ + c_2_7·c_4_27·a_1_0·b_1_3 + c_2_7·c_4_27·a_1_0·b_1_1
       + c_2_7²·b_1_3·a_3_0 + c_2_7²·a_1_0·b_3_15 + c_2_7²·a_1_0·b_3_11
       + c_2_7²·a_1_0·b_1_3³ + c_2_7·c_4_27·a_1_0² + c_2_7²·a_1_0·a_3_0
       + c_2_7²·a_1_0²·b_1_3² + c_2_7³·b_1_3² + c_2_7³·b_1_2² + c_2_7³·b_1_1·b_1_3
       + c_2_7³·b_1_1²
47. b_3_13·b_5_43 + b_3_11·b_5_43 + b_1_2³·b_5_43 + b_1_2⁵·b_3_12 + b_1_1³·b_5_43
       + b_1_1⁵·b_3_13 + b_1_1⁸ + a_3_0·b_5_43 + b_1_3²·a_3_0·b_3_14 + a_1_0·b_1_3⁴·b_3_15
       + a_1_0²·b_1_3·b_5_44 + a_1_0²·b_1_3³·b_3_14 + c_4_27·b_1_2·b_3_12
       + c_4_27·b_1_1·b_3_14 + c_4_27·b_1_1·b_3_13 + c_4_26·b_1_1·b_3_11
       + c_2_7·b_1_2³·b_3_13 + c_2_7·b_1_1·b_5_43 + c_2_7·b_1_1³·b_3_13 + c_2_7·b_1_1⁶
       + c_4_26·a_1_0·b_3_11 + c_4_26·a_1_0·b_1_3³ + c_2_7·a_3_0·b_3_14
       + c_2_7·b_1_3³·a_3_0 + c_2_7·a_1_0·b_1_3⁵ + c_4_27·a_1_0²·b_1_3²
       + c_4_26·a_1_0²·b_1_3² + c_2_7·a_1_0²·b_1_3·b_3_14 + c_2_7·c_4_27·b_1_2²
       + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_1² + c_2_7²·b_1_2·b_3_13
       + c_2_7²·b_1_2·b_3_12 + c_2_7²·b_1_1·b_3_13 + c_2_7²·b_1_1·b_3_11 + c_2_7²·b_1_1⁴
       + c_2_7·c_4_27·a_1_0·b_1_3 + c_2_7·c_4_27·a_1_0·b_1_1 + c_2_7·c_4_26·a_1_0·b_1_1
       + c_2_7²·b_1_3·a_3_0 + c_2_7²·a_1_0·b_3_15 + c_2_7²·a_1_0·b_3_11
       + c_2_7²·a_1_0·b_1_3³ + c_2_7·c_4_27·a_1_0² + c_2_7²·a_1_0·a_3_0
       + c_2_7²·a_1_0²·b_1_3² + c_2_7³·a_1_0²
48. b_3_12·b_5_44 + b_1_2⁵·b_3_13 + b_1_1³·b_5_43 + b_1_1⁸ + c_4_27·b_1_2·b_3_12
       + c_4_27·b_1_2⁴ + c_4_27·b_1_1·b_3_11 + c_4_27·b_1_1⁴ + c_4_26·b_1_2·b_3_13
       + c_4_26·b_1_2⁴ + c_4_26·b_1_1·b_3_11 + c_4_26·b_1_1⁴ + c_2_7·b_1_2³·b_3_13
       + c_2_7·b_1_1·b_5_43 + c_2_7·b_1_1·b_1_3²·b_3_14 + c_2_7·b_1_1³·b_3_13
       + c_4_27·b_1_3·a_3_0 + c_4_27·a_1_0·b_3_11 + c_4_26·a_1_0·b_3_15 + c_2_7·a_3_0·b_3_14
       + c_2_7·b_1_3³·a_3_0 + c_2_7·a_1_0·b_1_3²·b_3_14 + c_2_7·a_1_0·b_1_3⁵
       + c_4_27·a_1_0·a_3_0 + c_4_26·a_1_0·a_3_0 + c_4_26·a_1_0²·b_1_3²
       + c_2_7·a_1_0²·b_1_3·b_3_15 + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_1²
       + c_2_7²·b_1_2·b_3_13 + c_2_7²·b_1_2·b_3_12 + c_2_7²·b_1_2⁴ + c_2_7²·b_1_1·b_3_13
