David J. Green

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Cohomology of group number 1533 of order 128

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

General information on the group

• The group has 4 minimal generators and exponent 4.
• It is non-abelian.
• It has p-Rank 4.
• Its center has rank 3.
• It has 2 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 4.

Structure of the cohomology ring

General information

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

  ( − 1) · (t8  +  t7  −  2·t6  +  2·t5  −  3·t4  −  3·t3  −  t2  −  2·t  −  1)

  (t  +  1)2 · (t  −  1)4 · (t2  +  1)3

• The a-invariants are -∞,-∞,-∞,-4,-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 18 minimal generators of maximal degree 8:

1. a_1_0, a nilpotent element of degree 1
2. a_1_3, a nilpotent element of degree 1
3. b_1_1, an element of degree 1
4. b_1_2, an element of degree 1
5. a_3_5, a nilpotent element of degree 3
6. b_3_6, an element of degree 3
7. b_3_7, an element of degree 3
8. b_3_8, an element of degree 3
9. b_3_9, an element of degree 3
10. b_3_10, an element of degree 3
11. b_4_16, an element of degree 4
12. c_4_17, a Duflot regular element of degree 4
13. c_4_18, a Duflot regular element of degree 4
14. c_4_19, a Duflot regular element of degree 4
15. b_5_29, an element of degree 5
16. b_6_36, an element of degree 6
17. b_6_38, an element of degree 6
18. b_8_67, an element of degree 8

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring relations

There are 95 minimal relations of maximal degree 16:

