Mathematics:

Cohomology
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Jena:

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David Green

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Singular

Gap

Mod-2-Cohomology of J3.2, a group of order 100465920

About the group

Ring generators

Ring relations

Completion information

Restriction maps

General information on the group

• J3.2 is a group of order 100465920.
• The group order factors as 2⁸ · 3⁵ · 5 · 17 · 19.
• The group is defined by 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• It is non-abelian.
• It has 2-Rank 4.
• The centre of a Sylow 2-subgroup has rank 1.
• Its Sylow 2-subgroup has 4 conjugacy classes of maximal elementary abelian subgroups, which are of rank 3, 3, 3 and 4, respectively.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 4 and depth 3.
• The depth exceeds the Duflot bound, which is 1.
• The Poincaré series is

  ( − 1)·( − 1  +  t  −  t2  +  t3  −  t4  −  t6  −  t8  +  t9  −  t10  −  t11  −  t14  +  t15  −  t17  +  t19  −  t20  +  t21  +  t22  −  t23  +  t25  +  t28  −  t29  +  t30)

  (1  +  t) · ( − 1  +  t)4 · (1  −  t  +  t2) · (1  +  t2)2 · (1  +  t  +  t2)2 · (1  −  t2  +  t4) · (1  +  t4) · (1  +  t  +  t2  +  t3  +  t4) · (1  −  t  +  t3  −  t4  +  t5  −  t7  +  t8)

• The a-invariants are -∞,-∞,-∞,-4,-4. They were obtained using the filter regular HSOP of the Hilbert-Poincaré test.
• 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

Ring generators

The cohomology ring has 16 minimal generators of maximal degree 15:

1. b_1_0, an element of degree 1
2. b_5_0, an element of degree 5
3. b_6_2, an element of degree 6
4. b_7_0, an element of degree 7
5. c_8_4, a Duflot element of degree 8
6. b_8_3, an element of degree 8
7. b_9_0, an element of degree 9
8. b_10_5, an element of degree 10
9. b_11_4, an element of degree 11
10. b_11_3, an element of degree 11
11. b_12_6, an element of degree 12
12. b_12_0, an element of degree 12
13. b_13_3, an element of degree 13
14. b_14_6, an element of degree 14
15. b_15_9, an element of degree 15
16. b_15_5, an element of degree 15

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Ring relations

There are 74 minimal relations of maximal degree 30:

1. b_1_0⁴·b_5_0 + b_8_3·b_1_0
2. b_1_0·b_9_0 + b_6_2·b_1_0⁴
3. b_5_0² + b_6_2·b_1_0⁴ + c_8_4·b_1_0²
4. b_10_5·b_1_0 + b_6_2·b_5_0
5. b_1_0·b_11_3
6. b_5_0·b_7_0 + b_1_0·b_11_4 + b_6_2·b_1_0⁶ + c_8_4·b_1_0⁴
7. b_6_2·b_7_0 + b_6_2·b_1_0²·b_5_0
8. b_8_3·b_5_0 + b_6_2·b_1_0⁷ + c_8_4·b_1_0⁵
9. b_12_6·b_1_0 + b_6_2·b_1_0²·b_5_0 + b_6_2²·b_1_0
10. b_1_0·b_13_3
11. b_5_0·b_9_0 + b_6_2·b_1_0³·b_5_0
12. b_7_0² + b_12_0·b_1_0² + b_6_2·b_1_0⁸ + c_8_4·b_1_0⁶
13. b_10_5·b_5_0 + b_6_2²·b_1_0³ + b_6_2·c_8_4·b_1_0
14. b_14_6·b_1_0 + b_6_2²·b_1_0³ + b_6_2·c_8_4·b_1_0
15. b_1_0⁴·b_11_4 + b_8_3·b_7_0 + b_6_2·b_1_0⁹ + c_8_4·b_1_0⁷
16. b_1_0·b_15_5
17. b_1_0·b_15_9 + b_6_2·c_8_4·b_1_0²
18. b_5_0·b_11_3
19. b_5_0·b_11_4 + c_8_4·b_1_0·b_7_0 + c_8_4·b_1_0³·b_5_0
20. b_7_0·b_9_0 + b_6_2·b_8_3·b_1_0²
21. b_6_2·b_11_4
22. b_10_5·b_7_0 + b_6_2²·b_1_0⁵ + b_6_2·c_8_4·b_1_0³
23. b_12_6·b_5_0 + b_6_2²·b_5_0 + b_6_2²·b_1_0⁵ + b_6_2·c_8_4·b_1_0³
24. b_5_0·b_13_3
25. b_7_0·b_11_3
26. b_7_0·b_11_4 + b_12_0·b_1_0·b_5_0 + c_8_4·b_1_0³·b_7_0 + b_8_3·c_8_4·b_1_0²
27. b_9_0² + b_8_3·b_10_5 + b_6_2·b_12_6 + b_6_2²·b_1_0·b_5_0 + b_6_2³
       + b_6_2·c_8_4·b_1_0⁴
28. b_6_2·b_12_0·b_1_0
29. b_8_3·b_11_4 + c_8_4·b_1_0⁴·b_7_0 + b_8_3·c_8_4·b_1_0³
30. b_10_5·b_9_0 + b_8_3·b_11_3 + b_6_2·b_13_3 + b_6_2²·b_1_0²·b_5_0
31. b_12_6·b_7_0 + b_6_2²·b_1_0²·b_5_0 + b_6_2²·b_1_0⁷ + b_6_2·c_8_4·b_1_0⁵
32. b_14_6·b_5_0 + b_6_2²·b_1_0²·b_5_0 + b_6_2·c_8_4·b_5_0
33. b_10_5² + b_8_3·b_12_6 + b_6_2·b_14_6 + b_6_2²·b_1_0³·b_5_0 + b_6_2²·b_1_0⁸
       + b_6_2·c_8_4·b_1_0⁶
34. b_5_0·b_15_5
35. b_5_0·b_15_9 + b_6_2·c_8_4·b_1_0·b_5_0
36. b_7_0·b_13_3
37. b_9_0·b_11_3 + b_8_3·b_12_6 + b_6_2·b_14_6 + b_6_2²·b_1_0⁸ + b_6_2²·b_8_3
       + b_6_2³·b_1_0² + b_6_2·c_8_4·b_1_0⁶ + b_6_2²·c_8_4
38. b_9_0·b_11_4
39. b_10_5·b_11_3 + b_8_3·b_13_3 + b_6_2·b_15_9 + b_6_2²·b_9_0 + b_6_2³·b_1_0³
       + b_6_2²·c_8_4·b_1_0
40. b_10_5·b_11_4
41. b_12_6·b_9_0 + b_8_3·b_13_3 + b_6_2·b_15_5 + b_6_2²·b_9_0 + b_6_2²·b_8_3·b_1_0
42. b_14_6·b_7_0 + b_6_2²·b_8_3·b_1_0 + b_6_2·c_8_4·b_1_0²·b_5_0
43. b_10_5·b_12_0 + b_6_2·b_8_3² + b_6_2²·b_1_0¹⁰ + c_8_4·b_14_6
       + b_6_2·c_8_4·b_1_0³·b_5_0 + b_6_2·c_8_4·b_1_0⁸ + b_6_2·b_8_3·c_8_4
       + b_6_2²·c_8_4·b_1_0² + b_6_2·c_8_4²
44. b_7_0·b_15_5
45. b_7_0·b_15_9 + b_6_2·c_8_4·b_1_0³·b_5_0
46. b_9_0·b_13_3 + b_10_5·b_12_6 + b_6_2·b_8_3² + b_6_2²·b_1_0¹⁰ + b_6_2²·b_10_5
       + b_6_2³·b_1_0⁴ + b_6_2·c_8_4·b_1_0³·b_5_0 + b_6_2·c_8_4·b_1_0⁸
       + b_6_2·b_8_3·c_8_4 + b_6_2²·c_8_4·b_1_0²
47. b_11_3² + b_10_5·b_12_6 + b_6_2²·b_10_5 + b_6_2³·b_1_0⁴
       + b_6_2·c_8_4·b_1_0³·b_5_0 + b_6_2·b_8_3·c_8_4 + b_6_2²·c_8_4·b_1_0²
48. b_11_3·b_11_4
49. b_11_4² + c_8_4·b_12_0·b_1_0²
50. b_12_0·b_11_3 + b_8_3·b_15_9 + b_8_3·b_15_5 + b_6_2·b_8_3·b_9_0 + b_6_2²·b_8_3·b_1_0³
       + c_8_4·b_15_5 + b_6_2·b_8_3·c_8_4·b_1_0
51. b_12_6·b_11_3 + b_10_5·b_13_3 + b_6_2·b_8_3·b_9_0 + b_6_2²·b_11_3
       + b_6_2²·b_8_3·b_1_0³ + b_6_2·c_8_4·b_9_0 + b_6_2²·c_8_4·b_1_0³
52. b_12_6·b_11_4
53. b_14_6·b_9_0 + b_10_5·b_13_3 + b_8_3·b_15_9 + b_8_3·b_15_5 + b_6_2³·b_1_0⁵
       + b_6_2·b_8_3·c_8_4·b_1_0 + b_6_2²·c_8_4·b_1_0³
54. b_12_6² + b_10_5·b_14_6 + b_6_2·b_8_3·b_10_5 + b_6_2²·b_12_0 + b_6_2³·b_1_0·b_5_0
       + b_6_2⁴ + b_8_3²·c_8_4 + b_6_2·c_8_4·b_1_0¹⁰ + b_6_2·c_8_4·b_10_5
       + c_8_4²·b_1_0⁸
55. b_9_0·b_15_5 + b_10_5·b_14_6 + b_8_3³ + b_6_2·b_8_3·b_1_0¹⁰ + b_6_2·b_8_3·b_10_5
       + b_6_2²·b_12_0 + b_6_2³·b_1_0·b_5_0 + b_6_2³·b_1_0⁶ + b_8_3·c_8_4·b_1_0⁸
       + b_6_2·c_8_4·b_10_5 + b_6_2²·c_8_4·b_1_0⁴
56. b_9_0·b_15_9 + b_10_5·b_14_6 + b_8_3³ + b_6_2·b_8_3·b_1_0¹⁰ + b_6_2·b_8_3·b_10_5
       + b_6_2²·b_12_6 + b_6_2³·b_1_0⁶ + b_6_2⁴ + b_8_3·c_8_4·b_1_0⁸ + b_8_3²·c_8_4
       + b_6_2·c_8_4·b_1_0¹⁰ + b_6_2·c_8_4·b_10_5 + c_8_4²·b_1_0⁸
57. b_11_3·b_13_3 + b_10_5·b_14_6 + b_6_2³·b_1_0·b_5_0 + b_8_3²·c_8_4
       + b_6_2·c_8_4·b_1_0¹⁰ + b_6_2·c_8_4·b_10_5 + c_8_4²·b_1_0⁸
58. b_11_4·b_13_3
59. b_10_5·b_15_9 + b_10_5·b_15_5 + b_6_2²·b_13_3 + b_8_3·c_8_4·b_9_0 + b_6_2·c_8_4·b_11_3
       + b_6_2·b_8_3·c_8_4·b_1_0³ + b_6_2²·c_8_4·b_5_0
60. b_12_6·b_13_3 + b_10_5·b_15_5 + b_8_3²·b_9_0 + b_6_2²·b_13_3 + b_6_2²·b_1_0¹³
       + b_8_3·c_8_4·b_9_0 + b_6_2·c_8_4·b_1_0¹¹ + b_6_2·b_8_3·c_8_4·b_1_0³
61. b_14_6·b_11_3 + b_10_5·b_15_5 + b_8_3²·b_9_0 + b_6_2²·b_1_0¹³ + b_6_2·c_8_4·b_11_3
       + b_6_2·c_8_4·b_1_0¹¹
62. b_14_6·b_11_4
63. b_11_3·b_15_5 + b_12_6·b_14_6 + b_8_3²·b_10_5 + b_6_2·b_8_3·b_12_0 + b_6_2²·b_14_6
       + b_6_2²·b_8_3·b_1_0⁶ + b_6_2³·b_1_0³·b_5_0 + b_6_2·c_8_4·b_12_6
       + b_6_2·b_8_3·c_8_4·b_1_0⁴ + b_6_2³·c_8_4
64. b_11_3·b_15_9 + b_12_6·b_14_6 + b_8_3²·b_10_5 + b_6_2·b_8_3·b_12_0
       + b_6_2²·b_8_3·b_1_0⁶ + b_6_2³·b_1_0³·b_5_0 + b_6_2⁴·b_1_0²
       + b_8_3·c_8_4·b_10_5 + b_6_2·b_8_3·c_8_4·b_1_0⁴ + b_6_2²·c_8_4·b_1_0·b_5_0
       + b_6_2²·c_8_4·b_1_0⁶ + b_6_2³·c_8_4 + b_6_2·c_8_4²·b_1_0⁴
65. b_11_4·b_15_5
66. b_11_4·b_15_9
67. b_13_3² + b_12_6·b_14_6 + b_6_2·b_8_3·b_12_6 + b_6_2·b_8_3·b_12_0 + b_6_2²·b_14_6
       + b_6_2³·b_1_0³·b_5_0 + b_6_2³·b_1_0⁸ + b_6_2³·b_8_3 + b_8_3·c_8_4·b_10_5
       + b_6_2²·c_8_4·b_1_0·b_5_0 + b_6_2·c_8_4²·b_1_0⁴
68. b_12_6·b_15_9 + b_12_6·b_15_5 + b_6_2·b_12_0·b_9_0 + b_6_2²·b_15_9 + b_8_3·c_8_4·b_11_3
       + b_6_2²·c_8_4·b_1_0²·b_5_0
69. b_14_6·b_13_3 + b_12_6·b_15_5 + b_8_3²·b_11_3 + b_6_2·b_12_0·b_9_0 + b_6_2·b_8_3·b_13_3
       + b_6_2²·b_15_5 + b_6_2·c_8_4·b_13_3
70. b_13_3·b_15_5 + b_14_6² + b_8_3²·b_12_6 + b_8_3²·b_12_0 + b_6_2²·b_8_3·b_1_0⁸
       + b_6_2²·b_8_3² + b_6_2⁴·b_1_0⁴ + c_8_4·b_12_0·b_1_0⁸
       + b_6_2·b_8_3·c_8_4·b_1_0⁶ + b_6_2²·c_8_4²
71. b_13_3·b_15_9 + b_14_6² + b_8_3²·b_12_6 + b_8_3²·b_12_0 + b_6_2·b_10_5·b_12_6
       + b_6_2·b_8_3·b_14_6 + b_6_2²·b_8_3·b_1_0⁸ + b_6_2³·b_1_0¹⁰ + b_6_2³·b_10_5
       + b_6_2³·b_8_3·b_1_0² + c_8_4·b_12_0·b_1_0⁸ + b_8_3·c_8_4·b_12_6
       + b_6_2·c_8_4·b_14_6 + b_6_2·b_8_3·c_8_4·b_1_0⁶ + b_6_2²·c_8_4·b_1_0³·b_5_0
       + b_6_2²·b_8_3·c_8_4 + b_6_2·c_8_4²·b_1_0⁶
72. b_14_6·b_15_9 + b_14_6·b_15_5 + b_8_3·b_12_0·b_9_0 + b_6_2·b_10_5·b_13_3
       + b_6_2·b_8_3·b_15_9 + b_6_2·c_8_4·b_15_9 + b_6_2²·c_8_4·b_9_0
       + b_6_2²·b_8_3·c_8_4·b_1_0
73. b_15_5·b_15_9 + b_15_5² + b_8_3·b_10_5·b_12_6 + b_8_3²·b_14_6 + b_6_2·b_12_0·b_12_6
       + b_6_2·b_10_5·b_14_6 + b_6_2·b_8_3³ + b_6_2²·b_8_3·b_1_0¹⁰ + b_6_2³·b_1_0¹²
       + b_6_2³·b_8_3·b_1_0⁴ + b_6_2⁴·b_1_0·b_5_0 + b_6_2⁴·b_1_0⁶ + b_8_3·c_8_4·b_14_6
       + b_6_2·b_8_3·c_8_4·b_1_0⁸ + b_6_2·b_8_3²·c_8_4 + b_6_2²·c_8_4·b_1_0¹⁰
       + b_6_2²·c_8_4·b_10_5 + b_6_2³·c_8_4·b_1_0⁴ + b_6_2·b_8_3·c_8_4²
74. b_15_9² + b_15_5² + b_6_2·b_12_0·b_12_6 + b_6_2²·b_8_3·b_10_5 + b_6_2³·b_12_6
       + b_6_2³·b_12_0 + b_6_2⁴·b_1_0·b_5_0 + b_6_2⁴·b_1_0⁶ + b_6_2⁵
       + c_8_4·b_10_5·b_12_6 + b_8_3·c_8_4·b_14_6 + b_6_2·b_8_3²·c_8_4
       + b_6_2²·c_8_4·b_1_0¹⁰ + b_6_2²·c_8_4·b_10_5 + b_6_2²·b_8_3·c_8_4·b_1_0²
       + b_6_2·c_8_4²·b_1_0³·b_5_0 + b_6_2·c_8_4²·b_1_0⁸