       + c_2_7²·b_1_1·b_1_3³ + c_2_7²·b_1_1⁴ + c_2_7·c_4_27·a_1_0·b_1_3
       + c_2_7²·b_1_3·a_3_0 + c_2_7²·a_1_0·b_3_15 + c_2_7²·a_1_0·b_3_14
       + c_2_7²·a_1_0·b_1_3³ + c_2_7·c_4_26·a_1_0² + c_2_7²·a_1_0·a_3_0
       + c_2_7²·a_1_0²·b_1_3² + c_2_7³·b_1_1·b_1_3 + c_2_7³·a_1_0·b_1_3
       + c_2_7³·a_1_0·b_1_1
49. b_3_13·b_5_44 + b_3_13·b_5_43 + b_3_11·b_5_44 + b_1_2³·b_5_43 + b_1_1³·b_5_43
       + b_1_1⁵·b_3_13 + b_1_1⁸ + a_3_0·b_5_43 + a_1_0²·b_1_3³·b_3_15 + c_4_27·b_1_2·b_3_13
       + c_4_27·b_1_1·b_3_14 + c_4_26·b_1_1·b_3_13 + c_4_26·b_1_1·b_3_11
       + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_2³·b_3_13 + c_2_7·b_1_1·b_5_43
       + c_2_7·b_1_1·b_1_3²·b_3_14 + c_2_7·b_1_1³·b_3_13 + c_4_27·a_1_0·b_3_15
       + c_4_27·a_1_0·b_3_14 + c_4_27·a_1_0·b_3_11 + c_4_26·b_1_3·a_3_0 + c_4_26·a_1_0·b_3_15
       + c_4_26·a_1_0·b_3_14 + c_2_7·a_3_0·b_3_14 + c_2_7·b_1_3³·a_3_0
       + c_4_26·a_1_0²·b_1_3² + c_2_7·a_1_0²·b_1_3·b_3_15 + c_2_7·a_1_0²·b_1_3·b_3_14
       + c_2_7·a_1_0²·b_1_3⁴ + c_2_7·c_4_27·b_1_3² + c_2_7·c_4_27·b_1_1·b_1_3
       + c_2_7·c_4_26·b_1_1² + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3⁴
       + c_2_7²·b_1_2·b_3_13 + c_2_7²·b_1_2⁴ + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_1·b_3_13
       + c_2_7²·b_1_1·b_3_11 + c_2_7·c_4_26·a_1_0·b_1_3 + c_2_7²·b_1_3·a_3_0
       + c_2_7²·a_1_0·b_3_11 + c_2_7²·a_1_0·b_1_3³ + c_2_7·c_4_26·a_1_0²
       + c_2_7³·b_1_3² + c_2_7³·b_1_2² + c_2_7³·b_1_1·b_1_3 + c_2_7³·b_1_1²
       + c_2_7³·a_1_0·b_1_3 + c_2_7³·a_1_0·b_1_1 + c_2_7³·a_1_0²
50. a_3_0·b_5_44 + c_2_7·b_1_1·b_1_3²·b_3_14 + c_4_27·b_1_3·a_3_0 + c_4_27·a_1_0·b_3_11
       + c_4_26·a_1_0·b_3_15 + c_4_26·a_1_0·b_3_11 + c_2_7·a_3_0·b_3_14 + c_2_7·a_1_0·b_1_3⁵
       + c_4_26·a_1_0·a_3_0 + c_4_26·a_1_0²·b_1_3² + c_2_7·a_1_0²·b_1_3·b_3_15
       + c_2_7²·b_1_1·b_1_3³ + c_2_7·c_4_27·a_1_0·b_1_3 + c_2_7·c_4_27·a_1_0·b_1_1
       + c_2_7²·a_1_0·b_3_15 + c_2_7·c_4_27·a_1_0² + c_2_7·c_4_26·a_1_0²
       + c_2_7²·a_1_0²·b_1_3² + c_2_7³·a_1_0·b_1_3 + c_2_7³·a_1_0·b_1_1
51. b_3_14·b_5_44 + b_3_13·b_5_43 + b_3_11·b_5_44 + b_1_2³·b_5_43 + b_1_2⁵·b_3_13