1. a_1_3·b_1_1 + a_1_0·b_1_2 + a_1_0·b_1_1 + a_1_3²
2. a_1_3·b_1_2 + a_1_0·b_1_1 + a_1_0·a_1_3
3. b_1_1·b_1_2 + b_1_1² + a_1_0²
4. a_1_3³ + a_1_0·a_1_3² + a_1_0³
5. a_1_0²·b_1_1 + a_1_0·a_1_3² + a_1_0³
6. a_1_0²·b_1_2
7. b_1_1·b_3_7 + b_1_1·b_3_6 + b_1_1⁴ + b_1_1·a_3_5 + a_1_3·b_3_6 + a_1_0·a_3_5
8. b_1_2·a_3_5 + a_1_0·b_3_8 + a_1_0·b_3_6 + a_1_0·a_3_5
9. b_1_1·a_3_5 + a_1_3·b_3_8 + a_1_3·b_3_6
10. b_1_2·b_3_8 + b_1_2·b_3_7 + b_1_2⁴ + b_1_1·b_3_8 + b_1_1·b_3_6 + b_1_2·a_3_5 + a_1_0·b_3_7
       + a_1_0·a_3_5
11. b_1_2·b_3_6 + b_1_1·b_3_6 + a_1_0·b_3_9 + a_1_0·b_3_6 + a_1_0·a_3_5
12. b_1_2·a_3_5 + b_1_1·a_3_5 + a_1_3·b_3_9 + a_1_3·b_3_6 + a_1_0·b_3_7 + a_1_0·b_3_6
       + a_1_3·a_3_5 + a_1_0·a_3_5
13. b_1_1·b_3_9 + b_1_1·b_3_6 + b_1_1⁴ + b_1_1·a_3_5 + a_1_0·b_3_6
14. b_1_1·a_3_5 + a_1_0·b_3_10 + a_1_0·b_3_7 + a_1_0·b_3_6 + a_1_3·a_3_5 + a_1_0·a_3_5
15. b_1_2·a_3_5 + b_1_1·a_3_5 + a_1_3·b_3_10 + a_1_3·b_3_7 + a_1_3·b_3_6 + a_1_3·a_3_5
16. b_1_2·b_3_10 + b_1_2·b_3_9 + b_1_2·b_3_7 + b_1_1·b_3_10 + a_1_3·b_3_7 + a_1_3·b_3_6
       + a_1_0·b_3_6 + a_1_3·a_3_5
17. a_1_3²·b_3_7 + a_1_3²·b_3_6 + a_1_0²·b_3_6 + a_1_0·a_1_3·a_3_5
18. a_1_0·a_1_3·b_3_6 + a_1_0²·b_3_9 + a_1_0²·b_3_8
19. a_1_3²·b_3_6 + a_1_0·a_1_3·b_3_6 + a_1_0²·b_3_10 + a_1_0²·b_3_8 + a_1_0²·b_3_6
       + a_1_0·a_1_3·a_3_5 + a_1_0²·a_3_5
20. b_4_16·a_1_0 + a_1_0²·b_3_8 + a_1_0²·b_3_7 + a_1_0·a_1_3·a_3_5 + a_1_0²·a_3_5
21. b_4_16·a_1_3 + a_1_0·a_1_3·b_3_7 + a_1_3²·a_3_5
22. b_1_1²·b_3_6 + b_4_16·b_1_1 + a_1_0·a_1_3·b_3_7 + a_1_0²·b_3_8 + a_1_0²·b_3_6
23. b_3_9·b_3_10 + b_3_9² + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_7² + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_3_6² + b_1_2³·b_3_7 + b_1_1³·b_3_10 + b_1_1³·b_3_8 + a_3_5·b_3_10
       + a_3_5·b_3_9 + a_3_5·b_3_8 + c_4_17·b_1_1² + c_4_18·a_1_0² + c_4_17·a_1_3²
24. b_3_9·b_3_10 + b_3_9² + b_3_7·b_3_9 + b_3_6·b_3_10 + b_1_1³·b_3_10 + a_3_5·b_3_8
       + a_3_5·b_3_7 + a_3_5·b_3_6 + c_4_17·a_1_0·b_1_2 + c_4_18·a_1_0·a_1_3 + c_4_17·a_1_3²
       + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_0²
25. b_3_9·b_3_10 + b_3_9² + b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_9 + b_3_7² + b_3_6·b_3_8
       + b_3_6·b_3_7 + b_3_6² + b_1_2³·b_3_9 + b_1_1³·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_8
       + a_3_5·b_3_7 + a_3_5² + a_1_0³·b_3_6 + c_4_17·b_1_1² + c_4_18·a_1_3²
       + c_4_17·a_1_3² + c_4_17·a_1_0²
26. b_3_9·b_3_10 + b_3_9² + b_3_8·b_3_9 + b_3_6·b_3_10 + b_3_6·b_3_8 + b_3_6·b_3_7 + b_3_6²
       + b_1_2³·b_3_9 + b_1_1³·b_3_10 + b_1_1³·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_5·b_3_7
       + a_1_0³·b_3_6 + c_4_17·b_1_1² + c_4_18·a_1_0·b_1_2 + c_4_18·a_1_0·b_1_1
       + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_3² + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_0²
27. b_3_9·b_3_10 + b_3_9² + b_3_8² + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_1_2³·b_3_7 + b_1_2⁶ + b_1_1³·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_9
       + a_3_5·b_3_8 + a_3_5² + a_1_0³·b_3_6 + c_4_18·b_1_1² + c_4_17·b_1_1²
       + c_4_17·a_1_0²
28. b_3_10² + b_3_9·b_3_10 + b_3_7·b_3_10 + b_3_7² + b_3_6·b_3_9 + b_1_2³·b_3_7
       + b_1_1³·b_3_10 + b_1_1³·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_5²
       + a_1_0³·b_3_6 + c_4_19·b_1_2² + c_4_17·b_1_2² + c_4_18·a_1_0·b_1_2
       + c_4_17·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_3² + c_4_17·a_1_0·a_1_3
29. b_3_9·b_3_10 + b_3_9² + b_3_8·b_3_9 + b_3_7·b_3_8 + b_3_7² + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_7 + b_3_6² + b_1_2³·b_3_9 + b_1_2³·b_3_7 + b_1_1³·b_3_10 + a_3_5·b_3_10
       + a_3_5·b_3_9 + a_3_5·b_3_7 + a_3_5·b_3_6 + a_3_5² + a_1_0³·b_3_6 + c_4_17·b_1_1²
       + c_4_19·a_1_0·b_1_2 + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_3² + c_4_17·a_1_0·a_1_3
       + c_4_17·a_1_0²
30. b_3_9·b_3_10 + b_3_9² + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_7² + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_1_2³·b_3_7 + b_1_1³·b_3_10 + b_1_1³·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_9
       + a_3_5·b_3_8 + c_4_19·a_1_0² + c_4_17·a_1_3²
31. b_3_7·b_3_8 + b_3_7² + b_3_6·b_3_8 + b_3_6·b_3_7 + b_1_2³·b_3_7 + b_1_1³·b_3_8
       + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_5·b_3_7 + a_3_5·b_3_6 + a_3_5² + a_1_0³·b_3_6
       + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_2 + c_4_19·a_1_0·a_1_3 + c_4_17·a_1_3²
       + c_4_17·a_1_0·a_1_3
32. b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_7
       + b_3_6² + b_1_2³·b_3_9 + b_1_2³·b_3_7 + b_1_1³·b_3_10 + a_3_5·b_3_9 + a_3_5·b_3_7
       + c_4_17·b_1_1² + c_4_19·a_1_3²
33. b_3_9·b_3_10 + b_3_9² + b_3_8·b_3_9 + b_3_6·b_3_10 + b_3_6·b_3_8 + b_3_6·b_3_7 + b_3_6²
       + b_1_2³·b_3_9 + b_1_1³·b_3_10 + b_1_1³·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_7 + a_3_5·b_3_6
       + a_3_5² + a_1_0³·b_3_6 + c_4_17·b_1_1² + c_4_19·a_1_0·b_1_1 + c_4_17·a_1_0·b_1_2
       + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_3² + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_0²
34. b_3_10² + b_3_9² + b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_7² + b_3_6·b_3_10
       + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_6² + b_1_2³·b_3_9 + b_1_2³·b_3_7 + b_1_1³·b_3_8
       + a_3_5·b_3_9 + a_3_5·b_3_7 + a_1_0³·b_3_6 + c_4_19·b_1_1² + c_4_17·a_1_3²
       + c_4_17·a_1_0²
35. b_3_9·b_3_10 + b_3_8² + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_7² + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_1_2⁶ + b_1_1³·b_3_8 + b_1_1⁶ + b_4_16·b_1_2² + a_3_5·b_3_10
       + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_5² + a_1_0³·b_3_6 + c_4_18·b_1_2² + c_4_17·b_1_2²
       + c_4_17·a_1_3²
36. b_3_9·b_3_10 + b_3_9² + b_3_8·b_3_9 + b_3_7·b_3_8 + b_3_7² + b_3_6·b_3_10 + b_3_6·b_3_7
       + b_1_2³·b_3_9 + b_1_2³·b_3_7 + b_1_1³·b_3_10 + b_4_16·b_1_1² + a_3_5·b_3_10
       + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_5·b_3_7 + a_3_5·b_3_6 + c_4_17·b_1_1²
       + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_3²
       + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_0²
37. b_3_9·b_3_10 + b_3_8² + b_3_7·b_3_8 + b_3_7² + b_3_6·b_3_10 + b_3_6·b_3_8 + b_1_2·b_5_29
       + b_1_2³·b_3_7 + b_1_1⁶ + a_3_5·b_3_9 + a_3_5·b_3_6 + a_3_5² + c_4_18·b_1_2²
       + c_4_17·b_1_1² + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_0·a_1_3 + c_4_17·a_1_0²
38. b_3_9·b_3_10 + b_3_9² + b_3_8·b_3_9 + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_8
       + b_1_2³·b_3_9 + b_1_1³·b_3_10 + b_1_1³·b_3_8 + a_3_5·b_3_8 + a_3_5·b_3_6 + a_1_0·b_5_29
       + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_0·b_1_1 + c_4_17·a_1_0·a_1_3
39. b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_7
       + b_3_6² + b_1_2³·b_3_9 + b_1_2³·b_3_7 + b_1_1³·b_3_10 + a_3_5·b_3_10 + a_3_5·b_3_9
       + a_3_5·b_3_7 + a_1_3·b_5_29 + a_1_0³·b_3_6 + c_4_17·b_1_1² + c_4_18·a_1_0·b_1_2
40. b_3_9·b_3_10 + b_3_9² + b_3_7·b_3_10 + b_3_7² + b_3_6·b_3_7 + b_3_6² + b_1_1·b_5_29
       + b_1_1³·b_3_8 + b_1_1⁶ + a_3_5·b_3_10 + a_3_5·b_3_9 + a_1_0³·b_3_6
       + c_4_18·a_1_0·b_1_2 + c_4_17·a_1_3² + c_4_17·a_1_0·a_1_3
41. a_1_0·b_3_6·b_3_8 + a_1_0·a_3_5·b_3_6 + c_4_19·a_1_0·a_1_3² + c_4_19·a_1_0²·a_1_3
       + c_4_18·a_1_0·a_1_3² + c_4_18·a_1_0²·a_1_3 + c_4_17·a_1_0³
42. b_1_1·b_3_6·b_3_8 + b_4_16·b_3_8 + b_4_16·b_3_7 + b_4_16·b_1_2³ + a_1_0·b_3_6·b_3_8
       + a_1_3·a_3_5·b_3_6 + a_1_0·a_3_5·b_3_6 + c_4_17·b_1_1³ + c_4_19·a_1_0²·a_1_3
       + c_4_18·a_1_0·a_1_3² + c_4_18·a_1_0²·a_1_3 + c_4_18·a_1_0³ + c_4_17·a_1_0³
43. b_4_16·b_3_6 + a_1_0·b_3_6·b_3_8 + a_1_3·a_3_5·b_3_6 + a_1_0²·b_5_29 + c_4_17·b_1_1³
