David J. Green

Cohomology
→Theory
→Implementation

Jena:

Faculty

External links:

Singular

Gap

Cohomology of group number 1431 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 4 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. b_1_0, an 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. 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. b_1_1·b_1_2
2. b_1_1² + b_1_0·b_1_3 + b_1_0·b_1_2 + b_1_0²
3. b_1_2² + b_1_1·b_1_3 + b_1_1² + b_1_0·b_1_2 + b_1_0·b_1_1
4. b_1_1·b_1_3² + b_1_0²·b_1_3 + b_1_0²·b_1_2 + b_1_0²·b_1_1 + b_1_0³
5. b_1_1·b_1_3² + b_1_0·b_1_1·b_1_3
6. b_1_2·b_3_10 + c_2_7·b_1_2·b_1_3 + c_2_7·b_1_1·b_1_3 + c_2_7·b_1_0·b_1_3
      + c_2_7·b_1_0·b_1_1 + c_2_7·b_1_0²
7. b_1_3·b_3_10 + b_1_2·b_3_11 + b_1_1·b_3_10 + b_1_0·b_3_11 + b_1_0·b_3_10 + c_2_7·b_1_3²
      + c_2_7·b_1_2·b_1_3 + c_2_7·b_1_1·b_1_3 + c_2_7·b_1_0·b_1_3 + c_2_7·b_1_0·b_1_1
      + c_2_7·b_1_0²
8. b_1_1·b_3_11 + c_2_7·b_1_0·b_1_3 + c_2_7·b_1_0·b_1_2 + c_2_7·b_1_0·b_1_1
      + c_2_7·b_1_0²
9. b_1_3·b_3_11 + b_1_3·b_3_10 + b_1_2·b_3_12 + b_1_1·b_3_10 + b_1_0·b_3_10 + b_1_0³·b_1_2
      + c_2_7·b_1_3² + c_2_7·b_1_1·b_1_3 + c_2_7·b_1_0·b_1_3 + c_2_7·b_1_0·b_1_2
      + c_2_7·b_1_0·b_1_1 + c_2_7·b_1_0²
10. b_1_1·b_3_10 + b_1_0·b_3_12 + b_1_0·b_3_10 + b_1_0³·b_1_2 + b_1_0³·b_1_1
       + c_2_7·b_1_1·b_1_3 + c_2_7·b_1_0·b_1_1
11. b_1_3·b_3_10 + b_1_1·b_3_12 + b_1_1·b_3_10 + b_1_0·b_3_10 + b_1_0³·b_1_3 + b_1_0³·b_1_2
       + b_1_0⁴ + c_2_7·b_1_3² + c_2_7·b_1_2·b_1_3 + c_2_7·b_1_0²
12. b_1_2·b_3_14 + c_2_7·b_1_2·b_1_3 + c_2_7·b_1_1·b_1_3 + c_2_7·b_1_0·b_1_3
       + c_2_7·b_1_0·b_1_2 + c_2_7·b_1_0·b_1_1 + c_2_7·b_1_0²
13. b_1_3·b_3_10 + b_1_1·b_3_13 + b_1_0·b_3_14 + b_1_0·b_3_10 + b_1_0³·b_1_1 + c_2_7·b_1_3²
       + c_2_7·b_1_2·b_1_3 + c_2_7·b_1_0·b_1_3 + c_2_7·b_1_0·b_1_2
14. b_1_3·b_3_13 + b_1_3·b_3_12 + b_1_3·b_3_10 + b_1_2·b_3_13 + b_1_1·b_3_14 + b_1_1·b_3_10
       + b_1_0·b_3_13 + b_1_0³·b_1_1
15. b_1_3·b_3_14 + b_1_3·b_3_13 + b_1_3·b_3_12 + b_1_2·b_3_15 + b_1_2·b_3_13 + b_1_1·b_3_13
       + b_1_1·b_3_10 + b_1_0·b_3_13 + b_1_0·b_3_10 + c_2_7·b_1_2·b_1_3 + c_2_7·b_1_1·b_1_3
       + c_2_7·b_1_0·b_1_3 + c_2_7·b_1_0·b_1_2 + c_2_7·b_1_0·b_1_1 + c_2_7·b_1_0²
16. b_1_3·b_3_11 + b_1_2·b_3_13 + b_1_1·b_3_10 + b_1_0·b_3_15 + b_1_0·b_3_13 + b_1_0·b_3_10
       + b_1_0³·b_1_1 + c_2_7·b_1_0·b_1_3 + c_2_7·b_1_0·b_1_2 + c_2_7·b_1_0·b_1_1
       + c_2_7·b_1_0²
17. b_1_3·b_3_10 + b_1_1·b_3_15 + b_1_1·b_3_13 + b_1_1·b_3_10 + b_1_0·b_3_10 + b_1_0³·b_1_3
       + b_1_0³·b_1_2 + b_1_0⁴ + c_2_7·b_1_3² + c_2_7·b_1_2·b_1_3 + c_2_7·b_1_0·b_1_1
       + c_2_7·b_1_0²
18. b_1_1·b_1_3·b_3_12 + b_1_0·b_1_2·b_3_15 + b_1_0·b_1_1·b_3_12 + b_1_0⁴·b_1_3
       + b_1_0⁴·b_1_2 + b_1_0⁵ + c_2_7·b_1_0²·b_1_3 + c_2_7·b_1_0³
19. b_3_10·b_3_11 + c_2_7·b_1_2·b_3_12 + c_2_7·b_1_0·b_3_12 + c_2_7·b_1_0·b_3_11
       + c_2_7·b_1_0³·b_1_3 + c_2_7·b_1_0³·b_1_2 + c_2_7·b_1_0⁴ + c_2_7²·b_1_2·b_1_3
       + c_2_7²·b_1_0·b_1_3 + c_2_7²·b_1_0·b_1_1
20. b_3_11·b_3_14 + c_2_7·b_1_2·b_3_12 + c_2_7·b_1_1·b_3_14 + c_2_7·b_1_0·b_3_14
       + c_2_7·b_1_0³·b_1_2 + c_2_7²·b_1_2·b_1_3 + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_0·b_1_3
       + c_2_7²·b_1_0·b_1_1 + c_2_7²·b_1_0²
21. 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_14
       + b_3_11·b_3_12 + b_3_10·b_3_15 + b_3_10·b_3_14 + b_3_10·b_3_12 + b_3_10·b_3_11 + b_3_10²
       + b_1_0²·b_1_1·b_3_14 + b_1_0³·b_3_15 + b_1_0³·b_3_14 + b_1_0³·b_3_13
       + b_1_0³·b_3_12 + b_1_0³·b_3_11 + b_1_0⁵·b_1_3 + b_1_0⁵·b_1_2 + b_1_0⁵·b_1_1
       + b_1_0⁶ + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_2·b_3_12 + c_2_7·b_1_2·b_1_3³
       + c_2_7·b_1_1·b_3_12 + 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_7²·b_1_3² + c_2_7²·b_1_0·b_1_2 + c_2_7²·b_1_0·b_1_1 + c_2_7²·b_1_0²
22. b_3_12·b_3_13 + b_3_12² + b_3_11·b_3_14 + b_3_11·b_3_12 + b_3_10·b_3_14 + b_3_10·b_3_13
       + b_3_10² + b_1_0²·b_1_1·b_3_12 + b_1_0³·b_3_15 + b_1_0³·b_3_14 + b_1_0³·b_3_13
       + b_1_0³·b_3_12 + b_1_0³·b_3_11 + b_1_0⁵·b_1_1 + c_2_7·b_1_2·b_3_15
       + 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·b_1_0³·b_1_1
       + c_2_7²·b_1_3² + c_2_7²·b_1_2·b_1_3 + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_0·b_1_3
       + c_2_7²·b_1_0·b_1_2 + c_2_7²·b_1_0²
23. b_3_12·b_3_13 + b_3_12² + b_3_11·b_3_12 + b_3_10·b_3_15 + b_3_10·b_3_14 + b_3_10·b_3_12
       + b_3_10² + b_1_0²·b_1_1·b_3_12 + b_1_0³·b_3_15 + b_1_0³·b_3_14 + b_1_0³·b_3_13
       + b_1_0³·b_3_12 + b_1_0³·b_3_11 + b_1_0⁵·b_1_1 + c_2_7·b_1_3·b_3_15