       + b_1_2⁵·b_3_12 + b_1_1⁵·b_3_11 + a_3_0·b_5_43 + b_1_3²·a_3_0·b_3_14 + b_1_3⁵·a_3_0
       + a_1_0·b_1_3⁴·b_3_14 + c_4_27·b_1_3·b_3_14 + c_4_27·b_1_2⁴ + c_4_26·b_1_3·b_3_15
       + c_4_26·b_1_2·b_3_13 + c_4_26·b_1_2⁴ + c_4_26·b_1_1·b_3_14 + c_4_26·b_1_1·b_3_13
       + c_4_26·b_1_1·b_3_11 + c_4_26·b_1_1·b_1_3³ + c_2_7·b_1_3⁶ + c_2_7·b_1_2³·b_3_12
       + c_2_7·b_1_1·b_5_43 + c_2_7·b_1_1³·b_3_11 + c_2_7·b_1_1⁶ + c_4_27·a_1_0·b_3_11
       + c_4_26·a_1_0·b_3_15 + c_4_26·a_1_0·b_3_14 + c_4_26·a_1_0·b_3_11
       + c_4_26·a_1_0·b_1_3³ + c_2_7·a_1_0·b_1_3⁵ + c_4_27·a_1_0·a_3_0
       + c_4_27·a_1_0²·b_1_3² + c_2_7·a_1_0²·b_1_3·b_3_15 + c_2_7·a_1_0²·b_1_3⁴
       + c_2_7·c_4_26·b_1_1² + c_2_7²·b_1_3·b_3_14 + c_2_7²·b_1_2·b_3_13
       + c_2_7²·b_1_2·b_3_12 + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_1·b_3_13 + c_2_7²·b_1_1⁴
       + c_2_7·c_4_27·a_1_0·b_1_3 + c_2_7·c_4_26·a_1_0·b_1_3 + c_2_7²·b_1_3·a_3_0
       + c_2_7²·a_1_0·b_3_15 + c_2_7²·a_1_0²·b_1_3² + c_2_7³·b_1_2²
       + c_2_7³·b_1_1·b_1_3 + c_2_7³·b_1_1² + c_2_7³·a_1_0·b_1_3
52. b_3_15·b_5_44 + b_3_13·b_5_43 + b_3_12·b_5_43 + b_3_11·b_5_43 + b_1_2⁵·b_3_13
       + b_1_2⁵·b_3_12 + b_1_2⁸ + b_1_1⁵·b_3_11 + b_1_1⁸ + a_3_0·b_5_43
       + a_1_0²·b_1_3³·b_3_15 + c_4_27·b_1_3·b_3_15 + c_4_27·b_1_2·b_3_13
       + c_4_27·b_1_2·b_3_12 + c_4_27·b_1_2⁴ + c_4_27·b_1_1·b_3_14 + c_4_27·b_1_1·b_3_11
       + c_4_26·b_1_2⁴ + c_4_26·b_1_1·b_3_13 + c_4_26·b_1_1·b_3_11 + c_4_26·b_1_1⁴
       + c_2_7·b_1_3³·b_3_14 + c_2_7·b_1_2³·b_3_13 + c_2_7·b_1_2⁶ + c_2_7·b_1_1³·b_3_13
       + c_2_7·b_1_1⁶ + c_4_27·a_1_0·b_3_14 + c_4_26·b_1_3·a_3_0 + c_4_26·a_1_0·b_3_15
       + c_4_26·a_1_0·b_3_14 + c_2_7·a_3_0·b_3_14 + c_2_7·b_1_3³·a_3_0
       + c_2_7·a_1_0·b_1_3²·b_3_15 + c_2_7·a_1_0·b_1_3⁵ + c_2_7·a_1_0²·b_1_3·b_3_15
       + c_2_7·a_1_0²·b_1_3·b_3_14 + c_2_7·c_4_26·b_1_2² + c_2_7·c_4_26·b_1_1·b_1_3
       + 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_2⁴
       + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_1·b_3_11 + c_2_7²·b_1_1·b_1_3³
       + c_2_7²·b_1_1⁴ + c_2_7·c_4_27·a_1_0·b_1_3 + c_2_7·c_4_27·a_1_0·b_1_1