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Data used for the Hilbert-Poincaré test

• We proved completion in degree 38 using the Hilbert-Poincaré criterion.
• However, the last relation was already found in degree 30 and the last generator in degree 15.
• The following is a filter regular homogeneous system of parameters:
  1. b_1_0³·b_5_0 + b_1_0⁸ + b_8_3 + b_6_2·b_1_0² + c_8_4, an element of degree 8
  2. b_12_6 + b_12_0 + b_6_2·b_1_0·b_5_0 + b_6_2·b_1_0⁶ + c_8_4·b_1_0⁴, an element of degree 12
  3. b_14_6 + b_12_0·b_1_0² + b_6_2·c_8_4, an element of degree 14
  4. b_15_5, an element of degree 15
• A Duflot regular sequence is given by c_8_4.
• The Raw Filter Degree Type of the filter regular HSOP is [-1, -1, -1, 30, 45].
• Modifying the above filter regular HSOP, we obtained the following parameters:
1. b_1_0³·b_5_0 + b_1_0⁸ + b_8_3 + b_6_2·b_1_0² + c_8_4, an element of degree 8
2. b_12_6 + b_12_0 + b_6_2·b_1_0·b_5_0 + b_6_2·b_1_0⁶ + c_8_4·b_1_0⁴, an element of degree 12
3. b_6_2·b_1_0² + c_8_4, an element of degree 8
4. b_15_5, an element of degree 15
• We found that there exists some HSOP over a finite extension field, in degrees 8,12,15,6.

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Restriction maps

Expressing the generators as elements of H^*(Normalizer(J3.2,Centre(SylowSubgroup(J3.2,2))); GF(2))

1. b_1_0 → b_1_0
2. b_5_0 → b_5_0 + b_4_2·b_1_0 + b_2_1²·b_1_0
3. b_6_2 → b_6_4 + b_2_1·b_4_4 + b_2_1·b_4_2
4. b_7_0 → b_7_6 + b_7_0 + b_4_4·b_3_3 + b_4_2·b_3_3 + b_4_2·b_1_0³ + b_2_1²·b_1_0³
5. c_8_4 → b_4_4² + b_4_2·b_4_4 + b_4_2² + b_2_1·b_6_4 + b_2_1²·b_4_2 + b_2_1⁴ + c_8_4
6. b_8_3 → b_8_0 + b_4_4² + b_4_2·b_1_0⁴ + b_4_2·b_4_4 + b_2_1·b_3_3² + b_2_1²·b_1_0⁴
      + b_2_1²·b_4_4 + b_2_1²·b_4_2
7. b_9_0 → b_9_9 + b_3_3³ + b_4_4·b_5_4 + b_2_1·b_7_0 + b_2_1·b_4_4·b_3_3 + b_2_1·b_4_2·b_3_3
8. b_10_5 → b_2_1·b_4_4² + b_2_1·b_4_2·b_4_4 + b_2_1·b_4_2² + b_2_1²·b_1_0·b_5_0
      + b_2_1³·b_4_4 + b_2_1·c_8_4
9. b_11_4 → b_4_2·b_7_6 + b_4_2·b_7_0 + b_4_2·b_1_0²·b_5_0 + b_4_2·b_4_4·b_3_3 + b_4_2²·b_3_3
      + c_8_4·b_3_0
10. b_11_3 → b_4_4²·b_3_3 + b_4_2·b_4_4·b_3_3 + b_4_2²·b_3_3 + b_2_1·b_9_9 + b_2_1·b_3_3³
       + b_2_1²·b_4_4·b_3_3 + b_2_1²·b_4_2·b_3_3 + c_8_4·b_3_3
11. b_12_6 → b_4_2·b_1_0³·b_5_0 + b_4_2·b_8_0 + b_4_2·b_4_4² + b_4_2²·b_4_4
       + b_2_1·b_4_2·b_3_3² + b_2_1·b_4_2·b_6_4 + b_2_1²·b_8_0 + b_2_1²·b_4_4²
       + b_2_1²·b_4_2² + b_2_1³·b_3_3² + b_2_1³·b_1_0·b_5_0 + b_2_1³·b_6_4
       + b_2_1⁴·b_4_4 + b_4_4·c_8_4 + b_2_1·c_8_4·b_1_0² + b_2_1²·c_8_4
12. b_12_0 → b_3_3⁴ + b_4_2·b_4_4² + b_4_2²·b_4_4 + b_2_1²·b_4_4² + b_2_1²·b_4_2·b_4_4
       + b_4_4·c_8_4 + b_4_2·c_8_4
13. b_13_3 → b_4_4·b_9_9 + b_4_4·b_3_3³ + b_4_2·b_9_9 + b_4_2·b_3_3³ + b_4_2·b_4_4·b_5_4
       + b_2_1·b_4_2²·b_3_3 + b_2_1²·b_4_4·b_5_4 + b_2_1³·b_4_4·b_3_3 + c_8_4·b_5_4
       + b_2_1·c_8_4·b_3_3
14. b_14_6 → b_4_2·b_4_4·b_6_4 + b_4_2²·b_3_3² + b_4_2²·b_6_4 + b_2_1·b_4_2·b_8_0
       + b_2_1·b_4_2³ + b_2_1²·b_4_4·b_3_3² + b_2_1²·b_4_4·b_6_4
       + b_2_1²·b_4_2·b_3_3² + b_2_1³·b_8_0 + b_2_1³·b_4_4² + b_2_1³·b_4_2·b_4_4
       + b_2_1³·b_4_2² + b_2_1⁴·b_3_3² + b_2_1⁵·b_4_2 + c_8_4·b_3_3² + b_6_4·c_8_4
       + b_2_1·b_4_4·c_8_4 + b_2_1²·c_8_4·b_1_0² + b_2_1³·c_8_4
15. b_15_9 → b_4_2³·b_3_3 + b_2_1·b_4_4·b_9_9 + b_2_1·b_4_4·b_3_3³ + b_2_1·b_4_4²·b_5_4
       + b_2_1·b_4_2·b_9_9 + b_2_1·b_4_2·b_3_3³ + b_2_1·b_4_2·b_4_4·b_5_4
       + b_2_1·b_4_2²·b_5_4 + b_2_1²·b_4_2·b_7_0 + b_2_1³·b_9_9 + b_2_1³·b_3_3³
       + b_2_1³·b_4_4·b_5_4 + b_2_1⁴·b_7_0 + b_2_1⁴·b_4_4·b_3_3 + b_2_1⁴·b_4_2·b_3_3
       + c_8_4·b_7_6 + b_4_2·c_8_4·b_3_3 + b_2_1·c_8_4·b_5_0 + b_2_1³·c_8_4·b_1_0
16. b_15_5 → b_4_2·b_4_4·b_7_0 + b_2_1·b_4_2·b_4_4·b_5_4 + b_2_1·b_4_2²·b_5_4
       + b_2_1²·b_4_2·b_7_0 + b_2_1²·b_4_2²·b_3_3 + b_4_2·c_8_4·b_3_3