       + c_2_7·b_1_1·b_3_12 + 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·b_1_0³·b_1_2 + c_2_7·b_1_0³·b_1_1 + c_2_7²·b_1_2·b_1_3 + c_2_7²·b_1_0·b_1_3
       + c_2_7²·b_1_0·b_1_1 + c_2_7²·b_1_0²
24. 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_12
       + b_3_10·b_3_14 + b_3_10·b_3_13 + b_3_10² + b_1_0²·b_1_1·b_3_14 + b_1_0³·b_3_15
       + b_1_0³·b_3_14 + b_1_0³·b_3_13 + b_1_0³·b_3_12 + b_1_0³·b_3_11 + b_1_0⁵·b_1_3
       + b_1_0⁵·b_1_2 + b_1_0⁵·b_1_1 + b_1_0⁶ + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_1·b_3_12
       + c_2_7·b_1_0·b_3_15 + c_2_7·b_1_0·b_3_14 + c_2_7·b_1_0³·b_1_1 + c_2_7²·b_1_3²
       + c_2_7²·b_1_2·b_1_3 + c_2_7²·b_1_0·b_1_3 + c_2_7²·b_1_0·b_1_2
25. b_3_11² + b_3_10·b_3_12 + b_1_0³·b_3_12 + b_1_0³·b_3_11 + b_1_0³·b_3_10
       + b_1_0⁵·b_1_2 + b_1_0⁵·b_1_1 + c_4_26·b_1_0·b_1_2 + c_2_7·b_1_3·b_3_12
       + c_2_7·b_1_2·b_3_12 + c_2_7·b_1_1·b_3_12 + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_0³·b_1_3
       + c_2_7·b_1_0³·b_1_1 + c_2_7·b_1_0⁴ + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_0·b_1_3
       + c_2_7²·b_1_0·b_1_2 + c_2_7²·b_1_0²
26. b_3_11·b_3_12 + b_3_10·b_3_12 + b_3_10·b_3_11 + b_1_2·b_1_3²·b_3_12 + b_1_0³·b_3_12
       + b_1_0³·b_3_11 + b_1_0³·b_3_10 + b_1_0⁵·b_1_2 + b_1_0⁵·b_1_1 + c_4_26·b_1_2·b_1_3
       + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_2·b_3_12 + c_2_7·b_1_2·b_1_3³ + c_2_7·b_1_0·b_3_10
       + c_2_7·b_1_0³·b_1_3 + c_2_7·b_1_0³·b_1_2 + c_2_7·b_1_0⁴ + c_2_7²·b_1_0·b_1_1
       + c_2_7²·b_1_0²
27. b_3_12² + b_3_10·b_3_12 + b_1_3³·b_3_12 + b_1_0³·b_3_10 + b_1_0⁵·b_1_2
       + b_1_0⁵·b_1_1 + c_4_26·b_1_3² + c_4_26·b_1_0·b_1_3 + c_2_7·b_1_3·b_3_12
       + c_2_7·b_1_3⁴ + c_2_7·b_1_2·b_3_12 + c_2_7·b_1_2·b_1_3³ + c_2_7·b_1_1·b_3_12
       + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_0⁴ + c_2_7²·b_1_3² + c_2_7²·b_1_0·b_1_2
       + c_2_7²·b_1_0·b_1_1 + c_2_7²·b_1_0²
28. b_3_12² + b_3_11² + b_3_10² + b_1_3³·b_3_12 + b_1_0³·b_3_11 + b_1_0³·b_3_10
       + b_1_0⁵·b_1_3 + b_1_0⁵·b_1_1 + b_1_0⁶ + c_4_26·b_1_3² + c_4_26·b_1_0²
       + c_2_7·b_1_3⁴ + c_2_7·b_1_2·b_1_3³ + c_2_7²·b_1_0²
29. b_3_10·b_3_12 + b_3_10² + b_1_0²·b_1_1·b_3_12 + c_4_26·b_1_1·b_1_3
       + c_4_26·b_1_0·b_1_1 + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_2·b_3_12 + c_2_7·b_1_1·b_3_12
       + c_2_7·b_1_0·b_3_10 + c_2_7²·b_1_3² + c_2_7²·b_1_0·b_1_3 + c_2_7²·b_1_0·b_1_1
30. b_3_13·b_3_15 + b_3_13² + b_3_12·b_3_15 + b_3_12² + b_3_11·b_3_15 + b_3_11²
       + b_3_10·b_3_15 + b_3_10·b_3_13 + b_3_10·b_3_12 + b_3_10·b_3_11 + b_1_0⁵·b_1_2
       + c_4_27·b_1_0·b_1_2 + c_2_7·b_1_0·b_3_14 + c_2_7·b_1_0³·b_1_3 + c_2_7·b_1_0³·b_1_1
       + c_2_7·b_1_0⁴ + c_2_7²·b_1_0·b_1_1
31. b_3_14² + b_3_13·b_3_15 + b_3_12·b_3_15 + b_3_11·b_3_15 + b_3_10·b_3_15 + b_3_10·b_3_13
       + b_3_10·b_3_12 + b_3_10·b_3_11 + b_3_10² + b_1_0²·b_1_1·b_3_14 + b_1_0³·b_3_15
       + b_1_0³·b_3_12 + b_1_0³·b_3_10 + b_1_0⁶ + c_4_27·b_1_0·b_1_3 + c_2_7·b_1_0·b_3_14
       + c_2_7·b_1_0³·b_1_3 + c_2_7·b_1_0³·b_1_2 + c_2_7·b_1_0³·b_1_1 + c_2_7²·b_1_3²
       + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_0·b_1_3
32. 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_11·b_3_15 + b_3_11·b_3_14 + 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_10·b_3_11 + b_1_2·b_1_3²·b_3_15 + b_1_0²·b_1_1·b_3_12
       + b_1_0⁵·b_1_1 + c_4_27·b_1_1·b_1_3 + c_2_7·b_1_3⁴ + c_2_7·b_1_2·b_1_3³
       + c_2_7·b_1_0³·b_1_3 + c_2_7·b_1_0³·b_1_1 + c_2_7²·b_1_3² + c_2_7²·b_1_0·b_1_3
33. b_3_13² + b_3_12² + b_3_11² + b_3_10² + b_1_0²·b_1_1·b_3_14 + b_1_0³·b_3_15
       + b_1_0³·b_3_12 + b_1_0³·b_3_10 + b_1_0⁵·b_1_2 + b_1_0⁶ + c_4_27·b_1_0²
       + c_2_7·b_1_0³·b_1_3 + c_2_7²·b_1_0·b_1_3 + c_2_7²·b_1_0·b_1_2 + c_2_7²·b_1_0²
34. b_3_13·b_3_14 + b_3_12·b_3_14 + b_3_11·b_3_14 + b_3_10·b_3_14 + b_1_0²·b_1_1·b_3_12
       + b_1_0⁵·b_1_1 + c_4_27·b_1_0·b_1_1 + c_2_7·b_1_0·b_3_14 + c_2_7²·b_1_1·b_1_3
35. b_3_15² + b_3_13² + b_3_12·b_3_13 + b_3_11·b_3_14 + b_3_10·b_3_14 + b_3_10·b_3_13
       + b_3_10·b_3_12 + b_3_10·b_3_11 + b_3_10² + b_1_2·b_5_43 + b_1_2·b_1_3²·b_3_15
       + b_1_2·b_1_3²·b_3_12 + b_1_0³·b_3_14 + b_1_0³·b_3_12 + b_1_0³·b_3_10 + b_1_0⁵·b_1_3
       + b_1_0⁵·b_1_2 + b_1_0⁶ + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_3⁴ + c_2_7·b_1_2·b_3_12
       + c_2_7·b_1_2·b_1_3³ + c_2_7·b_1_1·b_3_12 + c_2_7·b_1_0·b_3_14 + c_2_7·b_1_0³·b_1_3
       + c_2_7·b_1_0⁴ + c_2_7²·b_1_3² + c_2_7²·b_1_0²
36. b_3_12·b_3_14 + b_3_11·b_3_12 + b_3_10·b_3_15 + b_3_10·b_3_14 + b_3_10·b_3_12 + b_3_10²