       + c_2_7·c_4_26·a_1_0·b_1_1 + c_2_7²·b_1_3·a_3_0 + c_2_7²·a_1_0·b_3_11
       + c_2_7·c_4_27·a_1_0² + c_2_7·c_4_26·a_1_0² + c_2_7²·a_1_0·a_3_0
       + c_2_7³·b_1_3² + c_2_7³·b_1_1² + c_2_7³·a_1_0·b_1_1 + c_2_7³·a_1_0²
53. b_3_13·b_5_43 + b_3_12·b_5_43 + b_3_11·b_5_44 + b_3_11·b_5_43 + b_1_2³·b_5_43
       + b_1_2⁵·b_3_12 + b_1_2⁸ + b_1_1⁵·b_3_13 + b_1_3²·a_3_0·b_3_14
       + a_1_0·b_1_3⁴·b_3_15 + a_1_0²·b_1_3³·b_3_15 + a_1_0²·b_1_3³·b_3_14
       + c_4_27·b_1_2·b_3_12 + c_4_27·b_1_2⁴ + c_4_26·b_1_2·b_3_13 + c_4_26·b_1_1·b_3_13
       + c_4_26·b_1_1·b_3_11 + c_2_7·b_1_3·b_5_44 + c_2_7·b_1_2³·b_3_13 + c_2_7·b_1_1·b_5_43
       + c_2_7·b_1_1·b_1_3²·b_3_14 + c_2_7·b_1_1·b_1_3⁵ + c_2_7·b_1_1³·b_3_13
       + c_2_7·b_1_1⁶ + c_4_27·b_1_3·a_3_0 + c_4_27·a_1_0·b_3_15 + c_4_27·a_1_0·b_3_14
       + c_4_26·b_1_3·a_3_0 + c_4_26·a_1_0·b_3_14 + c_4_26·a_1_0·b_3_11
       + c_4_26·a_1_0·b_1_3³ + c_2_7·a_3_0·b_3_14 + c_2_7·a_1_0·b_1_3⁵
       + c_4_26·a_1_0·a_3_0 + c_4_26·a_1_0²·b_1_3² + c_2_7·a_1_0²·b_1_3·b_3_15
       + c_2_7·a_1_0²·b_1_3⁴ + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_1²
       + c_2_7·c_4_26·b_1_2² + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7²·b_1_2·b_3_12
       + c_2_7²·b_1_2⁴ + c_2_7²·b_1_1·b_1_3³ + c_2_7·c_4_27·a_1_0·b_1_1
       + c_2_7·c_4_26·a_1_0·b_1_1 + c_2_7²·b_1_3·a_3_0 + c_2_7²·a_1_0·b_3_14
       + c_2_7²·a_1_0·b_1_3³ + c_2_7·c_4_27·a_1_0² + c_2_7·c_4_26·a_1_0²
       + c_2_7²·a_1_0²·b_1_3² + c_2_7³·a_1_0·b_1_3 + c_2_7³·a_1_0²
54. b_3_13·b_5_43 + b_3_12·b_5_43 + b_1_2³·b_5_43 + b_1_2⁵·b_3_12 + b_1_2⁸
       + b_1_1⁵·b_3_13 + c_4_27·b_1_2·b_3_12 + c_4_27·b_1_2⁴ + c_4_26·b_1_2·b_3_13
       + c_4_26·b_1_1·b_3_13 + c_4_26·b_1_1·b_3_11 + c_2_7·b_1_3³·b_3_15
       + c_2_7·b_1_2³·b_3_13 + c_2_7·b_1_2³·b_3_12 + c_2_7·b_1_1·b_5_43
       + c_2_7·b_1_1·b_1_3⁵ + c_2_7·b_1_1³·b_3_13 + c_2_7·b_1_1³·b_3_11
       + c_4_27·b_1_3·a_3_0 + c_4_27·a_1_0·b_3_15 + c_4_27·a_1_0·b_3_14 + c_2_7·a_3_0·b_3_14
       + c_2_7·a_1_0·b_5_44 + c_2_7·a_1_0·b_1_3²·b_3_15 + c_2_7·a_1_0·b_1_3²·b_3_14
       + c_2_7·a_1_0·b_1_3⁵ + c_4_27·a_1_0·a_3_0 + c_2_7·a_1_0²·b_1_3·b_3_15
       + c_2_7·a_1_0²·b_1_3·b_3_14 + c_2_7·a_1_0²·b_1_3⁴ + c_2_7·c_4_27·b_1_3²