Restriction map to the greatest el. ab. subgp. in the centre of a Sylow subgroup, which is of rank 1

1. b_1_0 → 0, an element of degree 1
2. b_5_0 → 0, an element of degree 5
3. b_6_2 → 0, an element of degree 6
4. b_7_0 → 0, an element of degree 7
5. c_8_4 → c_1_0⁸, an element of degree 8
6. b_8_3 → 0, an element of degree 8
7. b_9_0 → 0, an element of degree 9
8. b_10_5 → 0, an element of degree 10
9. b_11_4 → 0, an element of degree 11
10. b_11_3 → 0, an element of degree 11
11. b_12_6 → 0, an element of degree 12
12. b_12_0 → 0, an element of degree 12
13. b_13_3 → 0, an element of degree 13
14. b_14_6 → 0, an element of degree 14
15. b_15_9 → 0, an element of degree 15
16. b_15_5 → 0, an element of degree 15

Restriction map to a maximal el. ab. subgp. of rank 3 in a Sylow subgroup

1. b_1_0 → c_1_2, an element of degree 1
2. b_5_0 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2 + c_1_0·c_1_1·c_1_2³ + c_1_0·c_1_1²·c_1_2²
      + c_1_0²·c_1_2³ + c_1_0²·c_1_1·c_1_2² + c_1_0²·c_1_1²·c_1_2 + c_1_0⁴·c_1_2, an element of degree 5
3. b_6_2 → 0, an element of degree 6
4. b_7_0 → c_1_1²·c_1_2⁵ + c_1_1⁴·c_1_2³ + c_1_0·c_1_1·c_1_2⁵ + c_1_0·c_1_1⁴·c_1_2²
      + c_1_0²·c_1_2⁵ + c_1_0²·c_1_1²·c_1_2³ + c_1_0²·c_1_1⁴·c_1_2
      + c_1_0⁴·c_1_2³ + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
5. c_8_4 → c_1_1⁴·c_1_2⁴ + c_1_1⁸ + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2²
      + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1²·c_1_2² + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8
6. b_8_3 → c_1_1²·c_1_2⁶ + c_1_1⁴·c_1_2⁴ + c_1_0·c_1_1·c_1_2⁶ + c_1_0·c_1_1²·c_1_2⁵
      + c_1_0²·c_1_2⁶ + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1²·c_1_2⁴
      + c_1_0⁴·c_1_2⁴, an element of degree 8
7. b_9_0 → 0, an element of degree 9
8. b_10_5 → 0, an element of degree 10
9. b_11_4 → c_1_0·c_1_1⁴·c_1_2⁶ + c_1_0·c_1_1⁸·c_1_2² + c_1_0²·c_1_1⁴·c_1_2⁵
      + c_1_0²·c_1_1⁸·c_1_2 + c_1_0⁴·c_1_1·c_1_2⁶ + c_1_0⁴·c_1_1²·c_1_2⁵
      + c_1_0⁸·c_1_1·c_1_2² + c_1_0⁸·c_1_1²·c_1_2, an element of degree 11
10. b_11_3 → 0, an element of degree 11
11. b_12_6 → 0, an element of degree 12
12. b_12_0 → c_1_0²·c_1_1⁴·c_1_2⁶ + c_1_0²·c_1_1⁸·c_1_2² + c_1_0⁴·c_1_1²·c_1_2⁶
       + c_1_0⁴·c_1_1⁸ + c_1_0⁸·c_1_1²·c_1_2² + c_1_0⁸·c_1_1⁴, an element of degree 12
13. b_13_3 → 0, an element of degree 13
14. b_14_6 → 0, an element of degree 14
15. b_15_9 → 0, an element of degree 15
16. b_15_5 → 0, an element of degree 15

Restriction map to a maximal el. ab. subgp. of rank 3 in a Sylow subgroup

1. b_1_0 → c_1_2, an element of degree 1
2. b_5_0 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2 + c_1_0·c_1_1·c_1_2³ + c_1_0·c_1_1²·c_1_2²
      + c_1_0²·c_1_2³ + c_1_0²·c_1_1·c_1_2² + c_1_0²·c_1_1²·c_1_2 + c_1_0⁴·c_1_2, an element of degree 5
3. b_6_2 → c_1_0·c_1_1²·c_1_2³ + c_1_0·c_1_1⁴·c_1_2 + c_1_0²·c_1_1·c_1_2³
      + c_1_0²·c_1_1⁴ + c_1_0⁴·c_1_1·c_1_2 + c_1_0⁴·c_1_1², an element of degree 6
4. b_7_0 → c_1_1²·c_1_2⁵ + c_1_1⁴·c_1_2³ + c_1_0·c_1_1·c_1_2⁵ + c_1_0·c_1_1²·c_1_2⁴
      + c_1_0²·c_1_2⁵ + c_1_0²·c_1_1·c_1_2⁴ + c_1_0²·c_1_1²·c_1_2³
      + c_1_0⁴·c_1_2³, an element of degree 7
5. c_8_4 → c_1_1⁴·c_1_2⁴ + c_1_1⁸ + c_1_0·c_1_1²·c_1_2⁵ + c_1_0·c_1_1⁴·c_1_2³
      + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0⁴·c_1_2⁴
      + c_1_0⁴·c_1_1·c_1_2³ + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8
6. b_8_3 → c_1_1²·c_1_2⁶ + c_1_1⁴·c_1_2⁴ + c_1_0·c_1_1·c_1_2⁶ + c_1_0·c_1_1²·c_1_2⁵
      + c_1_0²·c_1_2⁶ + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1²·c_1_2⁴
      + c_1_0⁴·c_1_2⁴, an element of degree 8
7. b_9_0 → c_1_0·c_1_1²·c_1_2⁶ + c_1_0·c_1_1⁴·c_1_2⁴ + c_1_0²·c_1_1·c_1_2⁶
      + c_1_0²·c_1_1⁴·c_1_2³ + c_1_0⁴·c_1_1·c_1_2⁴ + c_1_0⁴·c_1_1²·c_1_2³, an element of degree 9
8. b_10_5 → c_1_0·c_1_1⁴·c_1_2⁵ + c_1_0·c_1_1⁸·c_1_2 + c_1_0²·c_1_1⁴·c_1_2⁴
      + c_1_0²·c_1_1⁸ + c_1_0⁴·c_1_1·c_1_2⁵ + c_1_0⁴·c_1_1²·c_1_2⁴
      + c_1_0⁸·c_1_1·c_1_2 + c_1_0⁸·c_1_1², an element of degree 10
9. b_11_4 → 0, an element of degree 11
10. b_11_3 → 0, an element of degree 11
11. b_12_6 → c_1_0·c_1_1⁴·c_1_2⁷ + c_1_0·c_1_1⁸·c_1_2³ + c_1_0⁴·c_1_1·c_1_2⁷
       + c_1_0⁴·c_1_1⁸ + c_1_0⁸·c_1_1·c_1_2³ + c_1_0⁸·c_1_1⁴, an element of degree 12
12. b_12_0 → 0, an element of degree 12
13. b_13_3 → 0, an element of degree 13
14. b_14_6 → c_1_0·c_1_1⁶·c_1_2⁷ + c_1_0·c_1_1⁸·c_1_2⁵ + c_1_0·c_1_1¹⁰·c_1_2³
       + c_1_0·c_1_1¹²·c_1_2 + c_1_0²·c_1_1⁵·c_1_2⁷ + c_1_0²·c_1_1⁸·c_1_2⁴
       + c_1_0²·c_1_1⁹·c_1_2³ + c_1_0²·c_1_1¹² + c_1_0³·c_1_1⁴·c_1_2⁷
       + c_1_0³·c_1_1⁸·c_1_2³ + c_1_0⁴·c_1_1³·c_1_2⁷ + c_1_0⁴·c_1_1⁸·c_1_2²
       + c_1_0⁴·c_1_1⁹·c_1_2 + c_1_0⁴·c_1_1¹⁰ + c_1_0⁵·c_1_1²·c_1_2⁷
       + c_1_0⁵·c_1_1⁸·c_1_2 + c_1_0⁶·c_1_1·c_1_2⁷ + c_1_0⁶·c_1_1⁸
       + c_1_0⁸·c_1_1·c_1_2⁵ + c_1_0⁸·c_1_1²·c_1_2⁴ + c_1_0⁸·c_1_1³·c_1_2³
       + c_1_0⁸·c_1_1⁴·c_1_2² + c_1_0⁸·c_1_1⁵·c_1_2 + c_1_0⁸·c_1_1⁶
       + c_1_0⁹·c_1_1²·c_1_2³ + c_1_0⁹·c_1_1⁴·c_1_2 + c_1_0¹⁰·c_1_1·c_1_2³
       + c_1_0¹⁰·c_1_1⁴ + c_1_0¹²·c_1_1·c_1_2 + c_1_0¹²·c_1_1², an element of degree 14
15. b_15_9 → c_1_0·c_1_1⁶·c_1_2⁸ + c_1_0·c_1_1⁸·c_1_2⁶ + c_1_0·c_1_1¹⁰·c_1_2⁴
       + c_1_0·c_1_1¹²·c_1_2² + c_1_0²·c_1_1⁴·c_1_2⁹ + c_1_0²·c_1_1⁵·c_1_2⁸
       + c_1_0²·c_1_1⁹·c_1_2⁴ + c_1_0²·c_1_1¹²·c_1_2 + c_1_0³·c_1_1⁴·c_1_2⁸
       + c_1_0³·c_1_1⁸·c_1_2⁴ + c_1_0⁴·c_1_1²·c_1_2⁹ + c_1_0⁴·c_1_1³·c_1_2⁸
       + c_1_0⁴·c_1_1⁹·c_1_2² + c_1_0⁴·c_1_1¹⁰·c_1_2 + c_1_0⁵·c_1_1²·c_1_2⁸
       + c_1_0⁵·c_1_1⁸·c_1_2² + c_1_0⁶·c_1_1·c_1_2⁸ + c_1_0⁶·c_1_1⁸·c_1_2
       + c_1_0⁸·c_1_1·c_1_2⁶ + c_1_0⁸·c_1_1³·c_1_2⁴ + c_1_0⁸·c_1_1⁵·c_1_2²
       + c_1_0⁸·c_1_1⁶·c_1_2 + c_1_0⁹·c_1_1²·c_1_2⁴ + c_1_0⁹·c_1_1⁴·c_1_2²
       + c_1_0¹⁰·c_1_1·c_1_2⁴ + c_1_0¹⁰·c_1_1⁴·c_1_2 + c_1_0¹²·c_1_1·c_1_2²
       + c_1_0¹²·c_1_1²·c_1_2, an element of degree 15
16. b_15_5 → 0, an element of degree 15