       + c_4_19·a_1_0³ + c_4_18·a_1_0²·a_1_3 + c_4_17·a_1_0²·a_1_3 + c_4_17·a_1_0³
44. b_4_16·b_3_6 + a_1_0·b_3_6·b_3_8 + b_4_16·a_3_5 + a_1_0·a_1_3·b_5_29 + c_4_17·b_1_1³
45. b_1_1·b_3_6·b_3_10 + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_7 + b_4_16·b_3_6
       + a_1_0·b_3_6·b_3_8 + a_1_3²·b_5_29 + a_1_0·a_3_5·b_3_6 + c_4_17·b_1_1³
       + c_4_19·a_1_0²·a_1_3 + c_4_19·a_1_0³ + c_4_18·a_1_0·a_1_3² + c_4_18·a_1_0²·a_1_3
       + c_4_18·a_1_0³ + c_4_17·a_1_0²·a_1_3
46. b_1_2²·b_5_29 + b_1_2⁴·b_3_9 + b_1_2⁴·b_3_7 + b_1_2⁷ + b_1_1·b_3_6·b_3_10
       + b_1_1⁴·b_3_10 + b_1_1⁷ + b_6_36·b_1_2 + b_4_16·b_3_9 + b_4_16·b_1_2³
       + a_1_0·b_3_6·b_3_8 + a_1_3·a_3_5·b_3_6 + c_4_18·b_1_1³ + c_4_17·b_1_2³
       + c_4_19·a_1_0²·a_1_3 + c_4_18·a_1_0²·a_1_3 + c_4_18·a_1_0³ + c_4_17·a_1_0·a_1_3²
       + c_4_17·a_1_0²·a_1_3 + c_4_17·a_1_0³
47. b_1_1·b_3_6·b_3_10 + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_7 + b_6_36·a_1_0
       + b_4_16·a_3_5 + a_1_3·a_3_5·b_3_6 + a_1_0·a_3_5·b_3_6 + c_4_19·a_1_0²·a_1_3
       + c_4_18·a_1_0³ + c_4_17·a_1_0·a_1_3² + c_4_17·a_1_0³
48. b_1_1·b_3_6·b_3_10 + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_7 + b_4_16·b_3_6
       + b_6_36·a_1_3 + b_4_16·a_3_5 + a_1_3·a_3_5·b_3_6 + a_1_0·a_3_5·b_3_6 + c_4_17·b_1_1³
       + c_4_19·a_1_0³ + c_4_18·a_1_0²·a_1_3 + c_4_18·a_1_0³ + c_4_17·a_1_0³
49. b_1_1·b_3_6·b_3_10 + b_1_1⁴·b_3_10 + b_1_1⁴·b_3_8 + b_1_1⁷ + b_6_36·b_1_1
       + b_4_16·b_3_6 + b_4_16·b_1_1³ + b_4_16·a_3_5 + a_1_0·a_3_5·b_3_6 + c_4_18·b_1_1³
       + c_4_17·b_1_1³ + c_4_19·a_1_0³ + c_4_18·a_1_0·a_1_3² + c_4_18·a_1_0³
       + c_4_17·a_1_0·a_1_3²
50. b_1_2⁴·b_3_9 + b_1_2⁷ + b_1_1·b_3_6·b_3_10 + b_1_1⁴·b_3_8 + b_1_1⁷ + b_6_38·b_1_2
       + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_6 + b_4_16·b_1_1³ + b_4_16·a_3_5
       + a_1_3·a_3_5·b_3_6 + c_4_19·b_1_1³ + c_4_18·b_1_2³ + c_4_17·b_1_2³
       + c_4_17·b_1_1³ + c_4_17·a_1_0²·a_1_3
51. a_1_0·b_3_6·b_3_8 + b_6_38·a_1_0 + b_4_16·a_3_5 + a_1_0·a_3_5·b_3_6 + c_4_19·a_1_0³
       + c_4_18·a_1_0·a_1_3² + c_4_18·a_1_0³ + c_4_17·a_1_0·a_1_3²
       + c_4_17·a_1_0²·a_1_3
52. b_1_1·b_3_6·b_3_10 + b_4_16·b_3_10 + b_4_16·b_3_9 + b_4_16·b_3_7 + b_6_38·a_1_3
       + a_1_3·a_3_5·b_3_6 + a_1_0·a_3_5·b_3_6 + c_4_18·a_1_0·a_1_3² + c_4_18·a_1_0²·a_1_3
       + c_4_18·a_1_0³
53. b_1_1·b_3_6·b_3_10 + b_1_1⁴·b_3_8 + b_1_1⁷ + b_6_38·b_1_1 + b_4_16·b_3_10
       + b_4_16·b_3_9 + b_4_16·b_3_7 + b_4_16·b_1_1³ + a_1_3·a_3_5·b_3_6 + c_4_19·b_1_1³
       + c_4_18·b_1_1³ + c_4_19·a_1_0²·a_1_3 + c_4_19·a_1_0³ + c_4_18·a_1_0·a_1_3²
       + c_4_18·a_1_0²·a_1_3 + c_4_17·a_1_0·a_1_3² + c_4_17·a_1_0²·a_1_3
54. b_1_2⁵·b_3_7 + b_1_2⁸ + b_4_16·b_1_2⁴ + b_4_16² + c_4_17·b_1_2⁴
55. a_3_5·b_5_29 + a_1_0³·b_5_29 + c_4_19·a_1_3·b_3_7 + c_4_19·a_1_3·b_3_6
       + c_4_19·a_1_0·b_3_9 + c_4_19·a_1_0·b_3_6 + c_4_18·a_1_3·b_3_7 + c_4_18·a_1_3·b_3_6
       + c_4_17·a_1_0·b_3_10 + c_4_17·a_1_0·b_3_9 + c_4_17·a_1_0·b_3_8 + c_4_17·a_1_0·b_3_7
       + c_4_17·a_1_0·b_3_6 + c_4_19·a_1_3·a_3_5 + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_0·a_3_5
       + c_4_17·a_1_0·a_3_5
56. b_3_6·b_5_29 + b_4_16·b_1_1·b_3_8 + b_4_16·b_1_1⁴ + a_1_0²·a_1_3·b_5_29
       + c_4_17·b_1_1⁴ + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_6 + c_4_18·a_1_3·b_3_6
       + c_4_18·a_1_0·b_3_7 + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_10 + c_4_17·a_1_0·b_3_9
       + c_4_17·a_1_0·b_3_7 + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_0·a_3_5 + c_4_17·a_1_3·a_3_5
57. b_3_10·b_5_29 + b_3_7·b_5_29 + b_1_1²·b_3_8·b_3_10 + b_6_36·b_1_2²
       + b_4_16·b_1_2·b_3_7 + b_4_16·b_1_1·b_3_8 + a_1_0²·a_1_3·b_5_29 + a_1_0³·b_5_29
       + c_4_19·b_1_2·b_3_7 + c_4_19·b_1_1·b_3_6 + c_4_19·b_1_1⁴ + c_4_18·b_1_2·b_3_7
       + c_4_18·b_1_1·b_3_6 + c_4_17·b_1_2·b_3_9 + c_4_17·b_1_1·b_3_6 + c_4_17·b_1_1⁴
       + c_4_19·a_1_3·b_3_7 + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_7 + c_4_18·a_1_3·b_3_7
       + c_4_18·a_1_3·b_3_6 + c_4_18·a_1_0·b_3_9 + c_4_18·a_1_0·b_3_7 + c_4_18·a_1_0·b_3_6
       + c_4_17·a_1_3·b_3_7 + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_9 + c_4_17·a_1_0·b_3_7
       + c_4_18·a_1_3·a_3_5 + c_4_17·a_1_0·a_3_5
58. b_3_8·b_5_29 + b_1_2⁵·b_3_7 + b_1_2⁸ + b_1_1⁸ + b_6_36·b_1_1² + b_4_16·b_1_2·b_3_7
       + b_4_16·b_1_2⁴ + b_4_16·b_1_1·b_3_10 + b_4_16·b_1_1·b_3_8 + a_1_0²·a_1_3·b_5_29
       + a_1_0³·b_5_29 + c_4_19·b_1_2·b_3_9 + c_4_19·b_1_2⁴ + c_4_19·b_1_1·b_3_6
       + c_4_17·b_1_2·b_3_9 + c_4_17·b_1_2·b_3_7 + c_4_17·b_1_1⁴ + c_4_19·a_1_3·b_3_6
       + c_4_19·a_1_0·b_3_8 + c_4_19·a_1_0·b_3_7 + c_4_18·a_1_0·b_3_10 + c_4_18·a_1_0·b_3_8
       + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_7 + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_3·a_3_5
       + c_4_18·a_1_0·a_3_5 + c_4_17·a_1_0·a_3_5
59. b_3_10·b_5_29 + b_3_8·b_5_29 + b_1_2⁵·b_3_7 + b_1_1²·b_3_8·b_3_10 + b_6_38·b_1_2²
       + b_4_16·b_1_2·b_3_9 + b_4_16·b_1_2⁴ + b_4_16·b_1_1·b_3_10 + b_4_16·b_1_1·b_3_8
       + a_1_0³·b_5_29 + c_4_19·b_1_2·b_3_7 + c_4_19·b_1_1·b_3_6 + c_4_18·b_1_2·b_3_7
       + c_4_18·b_1_2⁴ + c_4_18·b_1_1·b_3_6 + c_4_17·b_1_2·b_3_9 + c_4_17·b_1_1·b_3_6
       + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_6 + c_4_18·a_1_3·b_3_7
       + c_4_18·a_1_0·b_3_10 + c_4_18·a_1_0·b_3_9 + c_4_18·a_1_0·b_3_8 + c_4_18·a_1_0·b_3_7
       + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_9 + c_4_17·a_1_0·b_3_8 + c_4_19·a_1_3·a_3_5
       + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_3·a_3_5 + c_4_17·a_1_3·a_3_5
60. b_3_10·b_5_29 + b_3_9·b_5_29 + b_3_8·b_5_29 + b_3_7·b_5_29 + b_1_2⁵·b_3_7 + b_1_2⁸
       + b_1_1²·b_3_8·b_3_10 + b_1_1⁸ + b_6_38·b_1_1² + b_4_16·b_1_2·b_3_7
       + b_4_16·b_1_2⁴ + b_4_16·b_1_1·b_3_10 + b_4_16·b_1_1·b_3_8 + a_1_0³·b_5_29
       + c_4_19·b_1_2·b_3_9 + c_4_19·b_1_2⁴ + c_4_19·b_1_1·b_3_6 + c_4_19·b_1_1⁴
       + c_4_17·b_1_2·b_3_9 + c_4_17·b_1_2·b_3_7 + c_4_17·b_1_1⁴ + c_4_19·a_1_3·b_3_6
       + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_7 + c_4_18·a_1_0·b_3_9 + c_4_18·a_1_0·b_3_8
       + c_4_18·a_1_0·b_3_6 + c_4_17·a_1_3·b_3_7 + c_4_17·a_1_3·b_3_6 + c_4_17·a_1_0·b_3_10
       + c_4_17·a_1_0·b_3_8 + c_4_17·a_1_0·b_3_6 + c_4_19·a_1_3·a_3_5 + c_4_18·a_1_3·a_3_5
       + c_4_17·a_1_0·a_3_5
61. b_6_36·a_3_5 + c_4_19·a_1_0²·b_3_10 + c_4_19·a_1_0²·b_3_7 + c_4_18·a_1_0·a_1_3·b_3_7
       + c_4_18·a_1_0²·b_3_10 + c_4_18·a_1_0²·b_3_8 + c_4_17·a_1_0·a_1_3·b_3_7
       + c_4_17·a_1_0²·b_3_7 + c_4_17·a_1_0²·b_3_6 + c_4_19·a_1_3²·a_3_5
       + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_19·a_1_0²·a_3_5 + c_4_18·a_1_3²·a_3_5
       + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_3²·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
62. b_6_36·b_3_6 + b_4_16·b_1_1²·b_3_10 + b_4_16·b_1_1²·b_3_8 + b_4_16·b_1_1⁵
       + c_4_17·b_1_1²·b_3_10 + c_4_17·b_1_1⁵ + b_4_16·c_4_18·b_1_1
       + c_4_19·a_1_0·a_1_3·b_3_7 + c_4_19·a_1_0²·b_3_9 + c_4_19·a_1_0²·b_3_8
       + c_4_18·a_1_0²·b_3_10 + c_4_18·a_1_0²·b_3_9 + c_4_18·a_1_0²·b_3_6
       + c_4_17·a_1_0²·b_3_10 + c_4_17·a_1_0²·b_3_8 + c_4_19·a_1_3²·a_3_5
       + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_3²·a_3_5 + c_4_17·a_1_0²·a_3_5
63. b_6_36·b_3_7 + b_6_36·b_1_1³ + b_4_16·b_5_29 + b_4_16·b_1_2²·b_3_7 + b_4_16·b_1_2⁵
       + b_4_16·b_1_1²·b_3_10 + b_4_16²·b_1_2 + c_4_19·b_1_2²·b_3_9 + c_4_19·b_1_1⁵
       + c_4_17·b_1_2²·b_3_9 + c_4_17·b_1_1²·b_3_10 + c_4_17·b_1_1⁵ + b_4_16·c_4_19·b_1_1
       + b_4_16·c_4_18·b_1_1 + b_4_16·c_4_17·b_1_2 + c_4_19·a_1_0·a_1_3·b_3_7
       + c_4_19·a_1_0²·b_3_9 + c_4_19·a_1_0²·b_3_6 + c_4_18·a_1_0²·b_3_9
       + c_4_18·a_1_0²·b_3_7 + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_0²·b_3_10