       + b_1_3·b_5_43 + b_1_2·b_1_3²·b_3_15 + b_1_0²·b_1_1·b_3_14 + b_1_0³·b_3_12
       + b_1_0³·b_3_11 + b_1_0³·b_3_10 + b_1_0⁵·b_1_3 + b_1_0⁵·b_1_2 + b_1_0⁵·b_1_1
       + c_4_27·b_1_2·b_1_3 + c_4_26·b_1_3² + c_4_26·b_1_1·b_1_3 + c_2_7·b_1_3⁴
       + c_2_7·b_1_1·b_3_12 + 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·b_1_0³·b_1_3 + c_2_7·b_1_0³·b_1_2 + c_2_7²·b_1_3² + c_2_7²·b_1_2·b_1_3
       + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_0·b_1_3 + c_2_7²·b_1_0·b_1_1
37. b_3_13·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_3_12²
       + b_3_11·b_3_12 + 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
       + b_1_3³·b_3_12 + b_1_0·b_5_43 + b_1_0²·b_1_1·b_3_12 + b_1_0³·b_3_14 + b_1_0³·b_3_12
       + b_1_0³·b_3_11 + b_1_0⁵·b_1_3 + b_1_0⁵·b_1_2 + b_1_0⁵·b_1_1 + c_4_26·b_1_3²
       + c_4_26·b_1_1·b_1_3 + c_2_7·b_1_3⁴ + c_2_7·b_1_2·b_1_3³ + c_2_7·b_1_0·b_3_13
       + c_2_7·b_1_0³·b_1_2 + c_2_7·b_1_0³·b_1_1 + c_2_7·b_1_0⁴ + c_2_7²·b_1_3²
       + c_2_7²·b_1_0·b_1_1
38. b_3_12·b_3_13 + b_3_12² + b_3_11·b_3_14 + b_3_11·b_3_12 + b_3_10·b_3_13 + b_1_1·b_5_43
       + b_1_0²·b_1_1·b_3_14 + b_1_0³·b_3_15 + b_1_0³·b_3_14 + b_1_0³·b_3_13
       + b_1_0³·b_3_11 + b_1_0³·b_3_10 + b_1_0⁵·b_1_2 + b_1_0⁵·b_1_1 + c_4_26·b_1_1·b_1_3
       + c_2_7·b_1_1·b_3_12 + 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·b_1_0³·b_1_3 + c_2_7²·b_1_3² + c_2_7²·b_1_0·b_1_2 + c_2_7²·b_1_0·b_1_1
       + c_2_7²·b_1_0²
39. b_3_15² + b_3_13·b_3_15 + b_3_12·b_3_15 + b_3_12·b_3_13 + b_3_12² + b_3_11·b_3_14
       + b_3_11·b_3_13 + b_3_10·b_3_15 + b_3_10·b_3_14 + b_3_10·b_3_12 + b_3_10·b_3_11 + b_3_10²
       + b_1_2·b_5_44 + b_1_0³·b_3_15 + b_1_0³·b_3_14 + b_1_0³·b_3_13 + b_1_0³·b_3_12
       + b_1_0⁵·b_1_3 + b_1_0⁵·b_1_1 + b_1_0⁶ + c_2_7·b_1_3⁴ + c_2_7·b_1_2·b_1_3³
       + c_2_7·b_1_0·b_3_11 + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_0³·b_1_2 + c_2_7²·b_1_3²
       + c_2_7²·b_1_2·b_1_3 + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_0·b_1_2 + c_2_7²·b_1_0²
40. b_3_14² + b_3_13·b_3_15 + b_3_11·b_3_14 + b_3_11·b_3_12 + b_3_10·b_3_15 + b_3_10·b_3_14
       + b_1_3·b_5_44 + b_1_3³·b_3_15 + b_1_2·b_1_3²·b_3_12 + b_1_0²·b_1_1·b_3_14
       + b_1_0³·b_3_15 + b_1_0³·b_3_14 + b_1_0³·b_3_12 + b_1_0³·b_3_11 + b_1_0⁵·b_1_3
       + b_1_0⁶ + c_4_27·b_1_2·b_1_3 + c_4_26·b_1_1·b_1_3 + c_2_7·b_1_3·b_3_12
       + c_2_7·b_1_1·b_3_12 + 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_11
       + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_0³·b_1_3 + c_2_7·b_1_0³·b_1_2 + c_2_7·b_1_0⁴
       + c_2_7²·b_1_3² + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_0·b_1_1
41. b_3_13·b_3_15 + b_3_12·b_3_15 + 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_3_10·b_3_15 + b_3_10·b_3_14 + b_3_10·b_3_12 + b_3_10² + b_1_0·b_5_44
       + b_1_0²·b_1_1·b_3_14 + b_1_0³·b_3_15 + b_1_0³·b_3_14 + b_1_0³·b_3_13
       + c_4_26·b_1_1·b_1_3 + c_2_7·b_1_3·b_3_12 + c_2_7·b_1_1·b_3_12 + c_2_7·b_1_0·b_3_14
       + c_2_7·b_1_0·b_3_10 + c_2_7·b_1_0³·b_1_3 + c_2_7·b_1_0³·b_1_2 + c_2_7·b_1_0⁴
       + c_2_7²·b_1_2·b_1_3 + c_2_7²·b_1_1·b_1_3 + c_2_7²·b_1_0·b_1_3 + c_2_7²·b_1_0²
42. b_3_13·b_3_14 + b_3_12·b_3_14 + b_3_11·b_3_14 + b_3_10·b_3_14 + b_3_10² + b_1_1·b_5_44
       + b_1_0²·b_1_1·b_3_14 + b_1_0³·b_3_14 + b_1_0⁵·b_1_1 + c_2_7·b_1_0·b_3_14
       + c_2_7·b_1_0³·b_1_3 + c_2_7·b_1_0³·b_1_1 + c_2_7²·b_1_3² + c_2_7²·b_1_1·b_1_3
       + c_2_7²·b_1_0·b_1_3 + c_2_7²·b_1_0²
43. b_3_14·b_5_43 + b_3_11·b_5_43 + b_1_0²·b_1_2·b_5_44 + b_1_0⁵·b_3_14 + b_1_0⁷·b_1_2
       + c_4_27·b_1_1·b_3_12 + c_4_27·b_1_0·b_3_12 + c_4_27·b_1_0·b_3_11 + c_4_27·b_1_0·b_3_10
       + c_4_27·b_1_0³·b_1_2 + c_4_27·b_1_0³·b_1_1 + c_4_26·b_1_2·b_3_15
       + c_4_26·b_1_2·b_3_12 + c_4_26·b_1_0·b_3_14 + c_4_26·b_1_0·b_3_11 + c_2_7·b_1_1·b_5_43
       + c_2_7·b_1_0·b_5_43 + c_2_7·b_1_0²·b_1_1·b_3_14 + c_2_7·b_1_0³·b_3_15
       + c_2_7·b_1_0³·b_3_14 + c_2_7·b_1_0³·b_3_13 + c_2_7·b_1_0³·b_3_11
       + c_2_7·b_1_0³·b_3_10 + c_2_7·b_1_0⁵·b_1_2 + c_2_7·c_4_27·b_1_2·b_1_3
       + c_2_7·c_4_27·b_1_0·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2 + c_2_7·c_4_26·b_1_3²
       + c_2_7·c_4_26·b_1_0·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_2 + 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_3·b_3_15 + c_2_7²·b_1_3⁴
       + c_2_7²·b_1_2·b_3_12 + c_2_7²·b_1_2·b_1_3³ + c_2_7²·b_1_0·b_3_15
       + c_2_7²·b_1_0·b_3_14 + c_2_7²·b_1_0·b_3_12 + c_2_7²·b_1_0·b_3_11
       + c_2_7²·b_1_0·b_3_10 + c_2_7²·b_1_0³·b_1_3 + c_2_7²·b_1_0³·b_1_1