Restriction map to a maximal el. ab. subgp. of rank 3 in a Sylow subgroup

1. b_1_0 → c_1_2, an element of degree 1
2. b_5_0 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2 + c_1_0·c_1_1·c_1_2³ + c_1_0·c_1_1²·c_1_2²
      + c_1_0²·c_1_2³ + c_1_0²·c_1_1·c_1_2² + c_1_0²·c_1_1²·c_1_2 + c_1_0⁴·c_1_2, an element of degree 5
3. b_6_2 → 0, an element of degree 6
4. b_7_0 → c_1_1²·c_1_2⁵ + c_1_1⁴·c_1_2³ + c_1_0·c_1_1·c_1_2⁵ + c_1_0·c_1_1⁴·c_1_2²
      + c_1_0²·c_1_2⁵ + c_1_0²·c_1_1²·c_1_2³ + c_1_0²·c_1_1⁴·c_1_2
      + c_1_0⁴·c_1_2³ + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_2, an element of degree 7
5. c_8_4 → c_1_1⁴·c_1_2⁴ + c_1_1⁸ + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2²
      + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1²·c_1_2² + c_1_0⁴·c_1_1⁴ + c_1_0⁸, an element of degree 8
6. b_8_3 → c_1_1²·c_1_2⁶ + c_1_1⁴·c_1_2⁴ + c_1_0·c_1_1·c_1_2⁶ + c_1_0·c_1_1²·c_1_2⁵
      + c_1_0²·c_1_2⁶ + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1²·c_1_2⁴
      + c_1_0⁴·c_1_2⁴, an element of degree 8
7. b_9_0 → 0, an element of degree 9
8. b_10_5 → 0, an element of degree 10
9. b_11_4 → c_1_0·c_1_1⁴·c_1_2⁶ + c_1_0·c_1_1⁸·c_1_2² + c_1_0²·c_1_1⁴·c_1_2⁵
      + c_1_0²·c_1_1⁸·c_1_2 + c_1_0⁴·c_1_1·c_1_2⁶ + c_1_0⁴·c_1_1²·c_1_2⁵
      + c_1_0⁸·c_1_1·c_1_2² + c_1_0⁸·c_1_1²·c_1_2, an element of degree 11
10. b_11_3 → 0, an element of degree 11
11. b_12_6 → 0, an element of degree 12
12. b_12_0 → c_1_0²·c_1_1⁴·c_1_2⁶ + c_1_0²·c_1_1⁸·c_1_2² + c_1_0⁴·c_1_1²·c_1_2⁶
       + c_1_0⁴·c_1_1⁸ + c_1_0⁸·c_1_1²·c_1_2² + c_1_0⁸·c_1_1⁴, an element of degree 12
13. b_13_3 → 0, an element of degree 13
14. b_14_6 → 0, an element of degree 14
15. b_15_9 → 0, an element of degree 15
16. b_15_5 → 0, an element of degree 15