       + c_4_17·a_1_0²·b_3_9 + c_4_17·a_1_0²·b_3_8 + c_4_17·a_1_0²·b_3_6
       + c_4_19·a_1_3²·a_3_5 + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_0²·a_3_5
64. b_3_6·b_3_8·b_3_10 + b_1_1³·b_3_8·b_3_10 + b_1_1⁹ + b_6_36·b_3_8 + b_6_36·b_1_2³
       + b_4_16·b_5_29 + b_4_16·b_1_2²·b_3_7 + b_4_16·b_1_2⁵ + b_4_16·b_1_1²·b_3_10
       + b_4_16²·b_1_2 + c_4_19·b_1_2²·b_3_9 + c_4_19·b_1_1⁵ + c_4_18·b_1_1²·b_3_8
       + c_4_17·b_1_2²·b_3_9 + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_17·b_1_2
       + c_4_19·a_1_0²·b_3_10 + c_4_19·a_1_0²·b_3_9 + c_4_18·a_1_0·a_1_3·b_3_7
       + c_4_18·a_1_0²·b_3_10 + c_4_18·a_1_0²·b_3_9 + c_4_18·a_1_0²·b_3_7
       + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_0²·b_3_10 + c_4_17·a_1_0²·b_3_7
       + c_4_17·a_1_0²·b_3_6 + c_4_19·a_1_3²·a_3_5 + c_4_19·a_1_0·a_1_3·a_3_5
       + c_4_19·a_1_0²·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
65. b_6_36·b_3_9 + b_6_36·b_1_1³ + b_4_16·b_1_2²·b_3_7 + b_4_16·b_1_2⁵
       + b_4_16·b_1_1²·b_3_10 + b_4_16·b_1_1²·b_3_8 + b_4_16·b_1_1⁵ + b_4_16²·b_1_2
       + c_4_19·b_1_2²·b_3_7 + c_4_19·b_1_2⁵ + c_4_18·b_1_2²·b_3_7 + c_4_18·b_1_2⁵
       + c_4_17·b_1_1²·b_3_10 + c_4_17·b_1_1⁵ + b_4_16·c_4_19·b_1_2 + b_4_16·c_4_18·b_1_2
       + b_4_16·c_4_18·b_1_1 + c_4_19·a_1_0²·b_3_9 + c_4_19·a_1_0²·b_3_7
       + c_4_19·a_1_0²·b_3_6 + c_4_18·a_1_0²·b_3_10 + c_4_18·a_1_0²·b_3_9
       + c_4_18·a_1_0²·b_3_8 + c_4_18·a_1_0²·b_3_6 + c_4_17·a_1_0·a_1_3·b_3_7
       + c_4_17·a_1_0²·b_3_10 + c_4_17·a_1_0²·b_3_9 + c_4_17·a_1_0²·b_3_8
       + c_4_19·a_1_3²·a_3_5 + c_4_18·a_1_3²·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5
       + c_4_17·a_1_3²·a_3_5 + c_4_17·a_1_0²·a_3_5
66. b_1_1³·b_3_8·b_3_10 + b_1_1⁹ + b_6_38·b_1_1³ + b_6_36·b_3_10 + b_4_16·b_5_29
       + c_4_19·b_1_2²·b_3_9 + c_4_19·b_1_2²·b_3_7 + c_4_19·b_1_2⁵ + c_4_19·b_1_1⁵
       + c_4_18·b_1_2²·b_3_7 + c_4_18·b_1_2⁵ + c_4_18·b_1_1²·b_3_10 + c_4_18·b_1_1⁵
       + c_4_17·b_1_2²·b_3_9 + c_4_17·b_1_1⁵ + b_4_16·c_4_19·b_1_2 + b_4_16·c_4_18·b_1_2
       + b_4_16·c_4_17·b_1_2 + b_4_16·c_4_17·b_1_1 + c_4_19·a_1_0²·b_3_6
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_0²·b_3_8 + c_4_18·a_1_0²·b_3_7
       + c_4_18·a_1_0²·b_3_6 + c_4_17·a_1_0²·b_3_9 + c_4_17·a_1_0²·b_3_8
       + c_4_19·a_1_3²·a_3_5 + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_3²·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_3²·a_3_5
       + c_4_17·a_1_0²·a_3_5
67. b_1_2⁹ + b_6_38·b_3_10 + b_6_36·b_3_10 + b_6_36·b_1_2³ + b_4_16·b_1_2²·b_3_9
       + b_4_16·b_1_2⁵ + b_4_16·b_1_1²·b_3_8 + b_4_16·b_1_1⁵ + c_4_19·b_1_2²·b_3_9
       + c_4_19·b_1_2²·b_3_7 + c_4_19·b_1_1²·b_3_10 + c_4_19·b_1_1⁵ + c_4_18·b_1_2²·b_3_9
       + c_4_17·b_1_2²·b_3_7 + c_4_17·b_1_2⁵ + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_18·b_1_2
       + b_4_16·c_4_17·b_1_2 + b_4_16·c_4_17·b_1_1 + c_4_19·a_1_0·a_1_3·b_3_7
       + c_4_19·a_1_0²·b_3_9 + c_4_19·a_1_0²·b_3_7 + c_4_18·a_1_0·a_1_3·b_3_7
       + c_4_18·a_1_0²·b_3_8 + c_4_18·a_1_0²·b_3_6 + c_4_17·a_1_0²·b_3_10
       + c_4_17·a_1_0²·b_3_8 + c_4_17·a_1_0²·b_3_7 + c_4_19·a_1_0·a_1_3·a_3_5
       + c_4_19·a_1_0²·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_0²·a_3_5
       + c_4_17·a_1_3²·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_0²·a_3_5
68. b_6_38·a_3_5 + c_4_19·a_1_0²·b_3_6 + c_4_18·a_1_0²·b_3_7 + c_4_17·a_1_0²·b_3_10
       + c_4_17·a_1_0²·b_3_8 + c_4_17·a_1_0²·b_3_6 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_3²·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_0²·a_3_5
       + c_4_17·a_1_0·a_1_3·a_3_5
69. b_6_38·b_3_6 + b_4_16·b_1_1²·b_3_8 + b_4_16·b_1_1⁵ + c_4_17·b_1_1⁵
       + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_18·b_1_1 + c_4_19·a_1_0²·b_3_9
       + c_4_19·a_1_0²·b_3_8 + c_4_19·a_1_0²·b_3_7 + c_4_19·a_1_0²·b_3_6
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_0²·b_3_9 + c_4_18·a_1_0²·b_3_8
       + c_4_18·a_1_0²·b_3_7 + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_0²·b_3_9
       + c_4_17·a_1_0²·b_3_8 + c_4_17·a_1_0²·b_3_7 + c_4_18·a_1_3²·a_3_5
70. b_6_38·b_3_7 + b_6_38·b_1_2³ + b_6_36·b_1_2³ + b_6_36·b_1_1³
       + b_4_16·b_1_2²·b_3_9 + b_4_16·b_1_2⁵ + b_4_16·b_1_1²·b_3_8 + b_4_16·b_1_1⁵
       + b_4_16²·b_1_2 + c_4_18·b_1_2²·b_3_7 + c_4_18·b_1_2⁵ + c_4_17·b_1_2²·b_3_7
       + b_4_16·c_4_19·b_1_2 + b_4_16·c_4_17·b_1_2 + c_4_19·a_1_0²·b_3_10
       + c_4_19·a_1_0²·b_3_9 + c_4_19·a_1_0²·b_3_7 + c_4_19·a_1_0²·b_3_6
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_0²·b_3_9 + c_4_18·a_1_0²·b_3_8
       + c_4_18·a_1_0²·b_3_7 + c_4_17·a_1_0²·b_3_10 + c_4_17·a_1_0²·b_3_9
       + c_4_17·a_1_0²·b_3_6 + c_4_19·a_1_0²·a_3_5 + c_4_18·a_1_3²·a_3_5
       + c_4_17·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_0²·a_3_5
71. b_1_1⁹ + b_6_38·b_3_8 + b_6_36·b_1_2³ + b_4_16·b_1_2²·b_3_9 + b_4_16·b_1_2⁵
       + b_4_16·b_1_1²·b_3_10 + b_4_16·b_1_1²·b_3_8 + b_4_16·b_1_1⁵ + b_4_16²·b_1_2
       + c_4_19·b_1_1²·b_3_8 + c_4_18·b_1_2²·b_3_7 + c_4_18·b_1_2⁵ + c_4_18·b_1_1²·b_3_8
       + c_4_17·b_1_2²·b_3_7 + c_4_17·b_1_1⁵ + b_4_16·c_4_19·b_1_2 + b_4_16·c_4_19·b_1_1
       + b_4_16·c_4_18·b_1_1 + b_4_16·c_4_17·b_1_2 + c_4_19·a_1_0·a_1_3·b_3_7
       + c_4_19·a_1_0²·b_3_10 + c_4_19·a_1_0²·b_3_8 + c_4_18·a_1_0²·b_3_8
       + c_4_18·a_1_0²·b_3_7 + c_4_18·a_1_0²·b_3_6 + c_4_17·a_1_0·a_1_3·b_3_7
       + c_4_17·a_1_0²·b_3_9 + c_4_17·a_1_0²·b_3_8 + c_4_17·a_1_0²·b_3_7
       + c_4_17·a_1_0²·b_3_6 + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5
       + c_4_17·a_1_3²·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
72. b_1_2⁹ + b_1_1⁹ + b_6_38·b_3_9 + b_6_38·b_1_2³ + b_4_16·b_5_29 + b_4_16²·b_1_2
       + c_4_19·b_1_2⁵ + c_4_19·b_1_1⁵ + c_4_18·b_1_2²·b_3_9 + c_4_18·b_1_1⁵
       + c_4_17·b_1_2²·b_3_9 + c_4_17·b_1_2⁵ + c_4_17·b_1_1⁵ + b_4_16·c_4_19·b_1_1
       + b_4_16·c_4_17·b_1_2 + c_4_19·a_1_0²·b_3_7 + c_4_19·a_1_0²·b_3_6
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_0²·b_3_9 + c_4_18·a_1_0²·b_3_7
       + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_0²·b_3_9 + c_4_17·a_1_0²·b_3_8
       + c_4_17·a_1_0²·b_3_7 + c_4_17·a_1_0²·b_3_6 + c_4_19·a_1_0²·a_3_5
       + c_4_17·a_1_0²·a_3_5
73. b_3_6·b_3_8·b_3_10 + b_1_1⁹ + b_8_67·b_1_2 + b_6_36·b_3_10 + b_6_36·b_1_2³
       + b_4_16·b_1_2²·b_3_9 + b_4_16·b_1_2⁵ + c_4_19·b_1_2²·b_3_9 + c_4_19·b_1_2⁵
       + c_4_19·b_1_1²·b_3_10 + c_4_19·b_1_1²·b_3_8 + c_4_18·b_1_2⁵ + c_4_18·b_1_1²·b_3_8
       + c_4_18·b_1_1⁵ + c_4_17·b_1_2⁵ + c_4_17·b_1_1²·b_3_8 + c_4_17·b_1_1⁵
       + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_18·b_1_1 + b_4_16·c_4_17·b_1_1
       + c_4_19·a_1_0·a_1_3·b_3_7 + c_4_19·a_1_0²·b_3_10 + c_4_19·a_1_0²·b_3_8
       + c_4_19·a_1_0²·b_3_6 + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_0²·b_3_8
       + c_4_18·a_1_0²·b_3_6 + c_4_17·a_1_0²·b_3_10 + c_4_17·a_1_0²·b_3_9
       + c_4_17·a_1_0²·b_3_7 + c_4_17·a_1_0²·b_3_6 + c_4_19·a_1_0·a_1_3·a_3_5
       + c_4_18·a_1_3²·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
74. b_8_67·a_1_0 + c_4_19·a_1_0²·b_3_10 + c_4_19·a_1_0²·b_3_9 + c_4_18·a_1_0·a_1_3·b_3_7
       + c_4_18·a_1_0²·b_3_10 + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_0²·b_3_9
       + c_4_17·a_1_0²·b_3_6 + c_4_18·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_0²·a_3_5
       + c_4_17·a_1_0²·a_3_5
75. b_8_67·a_1_3 + c_4_19·a_1_0·a_1_3·b_3_7 + c_4_19·a_1_0²·b_3_9 + c_4_19·a_1_0²·b_3_7
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_0²·b_3_10 + c_4_18·a_1_0²·b_3_6
       + c_4_17·a_1_0²·b_3_9 + c_4_17·a_1_0²·b_3_8 + c_4_17·a_1_0²·b_3_6
       + c_4_19·a_1_3²·a_3_5 + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_0²·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5