       + c_2_7³·b_1_3² + c_2_7³·b_1_2·b_1_3 + c_2_7³·b_1_0·b_1_2 + c_2_7³·b_1_0·b_1_1
44. b_3_15·b_5_43 + b_1_2·b_1_3²·b_5_44 + b_1_2·b_1_3⁴·b_3_15 + b_1_0²·b_1_1·b_5_43
       + b_1_0³·b_5_43 + b_1_0⁴·b_1_1·b_3_14 + b_1_0⁴·b_1_1·b_3_12 + b_1_0⁵·b_3_13
       + b_1_0⁵·b_3_11 + b_1_0⁷·b_1_3 + b_1_0⁷·b_1_2 + c_4_27·b_1_2·b_3_15
       + c_4_27·b_1_0·b_3_10 + c_4_27·b_1_0³·b_1_3 + c_4_27·b_1_0⁴ + c_4_26·b_1_3·b_3_15
       + c_4_26·b_1_2·b_3_15 + c_4_26·b_1_1·b_3_14 + c_4_26·b_1_0·b_3_14 + c_4_26·b_1_0·b_3_12
       + c_4_26·b_1_0·b_3_10 + c_4_26·b_1_0³·b_1_2 + c_4_26·b_1_0⁴ + c_2_7·b_1_3³·b_3_15
       + c_2_7·b_1_2·b_1_3⁵ + c_2_7·b_1_0²·b_1_1·b_3_12 + c_2_7·b_1_0³·b_3_15
       + c_2_7·b_1_0³·b_3_13 + c_2_7·b_1_0³·b_3_10 + c_2_7·b_1_0⁵·b_1_3
       + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2 + c_2_7·c_4_26·b_1_0·b_1_1
       + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3⁴ + c_2_7²·b_1_2·b_3_15 + c_2_7²·b_1_2·b_3_12
       + c_2_7²·b_1_2·b_1_3³ + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_1·b_3_12
       + c_2_7²·b_1_0·b_3_14 + c_2_7²·b_1_0·b_3_12 + c_2_7²·b_1_0·b_3_11
       + c_2_7²·b_1_0³·b_1_3 + c_2_7²·b_1_0³·b_1_2 + c_2_7²·b_1_0³·b_1_1
       + c_2_7³·b_1_3² + c_2_7³·b_1_1·b_1_3 + c_2_7³·b_1_0·b_1_3 + c_2_7³·b_1_0·b_1_1
       + c_2_7³·b_1_0²
45. b_3_11·b_5_43 + b_3_10·b_5_43 + b_1_0³·b_5_44 + b_1_0⁵·b_3_15 + b_1_0⁵·b_3_12
       + b_1_0⁵·b_3_10 + b_1_0⁷·b_1_2 + b_1_0⁸ + c_4_27·b_1_1·b_3_12 + c_4_27·b_1_0·b_3_11
       + c_4_27·b_1_0³·b_1_3 + c_4_26·b_1_2·b_3_12 + c_4_26·b_1_1·b_3_14
       + c_4_26·b_1_1·b_3_12 + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_10
       + c_4_26·b_1_0³·b_1_3 + c_4_26·b_1_0³·b_1_2 + c_4_26·b_1_0³·b_1_1 + c_4_26·b_1_0⁴
       + c_2_7·b_1_2·b_1_3²·b_3_15 + c_2_7·b_1_1·b_5_43 + c_2_7·b_1_0·b_5_43
       + c_2_7·b_1_0²·b_1_1·b_3_12 + c_2_7·b_1_0³·b_3_15 + c_2_7·b_1_0³·b_3_14
       + c_2_7·b_1_0³·b_3_10 + c_2_7·b_1_0⁵·b_1_3 + c_2_7·b_1_0⁵·b_1_2
       + c_2_7·c_4_27·b_1_2·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2 + 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_2·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_2
       + c_2_7·c_4_26·b_1_0·b_1_1 + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3⁴
       + c_2_7²·b_1_2·b_3_12 + c_2_7²·b_1_2·b_1_3³ + c_2_7²·b_1_1·b_3_14
       + c_2_7²·b_1_0·b_3_14 + c_2_7²·b_1_0·b_3_12 + c_2_7²·b_1_0⁴ + c_2_7³·b_1_3²
       + c_2_7³·b_1_2·b_1_3 + c_2_7³·b_1_1·b_1_3 + c_2_7³·b_1_0·b_1_3 + c_2_7³·b_1_0·b_1_2
       + c_2_7³·b_1_0·b_1_1
46. b_3_15·b_5_43 + b_3_13·b_5_43 + b_3_12·b_5_44 + b_3_12·b_5_43 + b_1_0²·b_1_1·b_5_43
       + b_1_0³·b_5_43 + b_1_0⁴·b_1_1·b_3_14 + b_1_0⁴·b_1_1·b_3_12 + b_1_0⁵·b_3_15
       + b_1_0⁵·b_3_14 + b_1_0⁵·b_3_13 + b_1_0⁵·b_3_12 + b_1_0⁵·b_3_11 + b_1_0⁵·b_3_10
       + b_1_0⁷·b_1_3 + b_1_0⁷·b_1_1 + c_4_27·b_1_2·b_3_15 + c_4_27·b_1_2·b_3_12
       + c_4_27·b_1_1·b_3_12 + c_4_27·b_1_0·b_3_15 + c_4_27·b_1_0·b_3_13
       + c_4_27·b_1_0³·b_1_3 + c_4_27·b_1_0³·b_1_2 + c_4_27·b_1_0⁴ + c_4_26·b_1_1·b_3_12
       + c_4_26·b_1_0·b_3_15 + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_12
       + c_4_26·b_1_0³·b_1_3 + c_2_7·b_1_3³·b_3_12 + c_2_7·b_1_2·b_1_3²·b_3_15
       + c_2_7·b_1_2·b_1_3⁵ + c_2_7·b_1_0·b_5_43 + c_2_7·b_1_0²·b_1_1·b_3_14
       + c_2_7·b_1_0²·b_1_1·b_3_12 + c_2_7·b_1_0³·b_3_14 + c_2_7·b_1_0³·b_3_12
       + c_2_7·b_1_0³·b_3_11 + c_2_7·b_1_0³·b_3_10 + c_2_7·b_1_0⁵·b_1_2
       + c_2_7·c_4_27·b_1_2·b_1_3 + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_3
       + c_2_7·c_4_26·b_1_2·b_1_3 + c_2_7·c_4_26·b_1_0² + c_2_7²·b_1_3·b_3_15
       + c_2_7²·b_1_3·b_3_12 + c_2_7²·b_1_3⁴ + c_2_7²·b_1_2·b_3_12 + c_2_7²·b_1_1·b_3_14
       + c_2_7²·b_1_0·b_3_15 + c_2_7²·b_1_0·b_3_11 + c_2_7²·b_1_0·b_3_10
       + c_2_7²·b_1_0³·b_1_2 + c_2_7²·b_1_0³·b_1_1 + c_2_7³·b_1_3²
       + c_2_7³·b_1_2·b_1_3 + c_2_7³·b_1_1·b_1_3 + c_2_7³·b_1_0·b_1_1
47. b_3_15·b_5_43 + b_3_13·b_5_44 + b_3_12·b_5_43 + b_3_10·b_5_43 + b_1_2·b_1_3⁴·b_3_12
       + b_1_0²·b_1_1·b_5_43 + b_1_0³·b_5_43 + b_1_0⁴·b_1_1·b_3_14 + b_1_0⁵·b_3_13
       + b_1_0⁵·b_3_11 + b_1_0⁵·b_3_10 + b_1_0⁷·b_1_1 + c_4_27·b_1_2·b_3_15
       + c_4_27·b_1_1·b_3_12 + c_4_27·b_1_0·b_3_15 + c_4_27·b_1_0·b_3_12 + c_4_27·b_1_0·b_3_11
       + c_4_27·b_1_0·b_3_10 + c_4_27·b_1_0³·b_1_3 + c_4_27·b_1_0³·b_1_2
       + c_4_26·b_1_3·b_3_12 + c_4_26·b_1_2·b_1_3³ + c_4_26·b_1_1·b_3_14
       + c_4_26·b_1_1·b_3_12 + c_4_26·b_1_0·b_3_15 + c_4_26·b_1_0·b_3_12 + c_4_26·b_1_0·b_3_11
       + c_4_26·b_1_0³·b_1_3 + c_4_26·b_1_0³·b_1_1 + c_2_7·b_1_3³·b_3_15