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

1. b_1_0 → 0, an element of degree 1
2. b_5_0 → 0, an element of degree 5
3. b_6_2 → c_1_2²·c_1_3⁴ + 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_1·c_1_2³·c_1_3² + c_1_1·c_1_2⁴·c_1_3 + c_1_1²·c_1_3⁴
      + c_1_1²·c_1_2·c_1_3³ + c_1_1²·c_1_2²·c_1_3² + c_1_1²·c_1_2³·c_1_3
      + c_1_1²·c_1_2⁴ + c_1_1³·c_1_2·c_1_3² + c_1_1³·c_1_2²·c_1_3 + c_1_1⁴·c_1_3²
      + c_1_1⁴·c_1_2·c_1_3 + c_1_1⁴·c_1_2² + c_1_0·c_1_2³·c_1_3² + c_1_0·c_1_2⁴·c_1_3
      + c_1_0·c_1_1·c_1_3⁴ + c_1_0·c_1_1·c_1_2²·c_1_3² + c_1_0·c_1_1·c_1_2⁴
      + c_1_0·c_1_1²·c_1_3³ + c_1_0·c_1_1²·c_1_2·c_1_3² + c_1_0·c_1_1²·c_1_2³
      + c_1_0²·c_1_3⁴ + c_1_0²·c_1_2³·c_1_3 + c_1_0²·c_1_2⁴ + c_1_0²·c_1_1·c_1_3³
      + c_1_0²·c_1_1·c_1_2²·c_1_3 + c_1_0²·c_1_1·c_1_2³ + c_1_0²·c_1_1²·c_1_3²
      + c_1_0²·c_1_1²·c_1_2·c_1_3 + c_1_0²·c_1_1²·c_1_2² + c_1_0³·c_1_2·c_1_3²
      + c_1_0³·c_1_2²·c_1_3 + c_1_0⁴·c_1_3² + c_1_0⁴·c_1_2·c_1_3 + c_1_0⁴·c_1_2², an element of degree 6
4. b_7_0 → 0, an element of degree 7
5. c_8_4 → c_1_3⁸ + c_1_2⁴·c_1_3⁴ + c_1_2⁸ + c_1_1·c_1_2²·c_1_3⁵ + c_1_1·c_1_2³·c_1_3⁴
      + c_1_1·c_1_2⁴·c_1_3³ + c_1_1·c_1_2⁵·c_1_3² + c_1_1²·c_1_2·c_1_3⁵
      + c_1_1²·c_1_2²·c_1_3⁴ + c_1_1²·c_1_2⁴·c_1_3² + c_1_1²·c_1_2⁵·c_1_3
      + c_1_1³·c_1_2·c_1_3⁴ + c_1_1³·c_1_2⁴·c_1_3 + c_1_1⁴·c_1_3⁴
      + c_1_1⁴·c_1_2·c_1_3³ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁴·c_1_2³·c_1_3
      + c_1_1⁴·c_1_2⁴ + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁸
      + c_1_0·c_1_2³·c_1_3⁴ + c_1_0·c_1_2⁵·c_1_3² + c_1_0·c_1_1²·c_1_3⁵
      + c_1_0·c_1_1²·c_1_2⁴·c_1_3 + c_1_0·c_1_1²·c_1_2⁵ + c_1_0·c_1_1⁴·c_1_3³
      + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0·c_1_1⁴·c_1_2³ + c_1_0²·c_1_2²·c_1_3⁴
      + c_1_0²·c_1_2⁵·c_1_3 + c_1_0²·c_1_1·c_1_3⁵ + c_1_0²·c_1_1·c_1_2·c_1_3⁴
      + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1²·c_1_3⁴
      + c_1_0²·c_1_1²·c_1_2²·c_1_3² + c_1_0²·c_1_1²·c_1_2⁴
      + c_1_0³·c_1_2·c_1_3⁴ + c_1_0³·c_1_2⁴·c_1_3 + c_1_0⁴·c_1_3⁴
      + c_1_0⁴·c_1_2³·c_1_3 + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_3³
      + c_1_0⁴·c_1_1·c_1_2·c_1_3² + c_1_0⁴·c_1_1·c_1_2³ + c_1_0⁴·c_1_1⁴
      + c_1_0⁵·c_1_2·c_1_3² + c_1_0⁵·c_1_2²·c_1_3 + c_1_0⁸, an element of degree 8
6. b_8_3 → c_1_1·c_1_2²·c_1_3⁵ + c_1_1·c_1_2³·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3³
      + c_1_1·c_1_2⁵·c_1_3² + c_1_1²·c_1_2·c_1_3⁵ + c_1_1²·c_1_2⁵·c_1_3
      + c_1_1³·c_1_2·c_1_3⁴ + c_1_1³·c_1_2⁴·c_1_3 + c_1_1⁴·c_1_2·c_1_3³
      + c_1_1⁴·c_1_2³·c_1_3 + c_1_1⁵·c_1_2·c_1_3² + c_1_1⁵·c_1_2²·c_1_3
      + c_1_0·c_1_2³·c_1_3⁴ + c_1_0·c_1_2⁵·c_1_3² + c_1_0·c_1_1·c_1_2²·c_1_3⁴
      + c_1_0·c_1_1·c_1_2⁴·c_1_3² + 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_2⁵ + c_1_0·c_1_1⁴·c_1_3³
      + c_1_0·c_1_1⁴·c_1_2·c_1_3² + c_1_0·c_1_1⁴·c_1_2³ + c_1_0²·c_1_2⁴·c_1_3²
      + c_1_0²·c_1_2⁵·c_1_3 + c_1_0²·c_1_1·c_1_3⁵ + c_1_0²·c_1_1·c_1_2⁴·c_1_3
      + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1⁴·c_1_3² + c_1_0²·c_1_1⁴·c_1_2·c_1_3
      + c_1_0²·c_1_1⁴·c_1_2² + c_1_0³·c_1_2·c_1_3⁴ + c_1_0³·c_1_2⁴·c_1_3
      + c_1_0⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_2³·c_1_3 + c_1_0⁴·c_1_1·c_1_3³
      + c_1_0⁴·c_1_1·c_1_2²·c_1_3 + c_1_0⁴·c_1_1·c_1_2³ + c_1_0⁴·c_1_1²·c_1_3²
      + c_1_0⁴·c_1_1²·c_1_2·c_1_3 + c_1_0⁴·c_1_1²·c_1_2² + c_1_0⁵·c_1_2·c_1_3²
      + c_1_0⁵·c_1_2²·c_1_3, an element of degree 8
7. b_9_0 → c_1_1·c_1_2²·c_1_3⁶ + c_1_1·c_1_2⁶·c_1_3² + c_1_1²·c_1_2·c_1_3⁶
      + c_1_1²·c_1_2³·c_1_3⁴ + c_1_1²·c_1_2⁴·c_1_3³ + c_1_1²·c_1_2⁶·c_1_3
      + c_1_1³·c_1_2²·c_1_3⁴ + c_1_1³·c_1_2⁴·c_1_3² + c_1_1⁴·c_1_2²·c_1_3³
      + c_1_1⁴·c_1_2³·c_1_3² + c_1_1⁶·c_1_2·c_1_3² + c_1_1⁶·c_1_2²·c_1_3
      + c_1_0·c_1_2⁴·c_1_3⁴ + c_1_0·c_1_2⁶·c_1_3² + c_1_0·c_1_1²·c_1_3⁶
      + c_1_0·c_1_1²·c_1_2⁴·c_1_3² + c_1_0·c_1_1²·c_1_2⁶ + c_1_0·c_1_1⁴·c_1_3⁴
      + c_1_0·c_1_1⁴·c_1_2²·c_1_3² + c_1_0·c_1_1⁴·c_1_2⁴ + c_1_0²·c_1_2³·c_1_3⁴
      + c_1_0²·c_1_2⁶·c_1_3 + c_1_0²·c_1_1·c_1_3⁶ + c_1_0²·c_1_1·c_1_2²·c_1_3⁴
      + c_1_0²·c_1_1·c_1_2⁶ + c_1_0²·c_1_1²·c_1_2·c_1_3⁴
      + c_1_0²·c_1_1²·c_1_2⁴·c_1_3 + c_1_0²·c_1_1⁴·c_1_3³
      + c_1_0²·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_1⁴·c_1_2³ + c_1_0³·c_1_2²·c_1_3⁴
      + c_1_0³·c_1_2⁴·c_1_3² + c_1_0⁴·c_1_2·c_1_3⁴ + c_1_0⁴·c_1_2³·c_1_3²
      + c_1_0⁴·c_1_1·c_1_3⁴ + c_1_0⁴·c_1_1·c_1_2²·c_1_3² + c_1_0⁴·c_1_1·c_1_2⁴
      + c_1_0⁴·c_1_1²·c_1_3³ + c_1_0⁴·c_1_1²·c_1_2·c_1_3²
      + c_1_0⁴·c_1_1²·c_1_2³ + c_1_0⁶·c_1_2·c_1_3² + c_1_0⁶·c_1_2²·c_1_3, an element of degree 9
8. b_10_5 → c_1_2²·c_1_3⁸ + c_1_2⁸·c_1_3² + c_1_1·c_1_2·c_1_3⁸ + c_1_1·c_1_2⁴·c_1_3⁵
      + c_1_1·c_1_2⁵·c_1_3⁴ + c_1_1·c_1_2⁸·c_1_3 + c_1_1²·c_1_3⁸
      + c_1_1²·c_1_2⁴·c_1_3⁴ + c_1_1²·c_1_2⁸ + c_1_1⁴·c_1_2·c_1_3⁵
      + c_1_1⁴·c_1_2²·c_1_3⁴ + c_1_1⁴·c_1_2⁴·c_1_3² + c_1_1⁴·c_1_2⁵·c_1_3
      + c_1_1⁵·c_1_2·c_1_3⁴ + c_1_1⁵·c_1_2⁴·c_1_3 + c_1_1⁸·c_1_3²
      + c_1_1⁸·c_1_2·c_1_3 + c_1_1⁸·c_1_2² + c_1_0·c_1_2⁵·c_1_3⁴ + c_1_0·c_1_2⁸·c_1_3
      + c_1_0·c_1_1·c_1_3⁸ + c_1_0·c_1_1·c_1_2⁴·c_1_3⁴ + c_1_0·c_1_1·c_1_2⁸
      + c_1_0·c_1_1⁴·c_1_3⁵ + c_1_0·c_1_1⁴·c_1_2·c_1_3⁴ + c_1_0·c_1_1⁴·c_1_2⁵
      + c_1_0²·c_1_3⁸ + c_1_0²·c_1_2⁴·c_1_3⁴ + c_1_0²·c_1_2⁸
      + c_1_0⁴·c_1_2²·c_1_3⁴ + c_1_0⁴·c_1_2⁵·c_1_3 + c_1_0⁴·c_1_1·c_1_3⁵
      + c_1_0⁴·c_1_1·c_1_2⁴·c_1_3 + c_1_0⁴·c_1_1·c_1_2⁵ + c_1_0⁴·c_1_1⁴·c_1_3²
      + c_1_0⁴·c_1_1⁴·c_1_2·c_1_3 + c_1_0⁴·c_1_1⁴·c_1_2² + c_1_0⁵·c_1_2·c_1_3⁴
      + c_1_0⁵·c_1_2⁴·c_1_3 + c_1_0⁸·c_1_3² + c_1_0⁸·c_1_2·c_1_3 + c_1_0⁸·c_1_2², an element of degree 10
9. b_11_4 → 0, an element of degree 11
10. b_11_3 → c_1_1·c_1_2²·c_1_3⁸ + c_1_1·c_1_2⁴·c_1_3⁶ + c_1_1·c_1_2⁶·c_1_3⁴
       + c_1_1·c_1_2⁸·c_1_3² + c_1_1²·c_1_2·c_1_3⁸ + c_1_1²·c_1_2⁴·c_1_3⁵
       + c_1_1²·c_1_2⁵·c_1_3⁴ + c_1_1²·c_1_2⁸·c_1_3 + c_1_1⁴·c_1_2·c_1_3⁶
       + c_1_1⁴·c_1_2²·c_1_3⁵ + c_1_1⁴·c_1_2⁵·c_1_3² + c_1_1⁴·c_1_2⁶·c_1_3