       + c_2_7·c_4_27·b_1_2² + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_2²
       + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3⁴
       + c_2_7²·b_1_2·b_3_13 + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_1·b_1_3³
       + c_2_7²·b_1_1⁴ + c_2_7·c_4_26·a_1_0·b_1_3 + c_2_7·c_4_26·a_1_0·b_1_1
       + c_2_7²·b_1_3·a_3_0 + c_2_7²·a_1_0·b_3_15 + c_2_7²·a_1_0·b_3_14
       + c_2_7²·a_1_0·b_1_3³ + c_2_7·c_4_27·a_1_0² + c_2_7²·a_1_0·a_3_0
       + c_2_7²·a_1_0²·b_1_3² + c_2_7³·b_1_3² + c_2_7³·b_1_2² + c_2_7³·b_1_1·b_1_3
       + c_2_7³·b_1_1² + c_2_7³·a_1_0·b_1_3 + c_2_7³·a_1_0²
55. b_5_43² + b_1_2⁷·b_3_13 + b_1_1⁷·b_3_11 + a_1_0·b_1_3⁶·b_3_15
       + c_4_27·b_1_2³·b_3_13 + c_4_27·b_1_1³·b_3_11 + c_4_26·b_1_2³·b_3_13
       + c_4_26·b_1_2⁶ + c_4_26·b_1_1³·b_3_13 + c_2_7·b_1_3⁸ + c_2_7·b_1_2⁸
       + c_2_7·a_1_0·b_1_3⁷ + c_4_27·a_1_0²·b_1_3⁴ + c_4_26·a_1_0²·b_1_3⁴
       + c_2_7·a_1_0²·b_1_3³·b_3_15 + c_2_7·a_1_0²·b_1_3⁶ + c_4_27²·b_1_3²
       + c_4_26·c_4_27·b_1_2² + c_4_26²·b_1_1² + c_2_7·c_4_27·b_1_2⁴
       + c_2_7·c_4_26·b_1_2⁴ + c_2_7·c_4_26·b_1_1⁴ + c_2_7²·b_1_2³·b_3_13
       + c_2_7²·b_1_2⁶ + c_2_7²·b_1_1³·b_3_13 + c_2_7²·b_1_1⁶
       + c_2_7²·a_1_0·b_1_3²·b_3_15 + c_4_27²·a_1_0² + c_4_26·c_4_27·a_1_0²
       + c_4_26²·a_1_0² + c_2_7·c_4_26·a_1_0²·b_1_3² + c_2_7²·a_1_0²·b_1_3·b_3_15
       + c_2_7²·c_4_26·b_1_2² + c_2_7²·c_4_26·b_1_1² + c_2_7³·b_1_3⁴
       + c_2_7³·b_1_2⁴ + c_2_7³·b_1_1⁴ + c_2_7³·a_1_0·b_1_3³
       + c_2_7²·c_4_27·a_1_0² + c_2_7²·c_4_26·a_1_0² + c_2_7⁴·b_1_2²
       + c_2_7⁴·b_1_1² + c_2_7⁴·a_1_0²
56. b_5_44² + b_1_2¹⁰ + b_1_1⁷·b_3_13 + b_1_1⁷·b_3_11 + b_1_1¹⁰
       + a_1_0²·b_1_3³·b_5_44 + a_1_0²·b_1_3⁵·b_3_15 + c_4_27·b_1_2³·b_3_13
       + c_4_27·b_1_1³·b_3_11 + c_4_26·b_1_2³·b_3_13 + c_4_26·b_1_1³·b_3_13
       + c_4_26·b_1_1⁶ + c_2_7·b_1_3⁵·b_3_15 + c_2_7·b_1_1⁸ + c_4_26·a_1_0·b_1_3²·b_3_15
       + c_2_7·b_1_3⁵·a_3_0 + c_2_7·a_1_0·b_1_3⁷ + c_4_27·a_1_0²·b_1_3·b_3_15
       + c_4_27·a_1_0²·b_1_3⁴ + c_4_26·a_1_0²·b_1_3·b_3_15
       + c_2_7·a_1_0²·b_1_3³·b_3_14 + c_4_27²·b_1_3² + c_4_27²·b_1_2²