       + c_2_7·b_1_2·b_1_3²·b_3_15 + c_2_7·b_1_2·b_1_3²·b_3_12 + c_2_7·b_1_1·b_5_43
       + c_2_7·b_1_0²·b_1_1·b_3_14 + c_2_7·b_1_0²·b_1_1·b_3_12 + c_2_7·b_1_0³·b_3_14
       + c_2_7·b_1_0³·b_3_12 + c_2_7·b_1_0³·b_3_11 + c_2_7·b_1_0³·b_3_10
       + c_2_7·b_1_0⁵·b_1_3 + c_2_7·b_1_0⁵·b_1_1 + c_2_7·c_4_27·b_1_0·b_1_3
       + 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_0·b_1_3
       + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3·b_3_12
       + c_2_7²·b_1_3⁴ + c_2_7²·b_1_2·b_3_15 + c_2_7²·b_1_0·b_3_15 + 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_10 + c_2_7²·b_1_0³·b_1_3
       + c_2_7²·b_1_0³·b_1_2 + c_2_7²·b_1_0³·b_1_1 + c_2_7²·b_1_0⁴
       + c_2_7³·b_1_0·b_1_1 + c_2_7³·b_1_0²
48. b_3_14·b_5_43 + b_3_13·b_5_43 + b_3_11·b_5_43 + b_3_10·b_5_44 + b_1_2·b_1_3⁴·b_3_12
       + b_1_0²·b_1_1·b_5_43 + b_1_0⁴·b_1_1·b_3_14 + b_1_0⁴·b_1_1·b_3_12 + b_1_0⁵·b_3_14
       + b_1_0⁵·b_3_13 + b_1_0⁵·b_3_12 + b_1_0⁵·b_3_11 + b_1_0⁵·b_3_10 + b_1_0⁷·b_1_2
       + c_4_27·b_1_2·b_3_12 + c_4_27·b_1_0·b_3_15 + 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_3_10 + c_4_27·b_1_0³·b_1_1 + c_4_26·b_1_3·b_3_12
       + c_4_26·b_1_2·b_3_12 + c_4_26·b_1_2·b_1_3³ + 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_4_26·b_1_0³·b_1_3
       + c_4_26·b_1_0³·b_1_1 + c_4_26·b_1_0⁴ + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_3³·b_3_12
       + c_2_7·b_1_2·b_1_3²·b_3_15 + c_2_7·b_1_2·b_1_3²·b_3_12 + c_2_7·b_1_2·b_1_3⁵
       + c_2_7·b_1_0²·b_1_1·b_3_14 + c_2_7·b_1_0³·b_3_13 + c_2_7·b_1_0³·b_3_12
       + c_2_7·b_1_0³·b_3_10 + c_2_7·b_1_0⁵·b_1_1 + c_2_7·b_1_0⁶
       + c_2_7·c_4_27·b_1_2·b_1_3 + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_3
       + 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_0·b_1_3
       + 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_2·b_3_15
       + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_1·b_3_12 + c_2_7²·b_1_0·b_3_14
       + c_2_7²·b_1_0·b_3_12 + c_2_7²·b_1_0·b_3_10 + c_2_7²·b_1_0³·b_1_3
       + c_2_7²·b_1_0⁴ + c_2_7³·b_1_3² + c_2_7³·b_1_1·b_1_3 + c_2_7³·b_1_0·b_1_3
       + c_2_7³·b_1_0·b_1_2
49. b_3_14·b_5_43 + b_3_11·b_5_44 + b_3_11·b_5_43 + b_3_10·b_5_43 + b_1_0⁴·b_1_1·b_3_14
       + b_1_0⁵·b_3_14 + b_1_0⁵·b_3_11 + b_1_0⁵·b_3_10 + c_4_27·b_1_0·b_3_12
       + c_4_27·b_1_0·b_3_11 + c_4_27·b_1_0·b_3_10 + c_4_27·b_1_0³·b_1_3
       + c_4_27·b_1_0³·b_1_1 + c_4_27·b_1_0⁴ + c_4_26·b_1_2·b_3_12 + c_4_26·b_1_1·b_3_14
       + c_4_26·b_1_0·b_3_15 + 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_12
       + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0·b_3_10 + c_4_26·b_1_0³·b_1_2
       + c_2_7·b_1_2·b_1_3²·b_3_15 + c_2_7·b_1_1·b_5_43 + c_2_7·b_1_0·b_5_43
       + c_2_7·b_1_0³·b_3_15 + c_2_7·b_1_0³·b_3_13 + c_2_7·b_1_0³·b_3_11
       + c_2_7·b_1_0³·b_3_10 + c_2_7·c_4_27·b_1_0·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2
       + c_2_7·c_4_27·b_1_0² + c_2_7·c_4_26·b_1_2·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_2
       + c_2_7·c_4_26·b_1_0·b_1_1 + 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_12 + c_2_7²·b_1_0·b_3_13 + c_2_7²·b_1_0·b_3_12
       + c_2_7²·b_1_0·b_3_11 + c_2_7²·b_1_0·b_3_10 + c_2_7²·b_1_0³·b_1_3
       + c_2_7²·b_1_0³·b_1_1 + c_2_7³·b_1_2·b_1_3
50. b_3_14·b_5_44 + b_3_12·b_5_43 + b_1_2·b_1_3⁴·b_3_12 + b_1_0⁴·b_1_1·b_3_12
       + b_1_0⁵·b_3_15 + b_1_0⁵·b_3_14 + b_1_0⁵·b_3_13 + b_1_0⁵·b_3_11 + b_1_0⁷·b_1_2
       + b_1_0⁷·b_1_1 + c_4_27·b_1_2·b_3_12 + c_4_27·b_1_0·b_3_14 + c_4_27·b_1_0³·b_1_3
       + c_4_27·b_1_0³·b_1_2 + c_4_27·b_1_0³·b_1_1 + c_4_27·b_1_0⁴ + c_4_26·b_1_3·b_3_12
       + c_4_26·b_1_2·b_3_15 + c_4_26·b_1_2·b_3_12 + c_4_26·b_1_2·b_1_3³
       + c_4_26·b_1_1·b_3_14 + c_4_26·b_1_1·b_3_12 + c_2_7·b_1_3³·b_3_15
       + c_2_7·b_1_3³·b_3_12 + c_2_7·b_1_2·b_1_3²·b_3_15 + c_2_7·b_1_1·b_5_43
       + c_2_7·b_1_0²·b_1_1·b_3_12 + c_2_7·b_1_0³·b_3_15 + c_2_7·b_1_0³·b_3_13
       + c_2_7·b_1_0³·b_3_12 + c_2_7·b_1_0⁵·b_1_3 + c_2_7·b_1_0⁵·b_1_2
       + c_2_7·b_1_0⁵·b_1_1 + c_2_7·b_1_0⁶ + c_2_7·c_4_27·b_1_2·b_1_3
       + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2
       + 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_2·b_1_3
       + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_7·c_4_26·b_1_0·b_1_1 + c_2_7²·b_1_2·b_1_3³
       + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_0·b_3_15 + 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_0³·b_1_3
       + c_2_7²·b_1_0³·b_1_2 + c_2_7³·b_1_3² + c_2_7³·b_1_2·b_1_3