       + c_1_1⁵·c_1_2²·c_1_3⁴ + c_1_1⁵·c_1_2⁴·c_1_3² + c_1_1⁶·c_1_2·c_1_3⁴
       + c_1_1⁶·c_1_2⁴·c_1_3 + c_1_1⁸·c_1_2·c_1_3² + c_1_1⁸·c_1_2²·c_1_3
       + c_1_0·c_1_2⁶·c_1_3⁴ + c_1_0·c_1_2⁸·c_1_3² + c_1_0·c_1_1²·c_1_3⁸
       + c_1_0·c_1_1²·c_1_2⁴·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁸ + c_1_0·c_1_1⁴·c_1_3⁶
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3⁴ + c_1_0·c_1_1⁴·c_1_2⁶ + c_1_0²·c_1_2⁵·c_1_3⁴
       + c_1_0²·c_1_2⁸·c_1_3 + c_1_0²·c_1_1·c_1_3⁸ + c_1_0²·c_1_1·c_1_2⁴·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2⁸ + c_1_0²·c_1_1⁴·c_1_3⁵ + c_1_0²·c_1_1⁴·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1⁴·c_1_2⁵ + c_1_0⁴·c_1_2⁵·c_1_3² + c_1_0⁴·c_1_2⁶·c_1_3
       + c_1_0⁴·c_1_1·c_1_3⁶ + c_1_0⁴·c_1_1·c_1_2⁴·c_1_3² + c_1_0⁴·c_1_1·c_1_2⁶
       + c_1_0⁴·c_1_1²·c_1_3⁵ + c_1_0⁴·c_1_1²·c_1_2⁴·c_1_3 + c_1_0⁴·c_1_1²·c_1_2⁵
       + c_1_0⁴·c_1_1⁴·c_1_2·c_1_3² + c_1_0⁴·c_1_1⁴·c_1_2²·c_1_3
       + c_1_0⁵·c_1_2²·c_1_3⁴ + c_1_0⁵·c_1_2⁴·c_1_3² + c_1_0⁶·c_1_2·c_1_3⁴
       + c_1_0⁶·c_1_2⁴·c_1_3 + c_1_0⁸·c_1_2·c_1_3² + c_1_0⁸·c_1_2²·c_1_3, an element of degree 11
11. b_12_6 → c_1_2⁴·c_1_3⁸ + c_1_2⁸·c_1_3⁴ + c_1_1·c_1_2²·c_1_3⁹ + c_1_1·c_1_2³·c_1_3⁸
       + c_1_1·c_1_2⁸·c_1_3³ + c_1_1·c_1_2⁹·c_1_3² + c_1_1²·c_1_2·c_1_3⁹
       + c_1_1²·c_1_2²·c_1_3⁸ + c_1_1²·c_1_2⁴·c_1_3⁶ + c_1_1²·c_1_2⁶·c_1_3⁴
       + c_1_1²·c_1_2⁸·c_1_3² + c_1_1²·c_1_2⁹·c_1_3 + c_1_1³·c_1_2·c_1_3⁸
       + c_1_1³·c_1_2⁸·c_1_3 + c_1_1⁴·c_1_3⁸ + c_1_1⁴·c_1_2²·c_1_3⁶
       + c_1_1⁴·c_1_2⁴·c_1_3⁴ + c_1_1⁴·c_1_2⁶·c_1_3² + c_1_1⁴·c_1_2⁸
       + c_1_1⁶·c_1_2²·c_1_3⁴ + c_1_1⁶·c_1_2⁴·c_1_3² + c_1_1⁸·c_1_3⁴
       + c_1_1⁸·c_1_2·c_1_3³ + c_1_1⁸·c_1_2²·c_1_3² + c_1_1⁸·c_1_2³·c_1_3
       + c_1_1⁸·c_1_2⁴ + c_1_1⁹·c_1_2·c_1_3² + c_1_1⁹·c_1_2²·c_1_3
       + c_1_0·c_1_2³·c_1_3⁸ + c_1_0·c_1_2⁹·c_1_3² + c_1_0·c_1_1·c_1_2²·c_1_3⁸
       + c_1_0·c_1_1·c_1_2⁸·c_1_3² + c_1_0·c_1_1²·c_1_3⁹
       + c_1_0·c_1_1²·c_1_2·c_1_3⁸ + c_1_0·c_1_1²·c_1_2⁹ + c_1_0·c_1_1⁸·c_1_3³
       + c_1_0·c_1_1⁸·c_1_2·c_1_3² + c_1_0·c_1_1⁸·c_1_2³ + c_1_0²·c_1_2⁶·c_1_3⁴
       + c_1_0²·c_1_2⁹·c_1_3 + c_1_0²·c_1_1·c_1_3⁹ + c_1_0²·c_1_1·c_1_2⁸·c_1_3
       + c_1_0²·c_1_1·c_1_2⁹ + c_1_0²·c_1_1²·c_1_3⁸
       + c_1_0²·c_1_1²·c_1_2⁴·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2⁸
       + c_1_0²·c_1_1⁴·c_1_3⁶ + c_1_0²·c_1_1⁴·c_1_2²·c_1_3⁴
       + c_1_0²·c_1_1⁴·c_1_2⁶ + c_1_0²·c_1_1⁸·c_1_3² + c_1_0²·c_1_1⁸·c_1_2·c_1_3
       + c_1_0²·c_1_1⁸·c_1_2² + c_1_0³·c_1_2·c_1_3⁸ + c_1_0³·c_1_2⁸·c_1_3
       + c_1_0⁴·c_1_3⁸ + c_1_0⁴·c_1_2⁶·c_1_3² + c_1_0⁴·c_1_2⁸
       + c_1_0⁴·c_1_1²·c_1_3⁶ + c_1_0⁴·c_1_1²·c_1_2⁴·c_1_3²
       + c_1_0⁴·c_1_1²·c_1_2⁶ + c_1_0⁴·c_1_1⁴·c_1_3⁴
       + c_1_0⁴·c_1_1⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_1⁴·c_1_2⁴
       + c_1_0⁶·c_1_2²·c_1_3⁴ + c_1_0⁶·c_1_2⁴·c_1_3² + c_1_0⁸·c_1_3⁴
       + c_1_0⁸·c_1_2³·c_1_3 + c_1_0⁸·c_1_2⁴ + c_1_0⁸·c_1_1·c_1_3³
       + c_1_0⁸·c_1_1·c_1_2²·c_1_3 + c_1_0⁸·c_1_1·c_1_2³ + c_1_0⁸·c_1_1²·c_1_3²
       + c_1_0⁸·c_1_1²·c_1_2·c_1_3 + c_1_0⁸·c_1_1²·c_1_2² + c_1_0⁹·c_1_2·c_1_3²
       + c_1_0⁹·c_1_2²·c_1_3, an element of degree 12
12. b_12_0 → c_1_1·c_1_2²·c_1_3⁹ + c_1_1·c_1_2³·c_1_3⁸ + c_1_1·c_1_2⁸·c_1_3³
       + c_1_1·c_1_2⁹·c_1_3² + c_1_1²·c_1_2·c_1_3⁹ + c_1_1²·c_1_2⁴·c_1_3⁶
       + c_1_1²·c_1_2⁶·c_1_3⁴ + c_1_1²·c_1_2⁹·c_1_3 + c_1_1³·c_1_2·c_1_3⁸
       + c_1_1³·c_1_2⁸·c_1_3 + c_1_1⁴·c_1_2²·c_1_3⁶ + c_1_1⁴·c_1_2⁶·c_1_3²
       + c_1_1⁶·c_1_2²·c_1_3⁴ + c_1_1⁶·c_1_2⁴·c_1_3² + c_1_1⁸·c_1_2·c_1_3³
       + c_1_1⁸·c_1_2³·c_1_3 + c_1_1⁹·c_1_2·c_1_3² + c_1_1⁹·c_1_2²·c_1_3
       + c_1_0·c_1_2³·c_1_3⁸ + c_1_0·c_1_2⁹·c_1_3² + c_1_0·c_1_1²·c_1_3⁹
       + c_1_0·c_1_1²·c_1_2⁸·c_1_3 + c_1_0·c_1_1²·c_1_2⁹ + c_1_0·c_1_1⁸·c_1_3³
       + c_1_0·c_1_1⁸·c_1_2²·c_1_3 + c_1_0·c_1_1⁸·c_1_2³ + c_1_0²·c_1_2²·c_1_3⁸
       + c_1_0²·c_1_2⁶·c_1_3⁴ + c_1_0²·c_1_2⁸·c_1_3² + c_1_0²·c_1_2⁹·c_1_3
       + c_1_0²·c_1_1·c_1_3⁹ + c_1_0²·c_1_1·c_1_2·c_1_3⁸ + c_1_0²·c_1_1·c_1_2⁹
       + c_1_0²·c_1_1⁴·c_1_3⁶ + c_1_0²·c_1_1⁴·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1⁴·c_1_2⁶ + c_1_0³·c_1_2·c_1_3⁸ + c_1_0³·c_1_2⁸·c_1_3
       + c_1_0⁴·c_1_2⁴·c_1_3⁴ + c_1_0⁴·c_1_2⁶·c_1_3² + c_1_0⁴·c_1_1²·c_1_3⁶
       + c_1_0⁴·c_1_1²·c_1_2²·c_1_3⁴ + c_1_0⁴·c_1_1²·c_1_2⁶ + c_1_0⁴·c_1_1⁸
       + c_1_0⁶·c_1_2²·c_1_3⁴ + c_1_0⁶·c_1_2⁴·c_1_3² + c_1_0⁸·c_1_2²·c_1_3²
       + c_1_0⁸·c_1_2³·c_1_3 + c_1_0⁸·c_1_1·c_1_3³ + c_1_0⁸·c_1_1·c_1_2·c_1_3²
       + c_1_0⁸·c_1_1·c_1_2³ + c_1_0⁸·c_1_1⁴ + c_1_0⁹·c_1_2·c_1_3²
       + c_1_0⁹·c_1_2²·c_1_3, an element of degree 12
13. b_13_3 → c_1_1·c_1_2²·c_1_3¹⁰ + c_1_1·c_1_2⁴·c_1_3⁸ + c_1_1·c_1_2⁸·c_1_3⁴
       + c_1_1·c_1_2¹⁰·c_1_3² + c_1_1²·c_1_2·c_1_3¹⁰ + c_1_1²·c_1_2³·c_1_3⁸
       + c_1_1²·c_1_2⁸·c_1_3³ + c_1_1²·c_1_2¹⁰·c_1_3 + c_1_1³·c_1_2²·c_1_3⁸
       + c_1_1³·c_1_2⁸·c_1_3² + c_1_1⁴·c_1_2·c_1_3⁸ + c_1_1⁴·c_1_2⁸·c_1_3
       + c_1_1⁸·c_1_2·c_1_3⁴ + c_1_1⁸·c_1_2²·c_1_3³ + c_1_1⁸·c_1_2³·c_1_3²
       + c_1_1⁸·c_1_2⁴·c_1_3 + c_1_1¹⁰·c_1_2·c_1_3² + c_1_1¹⁰·c_1_2²·c_1_3
       + c_1_0·c_1_2⁴·c_1_3⁸ + c_1_0·c_1_2¹⁰·c_1_3² + c_1_0·c_1_1²·c_1_3¹⁰
       + c_1_0·c_1_1²·c_1_2⁸·c_1_3² + c_1_0·c_1_1²·c_1_2¹⁰ + c_1_0·c_1_1⁸·c_1_3⁴
       + c_1_0·c_1_1⁸·c_1_2²·c_1_3² + c_1_0·c_1_1⁸·c_1_2⁴ + c_1_0²·c_1_2³·c_1_3⁸
       + c_1_0²·c_1_2¹⁰·c_1_3 + c_1_0²·c_1_1·c_1_3¹⁰ + c_1_0²·c_1_1·c_1_2²·c_1_3⁸
       + c_1_0²·c_1_1·c_1_2¹⁰ + c_1_0²·c_1_1²·c_1_2·c_1_3⁸
       + c_1_0²·c_1_1²·c_1_2⁸·c_1_3 + c_1_0²·c_1_1⁸·c_1_3³
       + c_1_0²·c_1_1⁸·c_1_2²·c_1_3 + c_1_0²·c_1_1⁸·c_1_2³ + c_1_0³·c_1_2²·c_1_3⁸
       + c_1_0³·c_1_2⁸·c_1_3² + c_1_0⁴·c_1_2·c_1_3⁸ + c_1_0⁴·c_1_2⁸·c_1_3
       + c_1_0⁸·c_1_2³·c_1_3² + c_1_0⁸·c_1_2⁴·c_1_3 + c_1_0⁸·c_1_1·c_1_3⁴
       + c_1_0⁸·c_1_1·c_1_2²·c_1_3² + c_1_0⁸·c_1_1·c_1_2⁴ + c_1_0⁸·c_1_1²·c_1_3³
       + c_1_0⁸·c_1_1²·c_1_2·c_1_3² + c_1_0⁸·c_1_1²·c_1_2³ + c_1_0¹⁰·c_1_2·c_1_3²
       + c_1_0¹⁰·c_1_2²·c_1_3, an element of degree 13