76. b_3_6·b_3_8·b_3_10 + b_1_1⁹ + b_8_67·b_1_1 + b_6_36·b_3_10 + b_6_36·b_1_1³
       + b_4_16·b_5_29 + b_4_16·b_1_1²·b_3_8 + b_4_16·b_1_1⁵ + c_4_19·b_1_2²·b_3_9
       + c_4_19·b_1_2²·b_3_7 + c_4_19·b_1_2⁵ + c_4_19·b_1_1²·b_3_10 + c_4_19·b_1_1²·b_3_8
       + c_4_19·b_1_1⁵ + c_4_18·b_1_2²·b_3_7 + c_4_18·b_1_2⁵ + c_4_18·b_1_1²·b_3_8
       + c_4_17·b_1_2²·b_3_9 + c_4_17·b_1_1²·b_3_8 + c_4_17·b_1_1⁵ + b_4_16·c_4_19·b_1_2
       + b_4_16·c_4_19·b_1_1 + b_4_16·c_4_18·b_1_2 + b_4_16·c_4_18·b_1_1 + b_4_16·c_4_17·b_1_2
       + b_4_16·c_4_17·b_1_1 + c_4_19·a_1_0·a_1_3·b_3_7 + c_4_19·a_1_0²·b_3_10
       + c_4_19·a_1_0²·b_3_9 + c_4_19·a_1_0²·b_3_8 + c_4_19·a_1_0²·b_3_7
       + c_4_18·a_1_0·a_1_3·b_3_7 + c_4_18·a_1_0²·b_3_8 + c_4_18·a_1_0²·b_3_6
       + c_4_17·a_1_0·a_1_3·b_3_7 + c_4_17·a_1_0²·b_3_10 + c_4_17·a_1_0²·b_3_9
       + c_4_19·a_1_0·a_1_3·a_3_5 + c_4_18·a_1_3²·a_3_5 + c_4_18·a_1_0·a_1_3·a_3_5
       + c_4_18·a_1_0²·a_3_5 + c_4_17·a_1_0·a_1_3·a_3_5 + c_4_17·a_1_0²·a_3_5
77. b_6_36·b_1_2⁴ + b_6_36·b_1_1⁴ + b_4_16·b_1_2·b_5_29 + b_4_16·b_1_2³·b_3_9
       + b_4_16·b_1_2³·b_3_7 + b_4_16·b_1_2⁶ + b_4_16·b_1_1³·b_3_10 + b_4_16·b_1_1⁶
       + b_4_16·b_6_36 + b_4_16²·b_1_2² + c_4_17·b_1_2³·b_3_9 + c_4_17·b_1_1³·b_3_10
       + b_4_16·c_4_18·b_1_1² + b_4_16·c_4_17·b_1_2² + c_4_17·a_1_0³·b_3_6
78. b_4_16·b_1_2³·b_3_9 + b_4_16·b_1_2³·b_3_7 + b_4_16·b_1_2⁶ + b_4_16·b_1_1³·b_3_8
       + b_4_16·b_6_38 + c_4_19·b_1_2⁶ + c_4_19·b_1_1⁶ + c_4_17·b_1_2³·b_3_7
       + c_4_17·b_1_2⁶ + c_4_17·b_1_1⁶ + b_4_16·c_4_19·b_1_1² + b_4_16·c_4_18·b_1_2²
       + b_4_16·c_4_17·b_1_2² + c_4_19·a_1_0³·b_3_6 + c_4_18·a_1_0³·b_3_6
79. b_5_29² + b_6_38·b_1_1·b_3_8 + b_6_36·b_1_1·b_3_10 + b_6_36·b_1_1·b_3_8
       + b_6_36·b_1_1⁴ + b_4_16·b_3_8·b_3_10 + b_4_16·b_1_2·b_5_29 + b_4_16·b_1_2³·b_3_9
       + b_4_16·b_1_1³·b_3_10 + b_4_16·b_1_1⁶ + b_4_16²·b_1_2² + c_4_19·b_1_2³·b_3_7
       + c_4_19·b_1_2⁶ + c_4_19·b_1_1³·b_3_8 + c_4_19·b_1_1⁶ + c_4_18·b_1_2³·b_3_7
       + c_4_18·b_1_1³·b_3_10 + c_4_18·b_1_1⁶ + c_4_17·b_1_1⁶ + b_4_16·c_4_18·b_1_1²
       + b_4_16·c_4_17·b_1_2² + c_4_18·a_1_0³·b_3_6 + c_4_17·a_1_0³·b_3_6
       + c_4_19²·b_1_2² + c_4_19²·b_1_1² + c_4_18·c_4_19·b_1_2²
       + c_4_18·c_4_19·b_1_1² + c_4_17·c_4_19·b_1_2² + c_4_17·c_4_19·b_1_1²
       + c_4_17·c_4_18·b_1_2² + c_4_17·c_4_18·b_1_1² + c_4_17²·b_1_2²
       + c_4_17²·b_1_1² + c_4_18²·a_1_3² + c_4_18²·a_1_0² + c_4_17·c_4_19·a_1_3²
       + c_4_17·c_4_19·a_1_0² + c_4_17·c_4_18·a_1_3² + c_4_17²·a_1_3²
       + c_4_17²·a_1_0²
80. b_6_36·b_5_29 + b_6_36·b_1_1²·b_3_8 + b_6_36·b_1_1⁵ + b_4_16·b_1_2⁷
       + b_4_16·b_1_1⁷ + b_4_16·b_6_38·b_1_2 + b_4_16·b_6_38·b_1_1 + b_4_16·b_6_36·b_1_1
       + c_4_19·b_1_2⁷ + c_4_19·b_1_1⁷ + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1
       + c_4_17·b_6_36·b_1_2 + c_4_17·b_6_36·b_1_1 + b_4_16·c_4_19·b_1_2³
       + b_4_16·c_4_19·b_1_1³ + b_4_16·c_4_18·b_3_7 + b_4_16·c_4_18·b_1_2³
       + c_4_19·a_1_3·a_3_5·b_3_6 + c_4_19·a_1_3²·b_5_29 + c_4_19·a_1_0²·b_5_29
       + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_3²·b_5_29 + c_4_18·a_1_0·a_1_3·b_5_29
       + c_4_18·a_1_0²·b_5_29 + c_4_17·a_1_3²·b_5_29 + c_4_19²·b_1_2³ + c_4_19²·b_1_1³
       + c_4_17·c_4_18·b_1_2³ + c_4_18·c_4_19·a_1_0·a_1_3² + c_4_18·c_4_19·a_1_0³
       + c_4_18²·a_1_0³ + c_4_17·c_4_18·a_1_0²·a_1_3 + c_4_17·c_4_18·a_1_0³
       + c_4_17²·a_1_0²·a_1_3 + c_4_17²·a_1_0³
81. b_6_38·b_5_29 + b_6_38·b_1_2²·b_3_9 + b_6_38·b_1_1²·b_3_8 + b_6_36·b_5_29
       + b_6_36·b_1_1²·b_3_8 + b_6_36·b_1_1⁵ + b_4_16·b_1_2⁷ + b_4_16·b_1_1⁷
       + b_4_16·b_6_36·b_1_1 + b_4_16²·b_3_7 + b_4_16²·b_1_2³ + c_4_19·b_1_2⁴·b_3_7
       + c_4_19·b_1_2⁷ + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1 + c_4_18·b_6_36·b_1_2
       + c_4_18·b_6_36·b_1_1 + c_4_17·b_1_2⁷ + c_4_17·b_1_1⁷ + c_4_17·b_6_38·b_1_2
       + c_4_17·b_6_38·b_1_1 + b_4_16·c_4_19·b_3_9 + b_4_16·c_4_18·b_3_9 + b_4_16·c_4_18·b_3_7
       + b_4_16·c_4_18·b_1_2³ + b_4_16·c_4_18·b_1_1³ + b_4_16·c_4_17·b_1_2³
       + c_4_19·a_1_3²·b_5_29 + c_4_19·a_1_0·a_1_3·b_5_29 + c_4_19·a_1_0²·b_5_29
       + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_3²·b_5_29 + c_4_18·a_1_0·a_3_5·b_3_6
       + c_4_18·a_1_0·a_1_3·b_5_29 + c_4_17·a_1_3·a_3_5·b_3_6 + c_4_17·a_1_3²·b_5_29
       + c_4_17·a_1_0·a_3_5·b_3_6 + c_4_17·a_1_0·a_1_3·b_5_29 + c_4_19²·b_1_2³
       + c_4_19²·b_1_1³ + c_4_17·c_4_19·b_1_1³ + c_4_17·c_4_18·b_1_2³
       + c_4_17·c_4_18·b_1_1³ + c_4_18·c_4_19·a_1_0²·a_1_3 + c_4_18²·a_1_0·a_1_3²
       + c_4_17·c_4_19·a_1_0²·a_1_3 + c_4_17·c_4_19·a_1_0³ + c_4_17·c_4_18·a_1_0²·a_1_3
       + c_4_17²·a_1_0·a_1_3²
82. b_8_67·b_3_10 + b_6_36·b_5_29 + b_6_36·b_1_1²·b_3_10 + b_6_36·b_1_1²·b_3_8
       + b_6_36·b_1_1⁵ + b_4_16·b_6_38·b_1_2 + b_4_16²·b_3_9 + c_4_19·b_1_1·b_3_8·b_3_10
       + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1 + c_4_19·b_6_36·b_1_2 + c_4_19·b_6_36·b_1_1
       + c_4_18·b_1_1·b_3_8·b_3_10 + c_4_18·b_6_38·b_1_2 + c_4_18·b_6_38·b_1_1
       + c_4_18·b_6_36·b_1_2 + c_4_17·b_1_2⁴·b_3_7 + c_4_17·b_1_2⁷
       + c_4_17·b_1_1·b_3_8·b_3_10 + c_4_17·b_6_38·b_1_2 + c_4_17·b_6_38·b_1_1
       + c_4_17·b_6_36·b_1_1 + b_4_16·c_4_19·b_3_10 + b_4_16·c_4_19·b_3_8
       + b_4_16·c_4_19·b_1_2³ + b_4_16·c_4_18·b_1_2³ + b_4_16·c_4_18·b_1_1³
       + b_4_16·c_4_17·b_3_10 + b_4_16·c_4_17·b_3_9 + b_4_16·c_4_17·b_3_8
       + b_4_16·c_4_17·b_3_7 + b_4_16·c_4_17·b_1_2³ + c_4_19·a_1_0·a_3_5·b_3_6
       + c_4_19·a_1_0·a_1_3·b_5_29 + c_4_19·a_1_0²·b_5_29 + c_4_18·a_1_3·a_3_5·b_3_6
       + c_4_18·a_1_3²·b_5_29 + c_4_18·a_1_0·a_3_5·b_3_6 + c_4_18·a_1_0²·b_5_29
       + c_4_17·a_1_3·a_3_5·b_3_6 + c_4_17·a_1_0·a_1_3·b_5_29 + c_4_17·a_1_0²·b_5_29
       + c_4_19²·b_1_1³ + c_4_18·c_4_19·b_1_2³ + c_4_18²·b_1_2³
       + c_4_17·c_4_19·b_1_1³ + c_4_17·c_4_18·b_1_2³ + c_4_17·c_4_18·b_1_1³
       + c_4_17²·b_1_2³ + c_4_17²·b_1_1³ + c_4_19²·a_1_0²·a_1_3
       + c_4_18²·a_1_0²·a_1_3 + c_4_18²·a_1_0³ + c_4_17·c_4_19·a_1_0²·a_1_3
       + c_4_17·c_4_19·a_1_0³ + c_4_17·c_4_18·a_1_0·a_1_3² + c_4_17²·a_1_0²·a_1_3
83. b_8_67·a_3_5 + c_4_19·a_1_3·a_3_5·b_3_6 + c_4_19·a_1_0·a_3_5·b_3_6
       + c_4_19·a_1_0·a_1_3·b_5_29 + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_3²·b_5_29
       + c_4_18·a_1_0·a_1_3·b_5_29 + c_4_17·a_1_3·a_3_5·b_3_6 + c_4_17·a_1_3²·b_5_29
       + c_4_17·a_1_0²·b_5_29 + c_4_19²·a_1_0·a_1_3² + c_4_19²·a_1_0³
       + c_4_18·c_4_19·a_1_0³ + c_4_18²·a_1_0²·a_1_3 + c_4_18²·a_1_0³
       + c_4_17·c_4_19·a_1_0·a_1_3² + c_4_17·c_4_19·a_1_0²·a_1_3
       + c_4_17·c_4_18·a_1_0·a_1_3² + c_4_17·c_4_18·a_1_0³
84. b_8_67·b_3_6 + b_6_36·b_5_29 + b_6_36·b_1_1²·b_3_8 + b_6_36·b_1_1⁵ + b_4_16·b_1_2⁷
       + b_4_16·b_1_1·b_3_8·b_3_10 + b_4_16·b_1_1⁷ + b_4_16·b_6_38·b_1_2 + c_4_19·b_1_2⁷
       + c_4_19·b_1_1⁷ + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1
       + c_4_17·b_1_1·b_3_8·b_3_10 + c_4_17·b_6_38·b_1_1 + c_4_17·b_6_36·b_1_2
       + c_4_17·b_6_36·b_1_1 + b_4_16·c_4_19·b_3_10 + b_4_16·c_4_19·b_3_9
       + b_4_16·c_4_19·b_3_8 + b_4_16·c_4_19·b_1_1³ + b_4_16·c_4_18·b_3_10
       + b_4_16·c_4_18·b_3_9 + b_4_16·c_4_18·b_3_8 + b_4_16·c_4_18·b_3_7
       + b_4_16·c_4_18·b_1_1³ + b_4_16·c_4_17·b_3_8 + b_4_16·c_4_17·b_3_7
       + b_4_16·c_4_17·b_1_2³ + b_4_16·c_4_17·b_1_1³ + c_4_19·a_1_3·a_3_5·b_3_6
       + c_4_19·a_1_3²·b_5_29 + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_3²·b_5_29
       + c_4_17·a_1_3·a_3_5·b_3_6 + c_4_17·a_1_0·a_3_5·b_3_6 + c_4_19²·b_1_2³
       + c_4_19²·b_1_1³ + c_4_17·c_4_19·b_1_1³ + c_4_17·c_4_18·b_1_2³
       + c_4_17·c_4_18·b_1_1³ + c_4_17²·b_1_1³ + c_4_19²·a_1_0²·a_1_3
       + c_4_17·c_4_19·a_1_0²·a_1_3 + c_4_17·c_4_19·a_1_0³ + c_4_17·c_4_18·a_1_0·a_1_3²