51. b_3_15·b_5_44 + b_3_15·b_5_43 + b_3_14·b_5_43 + b_3_13·b_5_43 + b_3_11·b_5_43
       + b_1_2·b_1_3⁴·b_3_15 + b_1_2·b_1_3⁴·b_3_12 + b_1_0²·b_1_1·b_5_43 + b_1_0³·b_5_43
       + b_1_0⁴·b_1_1·b_3_12 + b_1_0⁵·b_3_10 + b_1_0⁷·b_1_3 + b_1_0⁸ + c_4_27·b_1_2·b_3_12
       + c_4_27·b_1_1·b_3_12 + 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_3_10
       + c_4_27·b_1_0³·b_1_3 + c_4_27·b_1_0³·b_1_2 + c_4_27·b_1_0³·b_1_1
       + c_4_26·b_1_3·b_3_15 + c_4_26·b_1_3·b_3_12 + c_4_26·b_1_2·b_3_12
       + c_4_26·b_1_2·b_1_3³ + c_4_26·b_1_1·b_3_14 + c_4_26·b_1_0·b_3_13
       + c_4_26·b_1_0·b_3_12 + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0³·b_1_1 + c_4_26·b_1_0⁴
       + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_3⁶ + c_2_7·b_1_2·b_1_3²·b_3_15
       + c_2_7·b_1_2·b_1_3⁵ + c_2_7·b_1_0³·b_3_15 + c_2_7·b_1_0³·b_3_14
       + c_2_7·b_1_0³·b_3_12 + c_2_7·b_1_0⁵·b_1_3 + c_2_7·b_1_0⁵·b_1_2 + c_2_7·b_1_0⁶
       + c_2_7·c_4_27·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2 + c_2_7·c_4_27·b_1_0·b_1_1
       + c_2_7·c_4_26·b_1_2·b_1_3 + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_3
       + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_7·c_4_26·b_1_0² + c_2_7²·b_1_2·b_3_15
       + c_2_7²·b_1_2·b_3_12 + c_2_7²·b_1_2·b_1_3³ + c_2_7²·b_1_1·b_3_12
       + c_2_7²·b_1_0·b_3_15 + c_2_7²·b_1_0·b_3_12 + c_2_7²·b_1_0·b_3_11
       + c_2_7²·b_1_0³·b_1_2 + c_2_7²·b_1_0³·b_1_1 + c_2_7³·b_1_3²
       + c_2_7³·b_1_0·b_1_3 + c_2_7³·b_1_0·b_1_2 + c_2_7³·b_1_0·b_1_1 + c_2_7³·b_1_0²
52. b_3_13·b_5_43 + b_3_12·b_5_43 + b_3_11·b_5_43 + b_1_0²·b_1_1·b_5_43 + b_1_0³·b_5_43
       + b_1_0⁴·b_1_1·b_3_14 + b_1_0⁴·b_1_1·b_3_12 + b_1_0⁵·b_3_13 + b_1_0⁵·b_3_11
       + b_1_0⁷·b_1_3 + c_4_27·b_1_0·b_3_15 + c_4_27·b_1_0·b_3_13 + c_4_27·b_1_0·b_3_12
       + c_4_27·b_1_0·b_3_11 + c_4_27·b_1_0·b_3_10 + c_4_27·b_1_0³·b_1_3
       + c_4_27·b_1_0³·b_1_2 + c_4_27·b_1_0⁴ + c_4_26·b_1_1·b_3_12 + 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_12 + c_4_26·b_1_0·b_3_11
       + c_4_26·b_1_0³·b_1_3 + c_4_26·b_1_0³·b_1_2 + c_4_26·b_1_0³·b_1_1
       + c_2_7·b_1_2·b_5_44 + c_2_7·b_1_2·b_1_3²·b_3_12 + c_2_7·b_1_1·b_5_43
       + c_2_7·b_1_0²·b_1_1·b_3_14 + c_2_7·b_1_0³·b_3_15 + c_2_7·b_1_0³·b_3_11
       + c_2_7·b_1_0⁵·b_1_1 + c_2_7·b_1_0⁶ + c_2_7·c_4_27·b_1_2·b_1_3
       + c_2_7·c_4_27·b_1_0·b_1_3 + c_2_7·c_4_27·b_1_0·b_1_2 + 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_3 + c_2_7·c_4_26·b_1_0·b_1_2
       + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3⁴ + c_2_7²·b_1_2·b_3_15 + 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_12 + c_2_7²·b_1_0·b_3_14
       + c_2_7²·b_1_0·b_3_12 + c_2_7²·b_1_0·b_3_11 + c_2_7²·b_1_0³·b_1_3
       + c_2_7³·b_1_3² + c_2_7³·b_1_2·b_1_3 + c_2_7³·b_1_0·b_1_2
53. b_3_12·b_5_43 + b_3_10·b_5_43 + b_1_2·b_1_3⁴·b_3_12 + b_1_0²·b_1_1·b_5_43
       + b_1_0⁴·b_1_1·b_3_14 + b_1_0⁵·b_3_15 + b_1_0⁵·b_3_13 + b_1_0⁵·b_3_11
       + b_1_0⁵·b_3_10 + b_1_0⁷·b_1_2 + b_1_0⁷·b_1_1 + c_4_27·b_1_2·b_3_12
       + c_4_26·b_1_3·b_3_12 + c_4_26·b_1_2·b_3_15 + c_4_26·b_1_2·b_3_12
       + c_4_26·b_1_2·b_1_3³ + c_4_26·b_1_1·b_3_14 + c_4_26·b_1_0·b_3_10
       + c_4_26·b_1_0³·b_1_3 + c_4_26·b_1_0³·b_1_2 + c_4_26·b_1_0³·b_1_1 + c_4_26·b_1_0⁴
       + c_2_7·b_1_3·b_5_44 + c_2_7·b_1_3³·b_3_15 + c_2_7·b_1_3³·b_3_12
       + c_2_7·b_1_2·b_1_3⁵ + c_2_7·b_1_1·b_5_43 + c_2_7·b_1_0²·b_1_1·b_3_14
       + c_2_7·b_1_0³·b_3_14 + c_2_7·b_1_0³·b_3_11 + c_2_7·b_1_0⁵·b_1_1 + c_2_7·b_1_0⁶
       + c_2_7·c_4_27·b_1_1·b_1_3 + 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_2·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_3
       + c_2_7·c_4_26·b_1_0·b_1_2 + c_2_7²·b_1_3·b_3_15 + c_2_7²·b_1_3⁴
       + 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_12
       + c_2_7²·b_1_0·b_3_15 + c_2_7²·b_1_0·b_3_12 + c_2_7²·b_1_0·b_3_10
       + c_2_7²·b_1_0³·b_1_3 + c_2_7³·b_1_2·b_1_3 + c_2_7³·b_1_1·b_1_3
       + c_2_7³·b_1_0·b_1_3 + c_2_7³·b_1_0·b_1_2 + c_2_7³·b_1_0·b_1_1 + c_2_7³·b_1_0²
54. 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_1_0²·b_1_1·b_5_43
       + b_1_0³·b_5_43 + b_1_0⁴·b_1_1·b_3_14 + b_1_0⁵·b_3_14 + b_1_0⁵·b_3_13
       + b_1_0⁵·b_3_11 + b_1_0⁷·b_1_2 + b_1_0⁸ + c_4_27·b_1_0·b_3_15 + c_4_27·b_1_0·b_3_13
       + c_4_27·b_1_0·b_3_11 + c_4_27·b_1_0³·b_1_2 + c_4_27·b_1_0³·b_1_1
       + c_4_26·b_1_2·b_3_15 + c_4_26·b_1_1·b_3_12 + c_4_26·b_1_0·b_3_13 + c_4_26·b_1_0·b_3_12
       + c_4_26·b_1_0·b_3_11 + c_4_26·b_1_0³·b_1_3 + c_4_26·b_1_0³·b_1_2
       + c_4_26·b_1_0³·b_1_1 + c_2_7·b_1_2·b_1_3²·b_3_15 + c_2_7·b_1_1·b_5_43