14. b_14_6 → c_1_2²·c_1_3¹² + c_1_2⁴·c_1_3¹⁰ + c_1_2⁶·c_1_3⁸ + c_1_2⁸·c_1_3⁶
       + c_1_2¹⁰·c_1_3⁴ + c_1_2¹²·c_1_3² + c_1_1·c_1_2·c_1_3¹²
       + c_1_1·c_1_2²·c_1_3¹¹ + c_1_1·c_1_2³·c_1_3¹⁰ + c_1_1·c_1_2⁶·c_1_3⁷
       + c_1_1·c_1_2⁷·c_1_3⁶ + c_1_1·c_1_2¹⁰·c_1_3³ + c_1_1·c_1_2¹¹·c_1_3²
       + c_1_1·c_1_2¹²·c_1_3 + c_1_1²·c_1_3¹² + c_1_1²·c_1_2·c_1_3¹¹
       + c_1_1²·c_1_2²·c_1_3¹⁰ + c_1_1²·c_1_2³·c_1_3⁹ + c_1_1²·c_1_2⁵·c_1_3⁷
       + c_1_1²·c_1_2⁶·c_1_3⁶ + c_1_1²·c_1_2⁷·c_1_3⁵ + c_1_1²·c_1_2⁹·c_1_3³
       + c_1_1²·c_1_2¹⁰·c_1_3² + c_1_1²·c_1_2¹¹·c_1_3 + c_1_1²·c_1_2¹²
       + c_1_1³·c_1_2·c_1_3¹⁰ + c_1_1³·c_1_2²·c_1_3⁹ + c_1_1³·c_1_2³·c_1_3⁸
       + c_1_1³·c_1_2⁴·c_1_3⁷ + c_1_1³·c_1_2⁵·c_1_3⁶ + c_1_1³·c_1_2⁶·c_1_3⁵
       + c_1_1³·c_1_2⁷·c_1_3⁴ + c_1_1³·c_1_2⁸·c_1_3³ + c_1_1³·c_1_2⁹·c_1_3²
       + c_1_1³·c_1_2¹⁰·c_1_3 + c_1_1⁴·c_1_3¹⁰ + c_1_1⁴·c_1_2³·c_1_3⁷
       + c_1_1⁴·c_1_2⁴·c_1_3⁶ + c_1_1⁴·c_1_2⁵·c_1_3⁵ + c_1_1⁴·c_1_2⁶·c_1_3⁴
       + c_1_1⁴·c_1_2⁷·c_1_3³ + c_1_1⁴·c_1_2¹⁰ + c_1_1⁵·c_1_2²·c_1_3⁷
       + c_1_1⁵·c_1_2³·c_1_3⁶ + c_1_1⁵·c_1_2⁴·c_1_3⁵ + c_1_1⁵·c_1_2⁵·c_1_3⁴
       + c_1_1⁵·c_1_2⁶·c_1_3³ + c_1_1⁵·c_1_2⁷·c_1_3² + c_1_1⁶·c_1_3⁸
       + c_1_1⁶·c_1_2·c_1_3⁷ + c_1_1⁶·c_1_2²·c_1_3⁶ + c_1_1⁶·c_1_2³·c_1_3⁵
       + c_1_1⁶·c_1_2⁴·c_1_3⁴ + c_1_1⁶·c_1_2⁵·c_1_3³ + c_1_1⁶·c_1_2⁶·c_1_3²
       + c_1_1⁶·c_1_2⁷·c_1_3 + c_1_1⁶·c_1_2⁸ + c_1_1⁷·c_1_2·c_1_3⁶
       + c_1_1⁷·c_1_2²·c_1_3⁵ + c_1_1⁷·c_1_2³·c_1_3⁴ + c_1_1⁷·c_1_2⁴·c_1_3³
       + c_1_1⁷·c_1_2⁵·c_1_3² + c_1_1⁷·c_1_2⁶·c_1_3 + c_1_1⁸·c_1_3⁶
       + c_1_1⁸·c_1_2³·c_1_3³ + c_1_1⁸·c_1_2⁶ + c_1_1⁹·c_1_2²·c_1_3³
       + c_1_1⁹·c_1_2³·c_1_3² + c_1_1¹⁰·c_1_3⁴ + c_1_1¹⁰·c_1_2·c_1_3³
       + c_1_1¹⁰·c_1_2²·c_1_3² + c_1_1¹⁰·c_1_2³·c_1_3 + c_1_1¹⁰·c_1_2⁴
       + c_1_1¹¹·c_1_2·c_1_3² + c_1_1¹¹·c_1_2²·c_1_3 + c_1_1¹²·c_1_3²
       + c_1_1¹²·c_1_2·c_1_3 + c_1_1¹²·c_1_2² + c_1_0·c_1_2³·c_1_3¹⁰
       + c_1_0·c_1_2⁴·c_1_3⁹ + c_1_0·c_1_2⁵·c_1_3⁸ + c_1_0·c_1_2⁷·c_1_3⁶
       + c_1_0·c_1_2⁸·c_1_3⁵ + c_1_0·c_1_2⁹·c_1_3⁴ + c_1_0·c_1_2¹¹·c_1_3²
       + c_1_0·c_1_2¹²·c_1_3 + c_1_0·c_1_1·c_1_3¹² + c_1_0·c_1_1·c_1_2²·c_1_3¹⁰
       + c_1_0·c_1_1·c_1_2⁶·c_1_3⁶ + c_1_0·c_1_1·c_1_2¹⁰·c_1_3²
       + c_1_0·c_1_1·c_1_2¹² + c_1_0·c_1_1²·c_1_3¹¹ + c_1_0·c_1_1²·c_1_2·c_1_3¹⁰
       + c_1_0·c_1_1²·c_1_2³·c_1_3⁸ + c_1_0·c_1_1²·c_1_2⁵·c_1_3⁶
       + c_1_0·c_1_1²·c_1_2⁷·c_1_3⁴ + c_1_0·c_1_1²·c_1_2⁹·c_1_3²
       + c_1_0·c_1_1²·c_1_2¹¹ + c_1_0·c_1_1³·c_1_2²·c_1_3⁸
       + c_1_0·c_1_1³·c_1_2⁴·c_1_3⁶ + c_1_0·c_1_1³·c_1_2⁶·c_1_3⁴
       + c_1_0·c_1_1³·c_1_2⁸·c_1_3² + c_1_0·c_1_1⁴·c_1_3⁹
       + c_1_0·c_1_1⁴·c_1_2³·c_1_3⁶ + c_1_0·c_1_1⁴·c_1_2⁵·c_1_3⁴
       + c_1_0·c_1_1⁴·c_1_2⁷·c_1_3² + c_1_0·c_1_1⁴·c_1_2⁹ + c_1_0·c_1_1⁵·c_1_3⁸
       + c_1_0·c_1_1⁵·c_1_2²·c_1_3⁶ + c_1_0·c_1_1⁵·c_1_2⁴·c_1_3⁴
       + c_1_0·c_1_1⁵·c_1_2⁶·c_1_3² + c_1_0·c_1_1⁵·c_1_2⁸ + c_1_0·c_1_1⁶·c_1_3⁷
       + c_1_0·c_1_1⁶·c_1_2·c_1_3⁶ + c_1_0·c_1_1⁶·c_1_2³·c_1_3⁴
       + c_1_0·c_1_1⁶·c_1_2⁵·c_1_3² + c_1_0·c_1_1⁶·c_1_2⁷
       + c_1_0·c_1_1⁷·c_1_2²·c_1_3⁴ + c_1_0·c_1_1⁷·c_1_2⁴·c_1_3²
       + c_1_0·c_1_1⁸·c_1_3⁵ + c_1_0·c_1_1⁸·c_1_2³·c_1_3² + c_1_0·c_1_1⁸·c_1_2⁵
       + c_1_0·c_1_1⁹·c_1_3⁴ + c_1_0·c_1_1⁹·c_1_2²·c_1_3² + c_1_0·c_1_1⁹·c_1_2⁴
       + c_1_0·c_1_1¹⁰·c_1_3³ + c_1_0·c_1_1¹⁰·c_1_2·c_1_3² + c_1_0·c_1_1¹⁰·c_1_2³
       + c_1_0²·c_1_3¹² + c_1_0²·c_1_2³·c_1_3⁹ + c_1_0²·c_1_2⁷·c_1_3⁵
       + c_1_0²·c_1_2¹¹·c_1_3 + c_1_0²·c_1_2¹² + c_1_0²·c_1_1·c_1_3¹¹
       + c_1_0²·c_1_1·c_1_2²·c_1_3⁹ + c_1_0²·c_1_1·c_1_2³·c_1_3⁸
       + c_1_0²·c_1_1·c_1_2⁶·c_1_3⁵ + c_1_0²·c_1_1·c_1_2⁷·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2¹⁰·c_1_3 + c_1_0²·c_1_1·c_1_2¹¹ + c_1_0²·c_1_1²·c_1_3¹⁰
       + c_1_0²·c_1_1²·c_1_2·c_1_3⁹ + c_1_0²·c_1_1²·c_1_2⁵·c_1_3⁵
       + c_1_0²·c_1_1²·c_1_2⁶·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2⁸·c_1_3²
       + c_1_0²·c_1_1²·c_1_2⁹·c_1_3 + c_1_0²·c_1_1²·c_1_2¹⁰
       + c_1_0²·c_1_1³·c_1_2·c_1_3⁸ + c_1_0²·c_1_1³·c_1_2⁴·c_1_3⁵
       + c_1_0²·c_1_1³·c_1_2⁵·c_1_3⁴ + c_1_0²·c_1_1³·c_1_2⁸·c_1_3
       + c_1_0²·c_1_1⁴·c_1_2³·c_1_3⁵ + c_1_0²·c_1_1⁴·c_1_2⁷·c_1_3
       + c_1_0²·c_1_1⁵·c_1_3⁷ + c_1_0²·c_1_1⁵·c_1_2²·c_1_3⁵
       + c_1_0²·c_1_1⁵·c_1_2³·c_1_3⁴ + c_1_0²·c_1_1⁵·c_1_2⁶·c_1_3
       + c_1_0²·c_1_1⁵·c_1_2⁷ + c_1_0²·c_1_1⁶·c_1_3⁶
       + c_1_0²·c_1_1⁶·c_1_2·c_1_3⁵ + c_1_0²·c_1_1⁶·c_1_2²·c_1_3⁴
       + c_1_0²·c_1_1⁶·c_1_2⁵·c_1_3 + c_1_0²·c_1_1⁶·c_1_2⁶
       + c_1_0²·c_1_1⁷·c_1_2·c_1_3⁴ + c_1_0²·c_1_1⁷·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1⁸·c_1_2²·c_1_3² + c_1_0²·c_1_1⁸·c_1_2³·c_1_3
       + c_1_0²·c_1_1⁹·c_1_3³ + c_1_0²·c_1_1⁹·c_1_2²·c_1_3 + c_1_0²·c_1_1⁹·c_1_2³
       + c_1_0²·c_1_1¹⁰·c_1_3² + c_1_0²·c_1_1¹⁰·c_1_2·c_1_3
       + c_1_0²·c_1_1¹⁰·c_1_2² + c_1_0³·c_1_2·c_1_3¹⁰ + c_1_0³·c_1_2²·c_1_3⁹
       + c_1_0³·c_1_2⁷·c_1_3⁴ + c_1_0³·c_1_2⁸·c_1_3³ + c_1_0³·c_1_2⁹·c_1_3²
       + c_1_0³·c_1_2¹⁰·c_1_3 + c_1_0³·c_1_1·c_1_2⁶·c_1_3⁴
       + c_1_0³·c_1_1·c_1_2⁸·c_1_3² + c_1_0³·c_1_1²·c_1_2⁵·c_1_3⁴
       + c_1_0³·c_1_1²·c_1_2⁸·c_1_3 + c_1_0³·c_1_1³·c_1_3⁸
       + c_1_0³·c_1_1³·c_1_2⁴·c_1_3⁴ + c_1_0³·c_1_1³·c_1_2⁸
       + c_1_0³·c_1_1⁴·c_1_3⁷ + c_1_0³·c_1_1⁴·c_1_2³·c_1_3⁴
       + c_1_0³·c_1_1⁴·c_1_2⁷ + c_1_0³·c_1_1⁵·c_1_3⁶
       + c_1_0³·c_1_1⁵·c_1_2²·c_1_3⁴ + c_1_0³·c_1_1⁵·c_1_2⁶
       + c_1_0³·c_1_1⁶·c_1_3⁵ + c_1_0³·c_1_1⁶·c_1_2·c_1_3⁴
       + c_1_0³·c_1_1⁶·c_1_2⁵ + c_1_0³·c_1_1⁸·c_1_2·c_1_3²
       + c_1_0³·c_1_1⁸·c_1_2²·c_1_3 + c_1_0⁴·c_1_3¹⁰ + c_1_0⁴·c_1_2·c_1_3⁹
       + c_1_0⁴·c_1_2⁷·c_1_3³ + c_1_0⁴·c_1_2⁸·c_1_3² + c_1_0⁴·c_1_2¹⁰
       + c_1_0⁴·c_1_1·c_1_3⁹ + c_1_0⁴·c_1_1·c_1_2⁶·c_1_3³
       + c_1_0⁴·c_1_1·c_1_2⁷·c_1_3² + c_1_0⁴·c_1_1·c_1_2⁸·c_1_3
       + c_1_0⁴·c_1_1·c_1_2⁹ + c_1_0⁴·c_1_1²·c_1_2⁴·c_1_3⁴
       + c_1_0⁴·c_1_1²·c_1_2⁵·c_1_3³ + c_1_0⁴·c_1_1²·c_1_2⁶·c_1_3²
       + c_1_0⁴·c_1_1²·c_1_2⁷·c_1_3 + c_1_0⁴·c_1_1³·c_1_3⁷
       + c_1_0⁴·c_1_1³·c_1_2⁴·c_1_3³ + c_1_0⁴·c_1_1³·c_1_2⁵·c_1_3²
       + c_1_0⁴·c_1_1³·c_1_2⁶·c_1_3 + c_1_0⁴·c_1_1³·c_1_2⁷ + c_1_0⁴·c_1_1⁴·c_1_3⁶