       + c_4_17·c_4_18·a_1_0³ + c_4_17²·a_1_0³
85. b_8_67·b_3_7 + b_6_38·b_1_1²·b_3_8 + b_6_36·b_1_1²·b_3_10 + b_4_16·b_1_2⁷
       + b_4_16·b_1_1⁷ + b_4_16·b_6_38·b_1_2 + b_4_16·b_6_36·b_1_2 + b_4_16·b_6_36·b_1_1
       + b_4_16²·b_3_9 + b_4_16²·b_3_7 + c_4_19·b_1_2⁴·b_3_7 + c_4_19·b_1_1⁷
       + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_36·b_1_1 + c_4_18·b_1_2⁴·b_3_7 + c_4_18·b_1_1⁷
       + c_4_17·b_1_2⁷ + c_4_17·b_1_1·b_3_8·b_3_10 + c_4_17·b_6_38·b_1_1
       + c_4_17·b_6_36·b_1_2 + b_4_16·c_4_19·b_3_9 + b_4_16·c_4_19·b_3_8 + b_4_16·c_4_19·b_3_7
       + b_4_16·c_4_19·b_1_1³ + b_4_16·c_4_18·b_3_10 + b_4_16·c_4_18·b_3_9
       + b_4_16·c_4_18·b_3_8 + b_4_16·c_4_18·b_3_7 + b_4_16·c_4_17·b_3_10
       + b_4_16·c_4_17·b_3_9 + b_4_16·c_4_17·b_3_8 + b_4_16·c_4_17·b_1_2³
       + b_4_16·c_4_17·b_1_1³ + c_4_19·a_1_0·a_3_5·b_3_6 + c_4_19·a_1_0·a_1_3·b_5_29
       + c_4_18·a_1_3·a_3_5·b_3_6 + c_4_18·a_1_3²·b_5_29 + c_4_18·a_1_0·a_1_3·b_5_29
       + c_4_17·a_1_3²·b_5_29 + c_4_17·a_1_0·a_1_3·b_5_29 + c_4_19²·b_1_2³
       + c_4_17·c_4_18·b_1_2³ + c_4_17²·b_1_1³ + c_4_19²·a_1_0·a_1_3²
       + c_4_18·c_4_19·a_1_0·a_1_3² + c_4_18²·a_1_0·a_1_3² + c_4_18²·a_1_0³
       + c_4_17·c_4_19·a_1_0·a_1_3² + c_4_17·c_4_19·a_1_0²·a_1_3
       + c_4_17·c_4_18·a_1_0·a_1_3² + c_4_17·c_4_18·a_1_0²·a_1_3 + c_4_17²·a_1_0²·a_1_3
       + c_4_17²·a_1_0³
86. b_8_67·b_3_8 + b_6_36·b_1_1²·b_3_8 + b_4_16·b_1_2⁷ + b_4_16·b_6_38·b_1_2
       + b_4_16²·b_3_9 + b_4_16²·b_1_2³ + c_4_19·b_1_2⁷ + c_4_19·b_1_1·b_3_8·b_3_10
       + c_4_19·b_1_1⁷ + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_38·b_1_1 + c_4_19·b_6_36·b_1_1
       + c_4_18·b_1_1·b_3_8·b_3_10 + c_4_18·b_1_1⁷ + c_4_17·b_1_2⁴·b_3_7 + c_4_17·b_1_2⁷
       + c_4_17·b_6_38·b_1_1 + c_4_17·b_6_36·b_1_2 + b_4_16·c_4_19·b_3_10
       + b_4_16·c_4_19·b_3_8 + b_4_16·c_4_19·b_1_2³ + b_4_16·c_4_18·b_3_10
       + b_4_16·c_4_18·b_3_9 + b_4_16·c_4_18·b_3_8 + b_4_16·c_4_18·b_3_7
       + b_4_16·c_4_18·b_1_2³ + b_4_16·c_4_18·b_1_1³ + b_4_16·c_4_17·b_3_10
       + b_4_16·c_4_17·b_3_9 + b_4_16·c_4_17·b_3_7 + b_4_16·c_4_17·b_1_1³
       + c_4_19·a_1_3²·b_5_29 + c_4_19·a_1_0·a_3_5·b_3_6 + c_4_19·a_1_0·a_1_3·b_5_29
       + c_4_18·a_1_3²·b_5_29 + c_4_18·a_1_0·a_3_5·b_3_6 + c_4_18·a_1_0·a_1_3·b_5_29
       + c_4_17·a_1_3²·b_5_29 + c_4_17·a_1_0·a_3_5·b_3_6 + c_4_17·a_1_0·a_1_3·b_5_29
       + c_4_19²·b_1_2³ + c_4_19²·b_1_1³ + c_4_18²·b_1_1³ + c_4_17·c_4_19·b_1_1³
       + c_4_17·c_4_18·b_1_2³ + c_4_19²·a_1_0·a_1_3² + c_4_19²·a_1_0²·a_1_3
       + c_4_18·c_4_19·a_1_0³ + c_4_18²·a_1_0·a_1_3² + c_4_17·c_4_19·a_1_0³
       + c_4_17·c_4_18·a_1_0²·a_1_3 + c_4_17²·a_1_0²·a_1_3
87. b_8_67·b_3_9 + b_6_38·b_1_1²·b_3_8 + b_6_36·b_1_1²·b_3_10 + b_4_16·b_6_38·b_1_2
       + b_4_16·b_6_36·b_1_2 + b_4_16·b_6_36·b_1_1 + b_4_16²·b_3_7 + c_4_19·b_1_2⁴·b_3_7
       + c_4_19·b_1_2⁷ + c_4_19·b_6_38·b_1_2 + c_4_19·b_6_36·b_1_2 + c_4_18·b_1_2⁴·b_3_7
       + c_4_18·b_1_1⁷ + c_4_18·b_6_38·b_1_2 + c_4_18·b_6_38·b_1_1 + c_4_18·b_6_36·b_1_2
       + c_4_18·b_6_36·b_1_1 + c_4_17·b_1_2⁴·b_3_7 + c_4_17·b_1_1·b_3_8·b_3_10
       + c_4_17·b_1_1⁷ + c_4_17·b_6_38·b_1_2 + c_4_17·b_6_36·b_1_1 + b_4_16·c_4_19·b_3_8
       + b_4_16·c_4_19·b_3_7 + b_4_16·c_4_19·b_1_2³ + b_4_16·c_4_19·b_1_1³
       + b_4_16·c_4_18·b_3_10 + b_4_16·c_4_18·b_3_9 + b_4_16·c_4_18·b_3_8
       + b_4_16·c_4_18·b_1_1³ + b_4_16·c_4_17·b_3_10 + b_4_16·c_4_17·b_3_9
       + b_4_16·c_4_17·b_3_8 + b_4_16·c_4_17·b_3_7 + b_4_16·c_4_17·b_1_2³
       + c_4_19·a_1_3·a_3_5·b_3_6 + c_4_19·a_1_0·a_3_5·b_3_6 + c_4_18·a_1_0·a_1_3·b_5_29
       + c_4_17·a_1_3²·b_5_29 + c_4_19²·b_1_1³ + c_4_18·c_4_19·b_1_2³
       + c_4_18·c_4_19·b_1_1³ + c_4_18²·b_1_2³ + c_4_18²·b_1_1³
       + c_4_17·c_4_19·b_1_1³ + c_4_17·c_4_18·b_1_2³ + c_4_17·c_4_18·b_1_1³
       + c_4_17²·b_1_2³ + c_4_17²·b_1_1³ + c_4_19²·a_1_0³ + c_4_18²·a_1_0·a_1_3²
       + c_4_18²·a_1_0²·a_1_3 + c_4_17·c_4_19·a_1_0·a_1_3² + c_4_17·c_4_19·a_1_0²·a_1_3
       + c_4_17·c_4_19·a_1_0³ + c_4_17·c_4_18·a_1_0·a_1_3² + c_4_17²·a_1_0·a_1_3²
       + c_4_17²·a_1_0²·a_1_3 + c_4_17²·a_1_0³
88. b_6_36·b_1_1³·b_3_10 + b_6_36·b_6_38 + b_6_36² + b_4_16·b_1_1²·b_3_8·b_3_10
       + b_4_16·b_1_1⁸ + b_4_16·b_6_38·b_1_2² + b_4_16·b_6_36·b_1_2²
       + b_4_16·b_6_36·b_1_1² + c_4_19·b_6_38·b_1_2² + c_4_19·b_6_38·b_1_1²
       + c_4_19·b_6_36·b_1_1² + c_4_18·b_6_36·b_1_2² + c_4_18·b_6_36·b_1_1²
       + c_4_17·b_1_2⁸ + c_4_17·b_1_1⁸ + c_4_17·b_6_38·b_1_2²
       + b_4_16·c_4_19·b_1_2·b_3_9 + b_4_16·c_4_19·b_1_2·b_3_7 + b_4_16·c_4_18·b_1_1·b_3_10
       + b_4_16·c_4_18·b_1_1⁴ + b_4_16·c_4_17·b_1_2·b_3_7 + b_4_16·c_4_17·b_1_1⁴
       + b_4_16²·c_4_19 + b_4_16²·c_4_18 + b_4_16²·c_4_17 + c_4_19·a_1_0²·a_1_3·b_5_29
       + c_4_19·a_1_0³·b_5_29 + c_4_18·a_1_0²·a_1_3·b_5_29 + c_4_17·a_1_0²·a_1_3·b_5_29
       + c_4_19²·b_1_2⁴ + c_4_19²·b_1_1⁴ + c_4_17·c_4_19·b_1_1⁴ + c_4_17²·b_1_1⁴
89. b_6_36·b_1_1³·b_3_10 + b_6_36·b_1_1³·b_3_8 + b_6_36·b_1_1⁶ + b_6_36²
       + b_4_16·b_1_1²·b_3_8·b_3_10 + b_4_16·b_1_1⁸ + b_4_16·b_6_38·b_1_1²
       + b_4_16·b_6_36·b_1_1² + b_4_16²·b_1_2⁴ + c_4_18·b_6_36·b_1_1² + c_4_17·b_1_1⁸
       + c_4_17·b_6_38·b_1_1² + b_4_16·c_4_18·b_1_2⁴ + b_4_16·c_4_18·b_1_1·b_3_10
       + c_4_18·a_1_0²·a_1_3·b_5_29 + c_4_18·a_1_0³·b_5_29 + c_4_17·a_1_0³·b_5_29
       + c_4_19²·b_1_2⁴ + c_4_19²·b_1_1⁴ + c_4_18·c_4_19·b_1_2⁴
       + c_4_18·c_4_19·b_1_1⁴ + c_4_17·c_4_18·b_1_1⁴ + c_4_17²·b_1_1⁴
90. b_6_38·b_1_2³·b_3_9 + b_6_38·b_1_2⁶ + b_6_38² + b_6_36·b_3_8·b_3_10
       + b_6_36·b_1_1³·b_3_10 + b_6_36·b_1_1⁶ + b_6_36·b_6_38 + b_6_36²
       + b_4_16·b_1_1²·b_3_8·b_3_10 + b_4_16²·b_1_2·b_3_9 + b_4_16²·b_1_2·b_3_7
       + b_4_16²·b_1_2⁴ + c_4_19·b_6_38·b_1_2² + c_4_19·b_6_36·b_1_2²
       + c_4_18·b_1_1²·b_3_8·b_3_10 + c_4_18·b_1_1⁸ + c_4_18·b_6_38·b_1_2²
       + c_4_18·b_6_36·b_1_2² + c_4_17·b_1_2⁸ + c_4_17·b_1_1⁸ + c_4_17·b_6_36·b_1_2²
       + c_4_17·b_6_36·b_1_1² + b_4_16·c_4_19·b_1_2·b_3_9 + b_4_16·c_4_19·b_1_2⁴
       + b_4_16·c_4_19·b_1_1·b_3_8 + b_4_16·c_4_19·b_1_1⁴ + b_4_16·c_4_18·b_1_2⁴
       + b_4_16·c_4_18·b_1_1⁴ + b_4_16·c_4_17·b_1_1·b_3_8 + b_4_16·c_4_17·b_1_1⁴
       + b_4_16²·c_4_19 + c_4_19·a_1_0³·b_5_29 + c_4_17·a_1_0²·a_1_3·b_5_29
       + c_4_17·a_1_0³·b_5_29 + c_4_18·c_4_19·b_1_2⁴ + c_4_18·c_4_19·b_1_1⁴
       + c_4_18²·b_1_1⁴ + c_4_17·c_4_19·b_1_1⁴ + c_4_17²·b_1_1⁴
91. b_6_36·b_1_1³·b_3_10 + b_6_36·b_6_38 + b_6_36² + b_4_16·b_1_1⁸ + b_4_16·b_8_67
       + b_4_16·b_6_36·b_1_2² + b_4_16²·b_1_2·b_3_7 + b_4_16²·b_1_2⁴
       + c_4_19·b_6_36·b_1_1² + c_4_18·b_6_36·b_1_2² + c_4_18·b_6_36·b_1_1²
       + c_4_17·b_1_2⁸ + c_4_17·b_1_1²·b_3_8·b_3_10 + c_4_17·b_1_1⁸
       + c_4_17·b_6_38·b_1_2² + c_4_17·b_6_38·b_1_1² + c_4_17·b_6_36·b_1_2²
       + c_4_17·b_6_36·b_1_1² + b_4_16·c_4_19·b_1_2·b_3_9 + b_4_16·c_4_19·b_1_2·b_3_7
       + b_4_16·c_4_19·b_1_1·b_3_10 + b_4_16·c_4_19·b_1_1·b_3_8 + b_4_16·c_4_18·b_1_2·b_3_7
       + b_4_16·c_4_18·b_1_2⁴ + b_4_16·c_4_18·b_1_1·b_3_8 + b_4_16·c_4_17·b_1_2·b_3_7
       + b_4_16·c_4_17·b_1_1·b_3_8 + b_4_16·c_4_17·b_1_1⁴ + c_4_19·a_1_0²·a_1_3·b_5_29
       + c_4_19·a_1_0³·b_5_29 + c_4_17·a_1_0²·a_1_3·b_5_29 + c_4_17·a_1_0³·b_5_29
       + c_4_19²·b_1_2⁴ + c_4_19²·b_1_1⁴ + c_4_18·c_4_19·b_1_2⁴
       + c_4_18·c_4_19·b_1_1⁴ + c_4_17·c_4_19·b_1_2⁴ + c_4_17·c_4_19·b_1_1⁴
       + c_4_17²·b_1_2⁴ + c_4_17²·b_1_1⁴
92. b_8_67·b_5_29 + b_6_36·b_1_1·b_3_8·b_3_10 + b_4_16·b_6_38·b_3_8 + b_4_16·b_6_36·b_3_8
       + b_4_16·b_6_36·b_1_1³ + b_4_16²·b_5_29 + b_4_16²·b_1_2⁵ + b_4_16³·b_1_2
       + c_4_19·b_6_38·b_3_8 + c_4_19·b_6_36·b_3_10 + c_4_19·b_6_36·b_1_1³
       + c_4_18·b_6_38·b_3_9 + c_4_18·b_6_38·b_1_1³ + c_4_18·b_6_36·b_1_2³
       + c_4_18·b_6_36·b_1_1³ + c_4_17·b_6_38·b_3_9 + c_4_17·b_6_36·b_1_2³