       + c_4_27²·b_1_1² + c_4_26·c_4_27·b_1_2² + c_4_26²·b_1_1²
       + c_2_7·c_4_27·b_1_2⁴ + c_2_7·c_4_26·b_1_3⁴ + c_2_7·c_4_26·b_1_2⁴
       + c_2_7·c_4_26·b_1_1⁴ + c_2_7²·b_1_3³·b_3_15 + c_2_7²·b_1_3⁶
       + c_2_7²·b_1_2³·b_3_13 + c_2_7²·b_1_2⁶ + c_2_7²·b_1_1³·b_3_13 + c_2_7²·b_1_1⁶
       + c_2_7·c_4_26·a_1_0·b_1_3³ + c_2_7²·b_1_3³·a_3_0 + c_2_7²·a_1_0·b_1_3²·b_3_15
       + c_4_27²·a_1_0² + c_4_26²·a_1_0² + c_2_7·c_4_27·a_1_0²·b_1_3²
       + c_2_7²·a_1_0²·b_1_3·b_3_15 + c_2_7²·a_1_0²·b_1_3⁴ + c_2_7²·c_4_27·b_1_2²
       + c_2_7²·c_4_27·b_1_1² + c_2_7²·c_4_26·b_1_3² + c_2_7³·b_1_2⁴
       + c_2_7³·b_1_1⁴ + c_2_7³·a_1_0·b_1_3³ + c_2_7²·c_4_26·a_1_0²
       + c_2_7⁴·b_1_2²
57. b_5_43·b_5_44 + b_1_2⁷·b_3_13 + b_1_2¹⁰ + b_1_1⁷·b_3_11 + b_1_1¹⁰
       + b_1_3⁴·a_3_0·b_3_14 + a_1_0·b_1_3⁴·b_5_44 + a_1_0·b_1_3⁶·b_3_15
       + a_1_0²·b_1_3³·b_5_44 + a_1_0²·b_1_3⁵·b_3_15 + c_4_27·b_1_3·b_5_44
       + c_4_27·b_1_3³·b_3_15 + c_4_27·b_1_2·b_5_43 + c_4_27·b_1_2³·b_3_13 + c_4_27·b_1_2⁶
       + c_4_27·b_1_1·b_5_43 + c_4_27·b_1_1³·b_3_11 + c_4_27·b_1_1⁶ + c_4_26·b_1_2⁶
       + c_2_7·b_1_3³·b_5_44 + c_2_7·b_1_3⁵·b_3_14 + c_2_7·b_1_2³·b_5_43
       + c_2_7·b_1_1·b_1_3⁴·b_3_14 + c_2_7·b_1_1·b_1_3⁷ + c_2_7·b_1_1³·b_5_43
       + c_2_7·b_1_1⁸ + c_4_27·a_3_0·b_3_14 + c_4_27·b_1_3³·a_3_0 + c_4_27·a_1_0·b_1_3⁵
       + c_4_26·a_3_0·b_3_14 + c_4_26·b_1_3³·a_3_0 + c_4_26·a_1_0·b_5_44
       + c_4_26·a_1_0·b_1_3²·b_3_15 + c_4_26·a_1_0·b_1_3²·b_3_14 + c_4_26·a_1_0·b_1_3⁵
       + c_2_7·a_1_0·b_1_3⁴·b_3_15 + c_2_7·a_1_0·b_1_3⁴·b_3_14 + c_2_7·a_1_0·b_1_3⁷
       + c_4_27·a_1_0²·b_1_3·b_3_15 + c_4_27·a_1_0²·b_1_3·b_3_14
       + c_4_26·a_1_0²·b_1_3·b_3_15 + c_4_26·a_1_0²·b_1_3·b_3_14 + c_4_26·a_1_0²·b_1_3⁴
       + c_2_7·a_1_0²·b_1_3·b_5_44 + c_2_7·a_1_0²·b_1_3³·b_3_15
       + c_2_7·a_1_0²·b_1_3³·b_3_14 + c_2_7·a_1_0²·b_1_3⁶ + c_4_27²·b_1_1·b_1_3
       + c_4_26·c_4_27·b_1_2² + c_4_26·c_4_27·b_1_1·b_1_3 + c_4_26²·b_1_1²
       + c_2_7·c_4_27·b_1_3·b_3_15 + c_2_7·c_4_27·b_1_2·b_3_12 + c_2_7·c_4_27·b_1_1·b_3_14
       + c_2_7·c_4_27·b_1_1·b_3_13 + c_2_7·c_4_27·b_1_1·b_3_11 + c_2_7·c_4_27·b_1_1·b_1_3³