       + c_2_7·b_1_0·b_5_44 + c_2_7·b_1_0²·b_1_1·b_3_12 + c_2_7·b_1_0³·b_3_11
       + c_2_7·b_1_0³·b_3_10 + c_2_7·b_1_0⁵·b_1_2 + c_2_7·b_1_0⁵·b_1_1
       + c_2_7·c_4_27·b_1_0·b_1_2 + c_2_7·c_4_27·b_1_0² + c_2_7·c_4_26·b_1_2·b_1_3
       + c_2_7·c_4_26·b_1_1·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_3 + c_2_7·c_4_26·b_1_0·b_1_2
       + c_2_7·c_4_26·b_1_0² + c_2_7²·b_1_1·b_3_14 + c_2_7²·b_1_0·b_3_15
       + c_2_7²·b_1_0·b_3_11 + c_2_7²·b_1_0·b_3_10 + c_2_7²·b_1_0³·b_1_3
       + c_2_7²·b_1_0³·b_1_1 + c_2_7³·b_1_1·b_1_3 + c_2_7³·b_1_0·b_1_2 + c_2_7³·b_1_0²
55. b_5_44² + b_1_2·b_1_3⁴·b_5_44 + b_1_0⁶·b_1_1·b_3_14 + b_1_0⁷·b_3_15
       + b_1_0⁷·b_3_11 + b_1_0⁹·b_1_2 + b_1_0⁹·b_1_1 + c_4_27·b_1_0²·b_1_1·b_3_12
       + c_4_27·b_1_0³·b_3_11 + c_4_27·b_1_0⁵·b_1_2 + c_4_27·b_1_0⁶
       + c_4_26·b_1_2·b_1_3²·b_3_15 + c_4_26·b_1_0⁵·b_1_3 + c_4_26·b_1_0⁶
       + c_2_7·b_1_3⁵·b_3_12 + c_2_7·b_1_3⁸ + c_2_7·b_1_2·b_1_3⁴·b_3_15
       + c_2_7·b_1_2·b_1_3⁷ + c_2_7·b_1_0⁴·b_1_1·b_3_12 + c_2_7·b_1_0⁵·b_3_12
       + c_2_7·b_1_0⁵·b_3_11 + c_2_7·b_1_0⁷·b_1_3 + c_2_7·b_1_0⁷·b_1_2
       + c_4_27²·b_1_1·b_1_3 + c_4_27²·b_1_0·b_1_3 + c_4_27²·b_1_0·b_1_1
       + c_4_26·c_4_27·b_1_1·b_1_3 + c_4_26·c_4_27·b_1_0·b_1_3 + c_4_26·c_4_27·b_1_0·b_1_1
       + c_4_26·c_4_27·b_1_0² + c_4_26²·b_1_1·b_1_3 + c_4_26²·b_1_0·b_1_2
       + c_4_26²·b_1_0·b_1_1 + c_2_7·c_4_27·b_1_0⁴ + c_2_7·c_4_26·b_1_3⁴
       + c_2_7·c_4_26·b_1_2·b_1_3³ + c_2_7·c_4_26·b_1_0³·b_1_3
       + c_2_7·c_4_26·b_1_0³·b_1_2 + c_2_7²·b_1_2·b_1_3²·b_3_15 + c_2_7²·b_1_2·b_1_3⁵
       + c_2_7²·b_1_0⁵·b_1_2 + c_2_7²·c_4_27·b_1_1·b_1_3 + c_2_7²·c_4_27·b_1_0·b_1_3
       + c_2_7²·c_4_27·b_1_0·b_1_1 + c_2_7²·c_4_27·b_1_0² + c_2_7³·b_1_3⁴
       + c_2_7³·b_1_2·b_1_3³ + c_2_7³·b_1_0³·b_1_3 + c_2_7³·b_1_0³·b_1_2
       + c_2_7⁴·b_1_3² + c_2_7⁴·b_1_1·b_1_3 + c_2_7⁴·b_1_0·b_1_3 + c_2_7⁴·b_1_0·b_1_1
56. b_5_43² + b_1_0⁴·b_1_2·b_5_44 + b_1_0⁵·b_5_44 + b_1_0⁶·b_1_1·b_3_14
       + b_1_0⁷·b_3_15 + b_1_0⁷·b_3_12 + c_4_27·b_1_0³·b_3_12 + c_4_27·b_1_0³·b_3_10
       + c_4_27·b_1_0⁵·b_1_2 + c_4_27·b_1_0⁵·b_1_1 + c_4_27·b_1_0⁶ + c_4_26·b_1_0⁵·b_1_1
       + c_2_7·b_1_0⁴·b_1_1·b_3_14 + c_2_7·b_1_0⁴·b_1_1·b_3_12 + c_2_7·b_1_0⁵·b_3_15
       + c_2_7·b_1_0⁷·b_1_3 + c_2_7·b_1_0⁷·b_1_1 + c_2_7·b_1_0⁸ + c_4_27²·b_1_1·b_1_3
       + c_4_27²·b_1_0·b_1_3 + c_4_27²·b_1_0·b_1_1 + c_4_27²·b_1_0²
       + c_4_26·c_4_27·b_1_0·b_1_3 + c_4_26·c_4_27·b_1_0·b_1_2 + c_4_26·c_4_27·b_1_0²
       + c_4_26²·b_1_3² + c_4_26²·b_1_1·b_1_3 + c_4_26²·b_1_0·b_1_2
       + c_4_26²·b_1_0·b_1_1 + c_2_7·c_4_27·b_1_0³·b_1_3 + c_2_7·c_4_27·b_1_0³·b_1_1
       + c_2_7·c_4_26·b_1_0³·b_1_3 + c_2_7·c_4_26·b_1_0³·b_1_2 + c_2_7·c_4_26·b_1_0⁴
       + c_2_7²·b_1_3⁶ + c_2_7²·b_1_2·b_1_3²·b_3_15 + c_2_7²·b_1_0²·b_1_1·b_3_14
       + c_2_7²·b_1_0²·b_1_1·b_3_12 + c_2_7²·b_1_0³·b_3_15 + c_2_7²·b_1_0³·b_3_12
       + c_2_7²·b_1_0³·b_3_11 + c_2_7²·b_1_0³·b_3_10 + c_2_7²·b_1_0⁵·b_1_3
       + c_2_7²·b_1_0⁵·b_1_2 + c_2_7²·c_4_27·b_1_1·b_1_3 + c_2_7²·c_4_27·b_1_0·b_1_2
       + c_2_7²·c_4_27·b_1_0·b_1_1 + c_2_7²·c_4_27·b_1_0² + c_2_7²·c_4_26·b_1_1·b_1_3
       + c_2_7²·c_4_26·b_1_0·b_1_3 + c_2_7²·c_4_26·b_1_0·b_1_1 + c_2_7²·c_4_26·b_1_0²
       + c_2_7³·b_1_3⁴ + c_2_7³·b_1_2·b_1_3³ + c_2_7³·b_1_0³·b_1_3
       + c_2_7⁴·b_1_1·b_1_3 + c_2_7⁴·b_1_0·b_1_3 + c_2_7⁴·b_1_0·b_1_1 + c_2_7⁴·b_1_0²
57. b_5_43·b_5_44 + b_1_0⁶·b_1_1·b_3_12 + b_1_0⁷·b_3_13 + b_1_0⁷·b_3_12 + b_1_0⁹·b_1_3
       + b_1_0⁹·b_1_1 + c_4_27·b_1_2·b_5_44 + c_4_27·b_1_0·b_5_43 + c_4_27·b_1_0³·b_3_15
       + c_4_27·b_1_0³·b_3_13 + c_4_27·b_1_0⁵·b_1_2 + c_4_27·b_1_0⁵·b_1_1
       + c_4_26·b_1_3·b_5_44 + c_4_26·b_1_2·b_5_44 + c_4_26·b_1_2·b_1_3²·b_3_15
       + c_4_26·b_1_1·b_5_43 + c_4_26·b_1_0²·b_1_1·b_3_12 + c_4_26·b_1_0³·b_3_15
       + c_4_26·b_1_0³·b_3_14 + c_4_26·b_1_0³·b_3_13 + c_4_26·b_1_0³·b_3_11
       + c_4_26·b_1_0³·b_3_10 + c_4_26·b_1_0⁵·b_1_3 + c_4_26·b_1_0⁵·b_1_1 + c_4_26·b_1_0⁶
       + c_2_7·b_1_3³·b_5_44 + c_2_7·b_1_2·b_1_3⁴·b_3_15 + c_2_7·b_1_2·b_1_3⁷
       + c_2_7·b_1_0²·b_1_1·b_5_43 + c_2_7·b_1_0³·b_5_43 + c_2_7·b_1_0⁴·b_1_1·b_3_12
       + c_2_7·b_1_0⁵·b_3_14 + c_2_7·b_1_0⁵·b_3_13 + c_2_7·b_1_0⁵·b_3_11
       + c_2_7·b_1_0⁵·b_3_10 + c_2_7·b_1_0⁷·b_1_3 + c_2_7·b_1_0⁷·b_1_2
       + c_4_27²·b_1_0·b_1_2 + c_4_26·c_4_27·b_1_0·b_1_3 + c_4_26·c_4_27·b_1_0·b_1_2
       + c_4_26²·b_1_1·b_1_3 + c_2_7·c_4_27·b_1_2·b_3_15 + c_2_7·c_4_27·b_1_0·b_3_11
       + c_2_7·c_4_27·b_1_0³·b_1_3 + c_2_7·c_4_27·b_1_0³·b_1_1 + c_2_7·c_4_27·b_1_0⁴