       + b_4_16·c_4_19·b_1_2²·b_3_9 + b_4_16·c_4_19·b_1_2⁵ + b_4_16·c_4_18·b_1_2²·b_3_9
       + b_4_16·c_4_18·b_1_2⁵ + b_4_16·c_4_18·b_1_1²·b_3_8 + b_4_16·c_4_17·b_1_2²·b_3_9
       + b_4_16·c_4_17·b_1_2²·b_3_7 + b_4_16·c_4_17·b_1_2⁵ + b_4_16·c_4_17·b_1_1²·b_3_10
       + b_4_16·c_4_17·b_1_1²·b_3_8 + b_4_16·c_4_17·b_1_1⁵ + b_4_16²·c_4_19·b_1_2
       + b_4_16²·c_4_18·b_1_2 + b_4_16²·c_4_17·b_1_2 + c_4_19²·b_1_2²·b_3_7
       + c_4_19²·b_1_2⁵ + c_4_19²·b_1_1²·b_3_8 + c_4_19²·b_1_1⁵
       + c_4_18·c_4_19·b_1_2²·b_3_9 + c_4_18·c_4_19·b_1_2⁵ + c_4_18·c_4_19·b_1_1²·b_3_10
       + c_4_18·c_4_19·b_1_1²·b_3_8 + c_4_18·c_4_19·b_1_1⁵ + c_4_18²·b_1_2²·b_3_9
       + c_4_18²·b_1_2⁵ + c_4_18²·b_1_1⁵ + c_4_17·c_4_19·b_1_2²·b_3_7
       + c_4_17·c_4_19·b_1_2⁵ + c_4_17·c_4_19·b_1_1⁵ + c_4_17·c_4_18·b_1_2²·b_3_9
       + c_4_17·c_4_18·b_1_2⁵ + c_4_17·c_4_18·b_1_1⁵ + b_4_16·c_4_19²·b_1_2
       + b_4_16·c_4_19²·b_1_1 + b_4_16·c_4_17·c_4_19·b_1_2 + c_4_19²·a_1_0·a_1_3·b_3_7
       + c_4_19²·a_1_0²·b_3_10 + c_4_19²·a_1_0²·b_3_7 + c_4_19²·a_1_0²·b_3_6
       + c_4_18·c_4_19·a_1_0²·b_3_7 + c_4_18²·a_1_0²·b_3_7
       + c_4_17·c_4_19·a_1_0·a_1_3·b_3_7 + c_4_17·c_4_19·a_1_0²·b_3_10
       + c_4_17·c_4_19·a_1_0²·b_3_8 + c_4_17·c_4_19·a_1_0²·b_3_7
       + c_4_17·c_4_18·a_1_0²·b_3_8 + c_4_17·c_4_18·a_1_0²·b_3_6 + c_4_17²·a_1_0²·b_3_10
       + c_4_17²·a_1_0²·b_3_9 + c_4_17²·a_1_0²·b_3_7 + c_4_19²·a_1_3²·a_3_5
       + c_4_18·c_4_19·a_1_0·a_1_3·a_3_5 + c_4_18²·a_1_3²·a_3_5 + c_4_18²·a_1_0²·a_3_5
       + c_4_17·c_4_19·a_1_0·a_1_3·a_3_5 + c_4_17·c_4_18·a_1_3²·a_3_5
       + c_4_17·c_4_18·a_1_0·a_1_3·a_3_5 + c_4_17²·a_1_0²·a_3_5
93. b_6_36·b_1_1²·b_3_8·b_3_10 + b_6_36·b_8_67 + b_6_36·b_6_38·b_1_1²
       + b_6_36²·b_1_1² + b_4_16·b_6_38·b_1_1·b_3_8 + b_4_16·b_6_36·b_1_1·b_3_10
       + b_4_16·b_6_36·b_1_1⁴ + b_4_16²·b_1_2·b_5_29 + b_4_16²·b_1_2³·b_3_7
       + b_4_16²·b_1_2⁶ + b_4_16²·b_6_36 + c_4_19·b_6_36·b_1_1·b_3_10
       + c_4_19·b_6_36·b_1_1·b_3_8 + c_4_18·b_6_36·b_1_1·b_3_10 + c_4_18·b_6_36·b_1_1·b_3_8
       + c_4_18·b_6_36·b_1_1⁴ + c_4_17·b_6_36·b_1_1·b_3_10 + c_4_17·b_6_36·b_1_1·b_3_8
       + b_4_16·c_4_19·b_1_2·b_5_29 + b_4_16·c_4_19·b_6_38 + b_4_16·c_4_19·b_6_36
       + b_4_16·c_4_18·b_3_8·b_3_10 + b_4_16·c_4_18·b_1_2³·b_3_7 + b_4_16·c_4_18·b_1_2⁶
       + b_4_16·c_4_18·b_1_1³·b_3_8 + b_4_16·c_4_18·b_6_38 + b_4_16·c_4_18·b_6_36
       + b_4_16·c_4_17·b_1_2·b_5_29 + b_4_16·c_4_17·b_1_2³·b_3_7 + b_4_16·c_4_17·b_1_2⁶
       + b_4_16·c_4_17·b_1_1⁶ + b_4_16·c_4_17·b_6_36 + b_4_16²·c_4_19·b_1_2²
       + b_4_16²·c_4_18·b_1_2² + c_4_19²·b_1_2³·b_3_9 + c_4_19²·b_1_2⁶
       + c_4_18·c_4_19·b_1_2³·b_3_9 + c_4_18·c_4_19·b_1_2⁶ + c_4_17·c_4_19·b_1_2³·b_3_9
       + c_4_17·c_4_19·b_1_2³·b_3_7 + c_4_17·c_4_19·b_1_2⁶ + c_4_17·c_4_19·b_1_1³·b_3_8
       + c_4_17·c_4_18·b_1_2³·b_3_9 + c_4_17·c_4_18·b_1_2³·b_3_7 + c_4_17·c_4_18·b_1_2⁶
       + c_4_17·c_4_18·b_1_1³·b_3_10 + c_4_17²·b_1_2³·b_3_9 + c_4_17²·b_1_1³·b_3_10
       + c_4_17²·b_1_1³·b_3_8 + b_4_16·c_4_19²·b_1_2² + b_4_16·c_4_19²·b_1_1²
       + b_4_16·c_4_18·c_4_19·b_1_2² + b_4_16·c_4_18²·b_1_2²
       + b_4_16·c_4_17·c_4_19·b_1_1² + b_4_16·c_4_17·c_4_18·b_1_1²
       + b_4_16·c_4_17²·b_1_2² + b_4_16·c_4_17²·b_1_1² + c_4_17·c_4_19·a_1_0³·b_3_6
94. b_6_38·b_8_67 + b_6_36·b_1_1²·b_3_8·b_3_10 + b_4_16·b_6_38·b_1_1·b_3_8
       + b_4_16·b_6_36·b_1_1·b_3_8 + b_4_16·b_6_36·b_1_1⁴ + b_4_16²·b_1_2·b_5_29
       + b_4_16²·b_1_2³·b_3_7 + b_4_16²·b_1_2⁶ + b_4_16²·b_6_36 + c_4_19·b_6_36·b_1_1⁴
       + c_4_18·b_6_38·b_1_2⁴ + c_4_18·b_6_38·b_1_1·b_3_8 + c_4_18·b_6_36·b_1_1·b_3_8
       + c_4_18·b_6_36·b_1_1⁴ + c_4_17·b_6_38·b_1_2⁴ + c_4_17·b_6_38·b_1_1·b_3_8
       + c_4_17·b_6_36·b_1_1⁴ + b_4_16·c_4_19·b_3_8·b_3_10 + b_4_16·c_4_19·b_1_2·b_5_29
       + b_4_16·c_4_19·b_1_2⁶ + b_4_16·c_4_19·b_1_1³·b_3_10 + b_4_16·c_4_19·b_1_1⁶
       + b_4_16·c_4_18·b_1_2·b_5_29 + b_4_16·c_4_18·b_1_2³·b_3_7 + b_4_16·c_4_18·b_1_2⁶
       + b_4_16·c_4_18·b_1_1³·b_3_8 + b_4_16·c_4_18·b_6_38 + b_4_16·c_4_17·b_1_2·b_5_29
       + b_4_16·c_4_17·b_1_1³·b_3_10 + b_4_16·c_4_17·b_1_1⁶ + b_4_16·c_4_17·b_6_38
       + b_4_16·c_4_17·b_6_36 + b_4_16²·c_4_17·b_1_2² + c_4_19²·b_1_2⁶
       + c_4_19²·b_1_1³·b_3_10 + c_4_19²·b_1_1³·b_3_8 + c_4_18·c_4_19·b_1_2³·b_3_7
       + c_4_18·c_4_19·b_1_1³·b_3_8 + c_4_18²·b_1_2³·b_3_7 + c_4_18²·b_1_2⁶
       + c_4_18²·b_1_1³·b_3_10 + c_4_18²·b_1_1³·b_3_8 + c_4_17·c_4_19·b_1_2³·b_3_9
       + c_4_17·c_4_19·b_1_2⁶ + c_4_17·c_4_19·b_1_1⁶ + c_4_17·c_4_18·b_1_2³·b_3_9
       + c_4_17·c_4_18·b_1_2³·b_3_7 + c_4_17·c_4_18·b_1_1⁶ + c_4_17²·b_1_2³·b_3_9
       + c_4_17²·b_1_2³·b_3_7 + c_4_17²·b_1_1³·b_3_10 + b_4_16·c_4_19²·b_1_1²
       + b_4_16·c_4_18²·b_1_1² + b_4_16·c_4_17·c_4_18·b_1_2²
       + b_4_16·c_4_17·c_4_18·b_1_1² + c_4_19²·a_1_0³·b_3_6
       + c_4_18·c_4_19·a_1_0³·b_3_6 + c_4_18²·a_1_0³·b_3_6 + c_4_17·c_4_19·a_1_0³·b_3_6
       + c_4_17²·a_1_0³·b_3_6
95. b_8_67² + b_6_36·b_6_38·b_1_1·b_3_8 + b_6_36²·b_1_1·b_3_10
       + b_4_16·b_6_36·b_3_8·b_3_10 + b_4_16·b_6_36·b_1_1⁶ + b_4_16·b_6_36²
       + b_4_16³·b_1_2⁴ + b_4_16⁴ + c_4_19·b_6_36·b_3_8·b_3_10 + c_4_19·b_6_36·b_1_1⁶
       + c_4_19·b_6_36·b_6_38 + c_4_19·b_6_36² + c_4_18·b_6_36·b_3_8·b_3_10
       + c_4_18·b_6_36·b_1_1⁶ + c_4_18·b_6_36·b_6_38 + c_4_17·b_6_36·b_1_1⁶
       + c_4_17·b_6_36·b_6_38 + c_4_17·b_6_36² + b_4_16·c_4_19·b_6_38·b_1_2²
       + b_4_16·c_4_19·b_6_38·b_1_1² + b_4_16·c_4_18·b_8_67
       + b_4_16·c_4_18·b_6_38·b_1_1² + b_4_16·c_4_18·b_6_36·b_1_2²
       + b_4_16·c_4_17·b_8_67 + b_4_16·c_4_17·b_6_38·b_1_1²
       + b_4_16·c_4_17·b_6_36·b_1_1² + b_4_16²·c_4_19·b_1_2·b_3_7
       + b_4_16²·c_4_19·b_1_2⁴ + b_4_16²·c_4_18·b_1_2·b_3_7 + b_4_16²·c_4_18·b_1_2⁴
       + b_4_16²·c_4_17·b_1_2·b_3_7 + b_4_16²·c_4_17·b_1_2⁴ + b_4_16³·c_4_19
       + b_4_16³·c_4_18 + b_4_16³·c_4_17 + c_4_19²·b_1_1⁸ + c_4_19²·b_6_38·b_1_2²
       + c_4_19²·b_6_38·b_1_1² + c_4_19²·b_6_36·b_1_2²
       + c_4_18·c_4_19·b_1_1²·b_3_8·b_3_10 + c_4_18·c_4_19·b_1_1⁸
       + c_4_18·c_4_19·b_6_36·b_1_1² + c_4_18²·b_1_2⁸ + c_4_18²·b_1_1²·b_3_8·b_3_10
       + c_4_18²·b_1_1⁸ + c_4_18²·b_6_38·b_1_1² + c_4_18²·b_6_36·b_1_2²
       + c_4_17·c_4_19·b_1_2⁸ + c_4_17·c_4_19·b_6_38·b_1_2²
       + c_4_17·c_4_19·b_6_36·b_1_2² + c_4_17·c_4_18·b_1_2⁸
       + c_4_17·c_4_18·b_1_1²·b_3_8·b_3_10 + c_4_17·c_4_18·b_1_1⁸
       + c_4_17·c_4_18·b_6_38·b_1_2² + c_4_17·c_4_18·b_6_38·b_1_1²
       + c_4_17·c_4_18·b_6_36·b_1_2² + c_4_17²·b_1_1²·b_3_8·b_3_10 + c_4_17²·b_1_1⁸
       + c_4_17²·b_6_38·b_1_2² + c_4_17²·b_6_38·b_1_1² + c_4_17²·b_6_36·b_1_2²
       + b_4_16·c_4_19²·b_1_2·b_3_9 + b_4_16·c_4_19²·b_1_1·b_3_8
       + b_4_16·c_4_19²·b_1_1⁴ + b_4_16·c_4_18·c_4_19·b_1_2·b_3_9
       + b_4_16·c_4_18·c_4_19·b_1_2·b_3_7 + b_4_16·c_4_18·c_4_19·b_1_2⁴
       + b_4_16·c_4_18²·b_1_2⁴ + b_4_16·c_4_18²·b_1_1·b_3_10
       + b_4_16·c_4_18²·b_1_1·b_3_8 + b_4_16·c_4_17·c_4_19·b_1_2·b_3_9
       + b_4_16·c_4_17·c_4_19·b_1_1·b_3_10 + b_4_16·c_4_17·c_4_19·b_1_1⁴
       + b_4_16·c_4_17·c_4_18·b_1_2⁴ + b_4_16·c_4_17·c_4_18·b_1_1·b_3_10
       + b_4_16·c_4_17·c_4_18·b_1_1·b_3_8 + b_4_16·c_4_17·c_4_18·b_1_1⁴
       + b_4_16·c_4_17²·b_1_2·b_3_7 + b_4_16·c_4_17²·b_1_2⁴
       + b_4_16·c_4_17²·b_1_1·b_3_10 + b_4_16·c_4_17²·b_1_1·b_3_8 + b_4_16²·c_4_19²
       + b_4_16²·c_4_18² + c_4_18·c_4_19·a_1_0³·b_5_29 + c_4_18²·a_1_0³·b_5_29
       + c_4_17·c_4_19·a_1_0²·a_1_3·b_5_29 + c_4_17·c_4_18·a_1_0²·a_1_3·b_5_29
       + c_4_17·c_4_18·a_1_0³·b_5_29 + c_4_19³·b_1_2⁴ + c_4_18·c_4_19²·b_1_1⁴
       + c_4_17·c_4_19²·b_1_2⁴ + c_4_17·c_4_19²·b_1_1⁴ + c_4_17·c_4_18·c_4_19·b_1_1⁴
       + c_4_17·c_4_18²·b_1_1⁴ + c_4_17²·c_4_18·b_1_2⁴ + c_4_17²·c_4_18·b_1_1⁴
       + c_4_17³·b_1_2⁴ + c_4_17³·b_1_1⁴