       + c_2_7·c_4_27·b_1_1⁴ + c_2_7·c_4_26·b_1_2·b_3_13 + c_2_7·c_4_26·b_1_1·b_3_14
       + c_2_7·c_4_26·b_1_1⁴ + c_2_7²·b_1_3·b_5_44 + c_2_7²·b_1_3³·b_3_15
       + c_2_7²·b_1_3⁶ + c_2_7²·b_1_2·b_5_43 + c_2_7²·b_1_2⁶ + c_2_7²·b_1_1⁶
       + c_4_27²·a_1_0·b_1_1 + c_4_26·c_4_27·a_1_0·b_1_3 + c_4_26²·a_1_0·b_1_3
       + c_2_7·c_4_27·a_1_0·b_3_11 + c_2_7·c_4_26·a_1_0·b_3_14 + c_2_7·c_4_26·a_1_0·b_1_3³
       + c_2_7²·b_1_3³·a_3_0 + c_2_7²·a_1_0·b_5_44 + c_2_7²·a_1_0·b_1_3⁵
       + c_4_26²·a_1_0² + c_2_7·c_4_27·a_1_0·a_3_0 + c_2_7·c_4_26·a_1_0²·b_1_3²
       + c_2_7²·a_1_0²·b_1_3·b_3_14 + c_2_7²·a_1_0²·b_1_3⁴ + c_2_7²·c_4_27·b_1_2²
       + c_2_7²·c_4_27·b_1_1² + c_2_7³·b_1_3·b_3_15 + c_2_7³·b_1_3·b_3_14
       + c_2_7³·b_1_2·b_3_13 + c_2_7³·b_1_1·b_3_13 + c_2_7³·b_1_1·b_1_3³
       + c_2_7²·c_4_27·a_1_0·b_1_3 + c_2_7³·a_1_0·b_3_14 + c_2_7³·a_1_0·b_1_3³
       + c_2_7²·c_4_27·a_1_0² + c_2_7²·c_4_26·a_1_0² + c_2_7⁴·b_1_3²
       + c_2_7⁴·a_1_0·b_1_3 + c_2_7⁴·a_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_2², 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_0 → 0, an element of degree 1
2. b_1_1 → 0, an element of degree 1
3. b_1_2 → 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_0 → 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_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_0 → 0, an element of degree 1
2. b_1_1 → 0, an element of degree 1
3. b_1_2 → 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_0 → 0, an element of degree 3
7. b_3_11 → c_1_1²·c_1_3, 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 + c_1_1²·c_1_3, an element of degree 3
11. b_3_15 → 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_1·c_1_3³ + 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_2²·c_1_3³ + c_1_2⁴·c_1_3 + c_1_1·c_1_3⁴ + c_1_1²·c_1_3³ + c_1_1³·c_1_3²
       + c_1_1⁴·c_1_3 + c_1_0²·c_1_3³ + 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_2²·c_1_3² + c_1_1²·c_1_3³
       + c_1_1²·c_1_2²·c_1_3 + c_1_0²·c_1_3³ + 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_0 → 0, an element of degree 1
2. b_1_1 → 0, an element of degree 1
3. b_1_2 → 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_0 → 0, an element of degree 3