       + c_2_7·c_4_26·b_1_1·b_3_12 + c_2_7·c_4_26·b_1_0·b_3_15 + c_2_7·c_4_26·b_1_0·b_3_13
       + c_2_7·c_4_26·b_1_0·b_3_12 + c_2_7·c_4_26·b_1_0³·b_1_3 + c_2_7²·b_1_3³·b_3_15
       + c_2_7²·b_1_3³·b_3_12 + c_2_7²·b_1_3⁶ + c_2_7²·b_1_2·b_5_44
       + c_2_7²·b_1_2·b_1_3²·b_3_12 + c_2_7²·b_1_1·b_5_43 + c_2_7²·b_1_0·b_5_44
       + c_2_7²·b_1_0²·b_1_1·b_3_14 + c_2_7²·b_1_0²·b_1_1·b_3_12
       + c_2_7²·b_1_0³·b_3_15 + c_2_7²·b_1_0³·b_3_14 + c_2_7²·b_1_0³·b_3_13
       + c_2_7²·b_1_0³·b_3_10 + c_2_7²·b_1_0⁵·b_1_2 + c_2_7²·b_1_0⁵·b_1_1
       + c_2_7²·c_4_27·b_1_2·b_1_3 + c_2_7²·c_4_27·b_1_0·b_1_2
       + c_2_7²·c_4_27·b_1_0·b_1_1 + c_2_7²·c_4_26·b_1_1·b_1_3
       + c_2_7²·c_4_26·b_1_0·b_1_2 + c_2_7²·c_4_26·b_1_0² + c_2_7³·b_1_3·b_3_15
       + c_2_7³·b_1_3⁴ + c_2_7³·b_1_2·b_3_12 + c_2_7³·b_1_2·b_1_3³
       + c_2_7³·b_1_1·b_3_12 + c_2_7³·b_1_0·b_3_14 + c_2_7³·b_1_0·b_3_13
       + c_2_7³·b_1_0·b_3_11 + c_2_7³·b_1_0·b_3_10 + c_2_7³·b_1_0³·b_1_2
       + c_2_7³·b_1_0⁴ + c_2_7⁴·b_1_3² + c_2_7⁴·b_1_0·b_1_3

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 + b_1_1², 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. b_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_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_2⁴ + c_1_1⁴, an element of degree 4
13. c_4_27 → 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. b_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_2², an element of degree 2
6. b_3_10 → c_1_2²·c_1_3, an element of degree 3
7. b_3_11 → 0, an element of degree 3
8. b_3_12 → c_1_1·c_1_3² + c_1_1²·c_1_3, an element of degree 3
9. b_3_13 → c_1_2²·c_1_3 + c_1_1·c_1_3² + 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_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
12. c_4_26 → c_1_2²·c_1_3² + 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_1·c_1_3³ + c_1_1²·c_1_3² + 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_3⁴ + c_1_1⁴·c_1_3, an element of degree 5
15. b_5_44 → c_1_2·c_1_3⁴ + c_1_2²·c_1_3³ + c_1_2⁴·c_1_3 + c_1_1·c_1_2·c_1_3³
       + c_1_1²·c_1_2·c_1_3², an element of degree 5

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

1. b_1_0 → c_1_3, an element of degree 1
2. b_1_1 → c_1_3, 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_2·c_1_3 + 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, an element of degree 3
7. b_3_11 → 0, 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_0·c_1_3² + c_1_0²·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 + 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_1·c_1_3³ + c_1_1⁴, an element of degree 4
13. c_4_27 → c_1_2·c_1_3³ + c_1_2²·c_1_3² + c_1_0²·c_1_3² + 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_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_2·c_1_3⁴ + c_1_2²·c_1_3³ + c_1_1²·c_1_3³ + c_1_1⁴·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. b_1_0 → c_1_3, 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_2·c_1_3 + c_1_2², an element of degree 2
6. b_3_10 → c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
7. b_3_11 → c_1_3³ + 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_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 → 0, an element of degree 3
11. b_3_15 → c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
12. c_4_26 → c_1_2·c_1_3³ + c_1_2⁴ + c_1_1·c_1_3³ + c_1_1⁴, an element of degree 4
13. c_4_27 → c_1_2·c_1_3³ + c_1_2²·c_1_3² + c_1_0²·c_1_3² + 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_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_1⁴·c_1_3 + c_1_0·c_1_3⁴ + c_1_0⁴·c_1_3, an element of degree 5
15. b_5_44 → c_1_2·c_1_3⁴ + c_1_2⁴·c_1_3 + c_1_1²·c_1_3³ + c_1_1⁴·c_1_3 + c_1_0·c_1_3⁴
       + 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, an element of degree 5

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

1. b_1_0 → c_1_3, 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_2², an element of degree 2
6. b_3_10 → c_1_2·c_1_3² + c_1_2²·c_1_3, 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_3³ + 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_3³ + 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_3⁴ + c_1_2·c_1_3³ + 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_3⁴ + c_1_2·c_1_3³ + c_1_0·c_1_3³ + c_1_0⁴, an element of degree 4
14. b_5_43 → c_1_2⁴·c_1_3 + 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_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, an element of degree 5
15. b_5_44 → c_1_3⁵ + c_1_2·c_1_3⁴ + c_1_2²·c_1_3³ + c_1_0²·c_1_3³ + c_1_0⁴·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