About the group

Ring generators

Ring relations

Completion information

Restriction maps

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Data used for Benson′s test

• Benson′s completion test succeeded in degree 16.
• The completion test was perfect: It applied in the last degree in which a generator or relation was found.
• The following is a filter regular homogeneous system of parameters:
  1. c_4_17, a Duflot regular element of degree 4
  2. c_4_18, a Duflot regular element of degree 4
  3. c_4_19, a Duflot regular element of degree 4
  4. b_1_2², an element of degree 2
• The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 8, 10].
• 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. a_1_3 → 0, an element of degree 1
3. b_1_1 → 0, an element of degree 1
4. b_1_2 → 0, an element of degree 1
5. a_3_5 → 0, an element of degree 3
6. b_3_6 → 0, an element of degree 3
7. b_3_7 → 0, an element of degree 3
8. b_3_8 → 0, an element of degree 3
9. b_3_9 → 0, an element of degree 3
10. b_3_10 → 0, an element of degree 3
11. b_4_16 → 0, an element of degree 4
12. c_4_17 → c_1_2⁴, an element of degree 4
13. c_4_18 → c_1_0⁴, an element of degree 4
14. c_4_19 → c_1_2⁴ + c_1_1⁴ + c_1_0⁴, an element of degree 4
15. b_5_29 → 0, an element of degree 5
16. b_6_36 → 0, an element of degree 6
17. b_6_38 → 0, an element of degree 6
18. b_8_67 → 0, an element of degree 8

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

1. a_1_0 → 0, an element of degree 1
2. a_1_3 → 0, an element of degree 1
3. b_1_1 → 0, an element of degree 1
4. b_1_2 → c_1_3, an element of degree 1
5. a_3_5 → 0, an element of degree 3
6. b_3_6 → 0, an element of degree 3
7. b_3_7 → 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
8. b_3_8 → 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
9. b_3_9 → 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, an element of degree 3
10. b_3_10 → 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
11. b_4_16 → c_1_2·c_1_3³ + c_1_2²·c_1_3², an element of degree 4
12. c_4_17 → 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_0²·c_1_3², an element of degree 4
13. c_4_18 → c_1_3⁴ + c_1_0²·c_1_3² + c_1_0⁴, an element of degree 4
14. c_4_19 → c_1_2·c_1_3³ + 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
15. b_5_29 → c_1_3⁵ + c_1_2·c_1_3⁴ + 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
16. b_6_36 → c_1_2·c_1_3⁵ + c_1_2⁴·c_1_3² + c_1_1·c_1_3⁵ + c_1_1⁴·c_1_3² + c_1_0·c_1_3⁵
       + c_1_0·c_1_2·c_1_3⁴ + c_1_0·c_1_2²·c_1_3³ + c_1_0·c_1_1·c_1_3⁴
       + c_1_0·c_1_1²·c_1_3³ + c_1_0²·c_1_3⁴ + c_1_0²·c_1_2·c_1_3³
       + c_1_0²·c_1_2²·c_1_3² + c_1_0²·c_1_1·c_1_3³ + c_1_0²·c_1_1²·c_1_3², an element of degree 6
17. b_6_38 → c_1_3⁶ + c_1_2·c_1_3⁵ + c_1_2⁴·c_1_3² + c_1_1·c_1_2·c_1_3⁴
       + c_1_1·c_1_2²·c_1_3³ + c_1_1²·c_1_2·c_1_3³ + c_1_1²·c_1_2²·c_1_3²
       + c_1_0·c_1_3⁵ + c_1_0·c_1_2·c_1_3⁴ + c_1_0·c_1_2²·c_1_3³
       + c_1_0²·c_1_2·c_1_3³ + c_1_0²·c_1_2²·c_1_3² + c_1_0⁴·c_1_3², an element of degree 6
18. b_8_67 → c_1_3⁸ + c_1_2²·c_1_3⁶ + c_1_2⁴·c_1_3⁴ + c_1_1·c_1_2·c_1_3⁶
       + c_1_1·c_1_2⁴·c_1_3³ + c_1_1²·c_1_3⁶ + c_1_1²·c_1_2·c_1_3⁵
       + c_1_1²·c_1_2⁴·c_1_3² + c_1_1³·c_1_3⁵ + c_1_1⁵·c_1_3³ + c_1_1⁶·c_1_3²
       + c_1_0·c_1_2·c_1_3⁶ + c_1_0·c_1_2²·c_1_3⁵ + c_1_0·c_1_1·c_1_2·c_1_3⁵
       + c_1_0·c_1_1·c_1_2²·c_1_3⁴ + c_1_0·c_1_1²·c_1_3⁵
       + c_1_0·c_1_1²·c_1_2·c_1_3⁴ + c_1_0·c_1_1²·c_1_2²·c_1_3³
       + c_1_0·c_1_1⁴·c_1_3³ + c_1_0²·c_1_2·c_1_3⁵ + c_1_0²·c_1_2²·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2·c_1_3⁴ + c_1_0²·c_1_1·c_1_2²·c_1_3³
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2·c_1_3³
       + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0²·c_1_1⁴·c_1_3², an element of degree 8

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

1. a_1_0 → 0, an element of degree 1
2. a_1_3 → 0, an element of degree 1
3. b_1_1 → c_1_3, an element of degree 1
4. b_1_2 → c_1_3, an element of degree 1
5. a_3_5 → 0, an element of degree 3
6. b_3_6 → c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
7. b_3_7 → c_1_3³ + c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
8. b_3_8 → c_1_3³ + c_1_0·c_1_3² + c_1_0²·c_1_3, an element of degree 3
9. b_3_9 → c_1_3³ + c_1_2·c_1_3² + c_1_2²·c_1_3, an element of degree 3
10. b_3_10 → 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
11. b_4_16 → c_1_2·c_1_3³ + c_1_2²·c_1_3², an element of degree 4
12. c_4_17 → c_1_2²·c_1_3² + c_1_2⁴, an element of degree 4
13. c_4_18 → 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. c_4_19 → c_1_3⁴ + c_1_2²·c_1_3² + c_1_2⁴ + c_1_1·c_1_3³ + c_1_1⁴ + c_1_0²·c_1_3²
       + c_1_0⁴, an element of degree 4
15. b_5_29 → c_1_2·c_1_3⁴ + c_1_2²·c_1_3³ + c_1_0·c_1_3⁴ + c_1_0²·c_1_3³, an element of degree 5
16. b_6_36 → c_1_3⁶ + c_1_1·c_1_2·c_1_3⁴ + c_1_1·c_1_2²·c_1_3³ + c_1_1²·c_1_2·c_1_3³
       + c_1_1²·c_1_2²·c_1_3² + c_1_0·c_1_3⁵ + c_1_0·c_1_2·c_1_3⁴
       + c_1_0·c_1_2²·c_1_3³ + c_1_0²·c_1_2·c_1_3³ + c_1_0²·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_3², an element of degree 6
17. b_6_38 → c_1_3⁶ + c_1_2·c_1_3⁵ + c_1_2⁴·c_1_3² + c_1_1²·c_1_3⁴ + c_1_1⁴·c_1_3², an element of degree 6
18. b_8_67 → c_1_3⁸ + c_1_2·c_1_3⁷ + c_1_2²·c_1_3⁶ + c_1_2³·c_1_3⁵ + c_1_2⁴·c_1_3⁴
       + c_1_2⁵·c_1_3³ + c_1_2⁶·c_1_3² + c_1_1·c_1_3⁷ + c_1_1·c_1_2²·c_1_3⁵
       + c_1_1·c_1_2⁴·c_1_3³ + c_1_1²·c_1_2·c_1_3⁵ + c_1_1²·c_1_2⁴·c_1_3²
       + c_1_1³·c_1_3⁵ + c_1_1⁴·c_1_2·c_1_3³ + c_1_1⁴·c_1_2²·c_1_3²
       + c_1_1⁵·c_1_3³ + c_1_1⁶·c_1_3² + c_1_0·c_1_2·c_1_3⁶ + c_1_0·c_1_2⁴·c_1_3³
       + c_1_0·c_1_1·c_1_2·c_1_3⁵ + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2·c_1_3⁴ + c_1_0·c_1_1²·c_1_2²·c_1_3³ + c_1_0²·c_1_3⁶
       + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_2⁴·c_1_3² + c_1_0²·c_1_1·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2²·c_1_3³ + c_1_0²·c_1_1²·c_1_2·c_1_3³
       + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0⁴·c_1_3⁴ + c_1_0⁴·c_1_2·c_1_3³
       + c_1_0⁴·c_1_2²·c_1_3², an element of degree 8

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128