7. b_3_11 → c_1_1·c_1_3² + c_1_1²·c_1_3, an element of degree 3
8. b_3_12 → c_1_3³ + c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
9. b_3_13 → c_1_3³ + 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
10. b_3_14 → c_1_3³ + c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
11. b_3_15 → c_1_3³ + c_1_0·c_1_3² + c_1_0²·c_1_3, an element of degree 3
12. c_4_26 → c_1_3⁴ + c_1_2·c_1_3³ + c_1_2⁴ + c_1_1²·c_1_3² + c_1_1⁴ + c_1_0·c_1_3³
       + c_1_0²·c_1_3², an element of degree 4
13. c_4_27 → c_1_3⁴ + c_1_2·c_1_3³ + c_1_2⁴ + c_1_1²·c_1_3² + c_1_1⁴ + c_1_0·c_1_3³
       + c_1_0⁴, an element of degree 4
14. b_5_43 → c_1_3⁵ + 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_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_3⁴ + 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_3³ + 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
15. b_5_44 → c_1_3⁵ + 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_3³ + c_1_1²·c_1_2·c_1_3² + 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_0²·c_1_3³
       + 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

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

1. a_1_0 → 0, an element of degree 1
2. b_1_1 → c_1_3, an element of degree 1
3. b_1_2 → 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_0 → 0, an element of degree 3
7. b_3_11 → c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
8. b_3_12 → c_1_3³ + c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
9. b_3_13 → c_1_3³ + 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
10. b_3_14 → 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
11. b_3_15 → c_1_0·c_1_3² + c_1_0²·c_1_3, an element of degree 3
12. c_4_26 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1²·c_1_3² + c_1_1⁴ + c_1_0·c_1_3³
       + c_1_0²·c_1_3², 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_3⁵ + 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
15. b_5_44 → c_1_3⁵ + c_1_1²·c_1_3³ + 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_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

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128