       + c_1_0⁴·c_1_1⁴·c_1_2²·c_1_3⁴ + c_1_0⁴·c_1_1⁴·c_1_2³·c_1_3³
       + c_1_0⁴·c_1_1⁴·c_1_2⁵·c_1_3 + c_1_0⁴·c_1_1⁴·c_1_2⁶ + c_1_0⁴·c_1_1⁵·c_1_3⁵
       + c_1_0⁴·c_1_1⁵·c_1_2²·c_1_3³ + c_1_0⁴·c_1_1⁵·c_1_2³·c_1_3²
       + c_1_0⁴·c_1_1⁵·c_1_2⁴·c_1_3 + c_1_0⁴·c_1_1⁵·c_1_2⁵ + c_1_0⁴·c_1_1⁶·c_1_3⁴
       + c_1_0⁴·c_1_1⁶·c_1_2·c_1_3³ + c_1_0⁴·c_1_1⁶·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_1⁶·c_1_2³·c_1_3 + c_1_0⁴·c_1_1⁶·c_1_2⁴
       + c_1_0⁴·c_1_1⁷·c_1_2·c_1_3² + c_1_0⁴·c_1_1⁷·c_1_2²·c_1_3
       + c_1_0⁴·c_1_1⁸·c_1_3² + c_1_0⁴·c_1_1⁸·c_1_2·c_1_3 + c_1_0⁴·c_1_1⁸·c_1_2²
       + c_1_0⁵·c_1_2·c_1_3⁸ + c_1_0⁵·c_1_2⁷·c_1_3² + c_1_0⁵·c_1_1·c_1_3⁸
       + c_1_0⁵·c_1_1·c_1_2⁶·c_1_3² + c_1_0⁵·c_1_1·c_1_2⁸ + c_1_0⁵·c_1_1²·c_1_3⁷
       + c_1_0⁵·c_1_1²·c_1_2⁵·c_1_3² + c_1_0⁵·c_1_1²·c_1_2⁷
       + c_1_0⁵·c_1_1³·c_1_3⁶ + c_1_0⁵·c_1_1³·c_1_2⁴·c_1_3²
       + c_1_0⁵·c_1_1³·c_1_2⁶ + c_1_0⁵·c_1_1⁴·c_1_3⁵
       + c_1_0⁵·c_1_1⁴·c_1_2³·c_1_3² + c_1_0⁵·c_1_1⁴·c_1_2⁵
       + c_1_0⁵·c_1_1⁵·c_1_3⁴ + c_1_0⁵·c_1_1⁵·c_1_2²·c_1_3²
       + c_1_0⁵·c_1_1⁵·c_1_2⁴ + c_1_0⁵·c_1_1⁶·c_1_3³
       + c_1_0⁵·c_1_1⁶·c_1_2·c_1_3² + c_1_0⁵·c_1_1⁶·c_1_2³ + c_1_0⁶·c_1_3⁸
       + c_1_0⁶·c_1_2⁷·c_1_3 + c_1_0⁶·c_1_2⁸ + c_1_0⁶·c_1_1·c_1_3⁷
       + c_1_0⁶·c_1_1·c_1_2⁶·c_1_3 + c_1_0⁶·c_1_1·c_1_2⁷ + c_1_0⁶·c_1_1²·c_1_3⁶
       + c_1_0⁶·c_1_1²·c_1_2⁵·c_1_3 + c_1_0⁶·c_1_1²·c_1_2⁶ + c_1_0⁶·c_1_1³·c_1_3⁵
       + c_1_0⁶·c_1_1³·c_1_2⁴·c_1_3 + c_1_0⁶·c_1_1³·c_1_2⁵ + c_1_0⁶·c_1_1⁴·c_1_3⁴
       + c_1_0⁶·c_1_1⁴·c_1_2³·c_1_3 + c_1_0⁶·c_1_1⁴·c_1_2⁴ + c_1_0⁶·c_1_1⁵·c_1_3³
       + c_1_0⁶·c_1_1⁵·c_1_2²·c_1_3 + c_1_0⁶·c_1_1⁵·c_1_2³ + c_1_0⁶·c_1_1⁶·c_1_3²
       + c_1_0⁶·c_1_1⁶·c_1_2·c_1_3 + c_1_0⁶·c_1_1⁶·c_1_2² + c_1_0⁷·c_1_2·c_1_3⁶
       + c_1_0⁷·c_1_2²·c_1_3⁵ + c_1_0⁷·c_1_2³·c_1_3⁴ + c_1_0⁷·c_1_2⁴·c_1_3³
       + c_1_0⁷·c_1_2⁵·c_1_3² + c_1_0⁷·c_1_2⁶·c_1_3 + c_1_0⁷·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0⁷·c_1_1·c_1_2⁴·c_1_3² + c_1_0⁷·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0⁷·c_1_1²·c_1_2⁴·c_1_3 + c_1_0⁷·c_1_1⁴·c_1_2·c_1_3²
       + c_1_0⁷·c_1_1⁴·c_1_2²·c_1_3 + c_1_0⁸·c_1_3⁶ + c_1_0⁸·c_1_2·c_1_3⁵
       + c_1_0⁸·c_1_2³·c_1_3³ + c_1_0⁸·c_1_2⁴·c_1_3² + c_1_0⁸·c_1_2⁶
       + c_1_0⁸·c_1_1·c_1_3⁵ + c_1_0⁸·c_1_1·c_1_2²·c_1_3³
       + c_1_0⁸·c_1_1·c_1_2³·c_1_3² + c_1_0⁸·c_1_1·c_1_2⁴·c_1_3
       + c_1_0⁸·c_1_1·c_1_2⁵ + c_1_0⁸·c_1_1²·c_1_2·c_1_3³
       + c_1_0⁸·c_1_1²·c_1_2³·c_1_3 + c_1_0⁸·c_1_1³·c_1_2·c_1_3²
       + c_1_0⁸·c_1_1³·c_1_2²·c_1_3 + c_1_0⁸·c_1_1⁴·c_1_3²
       + c_1_0⁸·c_1_1⁴·c_1_2·c_1_3 + c_1_0⁸·c_1_1⁴·c_1_2² + c_1_0⁹·c_1_2·c_1_3⁴
       + c_1_0⁹·c_1_2³·c_1_3² + c_1_0⁹·c_1_1·c_1_3⁴ + c_1_0⁹·c_1_1·c_1_2²·c_1_3²
       + c_1_0⁹·c_1_1·c_1_2⁴ + c_1_0⁹·c_1_1²·c_1_3³ + c_1_0⁹·c_1_1²·c_1_2·c_1_3²
       + c_1_0⁹·c_1_1²·c_1_2³ + c_1_0¹⁰·c_1_3⁴ + c_1_0¹⁰·c_1_2³·c_1_3
       + c_1_0¹⁰·c_1_2⁴ + c_1_0¹⁰·c_1_1·c_1_3³ + c_1_0¹⁰·c_1_1·c_1_2²·c_1_3
       + c_1_0¹⁰·c_1_1·c_1_2³ + c_1_0¹⁰·c_1_1²·c_1_3² + c_1_0¹⁰·c_1_1²·c_1_2·c_1_3
       + c_1_0¹⁰·c_1_1²·c_1_2² + c_1_0¹¹·c_1_2·c_1_3² + c_1_0¹¹·c_1_2²·c_1_3
       + c_1_0¹²·c_1_3² + c_1_0¹²·c_1_2·c_1_3 + c_1_0¹²·c_1_2², an element of degree 14
15. b_15_9 → c_1_1·c_1_2²·c_1_3¹² + c_1_1·c_1_2⁴·c_1_3¹⁰ + c_1_1·c_1_2¹⁰·c_1_3⁴
       + c_1_1·c_1_2¹²·c_1_3² + c_1_1²·c_1_2·c_1_3¹² + c_1_1²·c_1_2⁵·c_1_3⁸
       + c_1_1²·c_1_2⁸·c_1_3⁵ + c_1_1²·c_1_2¹²·c_1_3 + c_1_1³·c_1_2⁴·c_1_3⁸
       + c_1_1³·c_1_2⁸·c_1_3⁴ + c_1_1⁴·c_1_2·c_1_3¹⁰ + c_1_1⁴·c_1_2³·c_1_3⁸
       + c_1_1⁴·c_1_2⁸·c_1_3³ + c_1_1⁴·c_1_2¹⁰·c_1_3 + c_1_1⁵·c_1_2²·c_1_3⁸
       + c_1_1⁵·c_1_2⁸·c_1_3² + c_1_1⁸·c_1_2²·c_1_3⁵ + c_1_1⁸·c_1_2³·c_1_3⁴
       + c_1_1⁸·c_1_2⁴·c_1_3³ + c_1_1⁸·c_1_2⁵·c_1_3² + c_1_1¹⁰·c_1_2·c_1_3⁴
       + c_1_1¹⁰·c_1_2⁴·c_1_3 + c_1_1¹²·c_1_2·c_1_3² + c_1_1¹²·c_1_2²·c_1_3
       + c_1_0·c_1_2¹⁰·c_1_3⁴ + c_1_0·c_1_2¹²·c_1_3² + c_1_0·c_1_1²·c_1_3¹²
       + c_1_0·c_1_1²·c_1_2⁸·c_1_3⁴ + c_1_0·c_1_1²·c_1_2¹² + c_1_0·c_1_1⁴·c_1_3¹⁰
       + c_1_0·c_1_1⁴·c_1_2⁸·c_1_3² + c_1_0·c_1_1⁴·c_1_2¹⁰
       + c_1_0·c_1_1⁸·c_1_2²·c_1_3⁴ + c_1_0·c_1_1⁸·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_2⁵·c_1_3⁸ + c_1_0²·c_1_2¹²·c_1_3 + c_1_0²·c_1_1·c_1_3¹²
       + c_1_0²·c_1_1·c_1_2⁴·c_1_3⁸ + c_1_0²·c_1_1·c_1_2¹²
       + c_1_0²·c_1_1⁴·c_1_2·c_1_3⁸ + c_1_0²·c_1_1⁴·c_1_2⁸·c_1_3
       + c_1_0²·c_1_1⁸·c_1_3⁵ + c_1_0²·c_1_1⁸·c_1_2⁴·c_1_3 + c_1_0²·c_1_1⁸·c_1_2⁵
       + c_1_0³·c_1_2⁴·c_1_3⁸ + c_1_0³·c_1_2⁸·c_1_3⁴ + c_1_0⁴·c_1_2³·c_1_3⁸
       + c_1_0⁴·c_1_2¹⁰·c_1_3 + c_1_0⁴·c_1_1·c_1_3¹⁰ + c_1_0⁴·c_1_1·c_1_2²·c_1_3⁸
       + c_1_0⁴·c_1_1·c_1_2¹⁰ + c_1_0⁴·c_1_1²·c_1_2·c_1_3⁸
       + c_1_0⁴·c_1_1²·c_1_2⁸·c_1_3 + c_1_0⁴·c_1_1⁸·c_1_3³
       + c_1_0⁴·c_1_1⁸·c_1_2²·c_1_3 + c_1_0⁴·c_1_1⁸·c_1_2³ + c_1_0⁵·c_1_2²·c_1_3⁸
       + c_1_0⁵·c_1_2⁸·c_1_3² + c_1_0⁸·c_1_2³·c_1_3⁴ + c_1_0⁸·c_1_2⁵·c_1_3²
       + c_1_0⁸·c_1_1·c_1_2²·c_1_3⁴ + c_1_0⁸·c_1_1·c_1_2⁴·c_1_3²
       + c_1_0⁸·c_1_1²·c_1_3⁵ + c_1_0⁸·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0⁸·c_1_1²·c_1_2⁵ + c_1_0⁸·c_1_1⁴·c_1_3³
       + c_1_0⁸·c_1_1⁴·c_1_2·c_1_3² + c_1_0⁸·c_1_1⁴·c_1_2³ + c_1_0¹⁰·c_1_2·c_1_3⁴
       + c_1_0¹⁰·c_1_2⁴·c_1_3 + c_1_0¹²·c_1_2·c_1_3² + c_1_0¹²·c_1_2²·c_1_3, an element of degree 15
16. b_15_5 → c_1_0·c_1_1²·c_1_2⁴·c_1_3⁸ + c_1_0·c_1_1²·c_1_2⁸·c_1_3⁴
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3⁸ + c_1_0·c_1_1⁴·c_1_2⁸·c_1_3²
       + c_1_0·c_1_1⁸·c_1_2²·c_1_3⁴ + c_1_0·c_1_1⁸·c_1_2⁴·c_1_3²
       + c_1_0²·c_1_1·c_1_2⁴·c_1_3⁸ + c_1_0²·c_1_1·c_1_2⁸·c_1_3⁴
       + c_1_0²·c_1_1⁴·c_1_2·c_1_3⁸ + c_1_0²·c_1_1⁴·c_1_2⁸·c_1_3
       + c_1_0²·c_1_1⁸·c_1_2·c_1_3⁴ + c_1_0²·c_1_1⁸·c_1_2⁴·c_1_3
       + c_1_0⁴·c_1_1·c_1_2²·c_1_3⁸ + c_1_0⁴·c_1_1·c_1_2⁸·c_1_3²
       + c_1_0⁴·c_1_1²·c_1_2·c_1_3⁸ + c_1_0⁴·c_1_1²·c_1_2⁸·c_1_3
       + c_1_0⁴·c_1_1⁸·c_1_2·c_1_3² + c_1_0⁴·c_1_1⁸·c_1_2²·c_1_3
       + c_1_0⁸·c_1_1·c_1_2²·c_1_3⁴ + c_1_0⁸·c_1_1·c_1_2⁴·c_1_3²
       + c_1_0⁸·c_1_1²·c_1_2·c_1_3⁴ + c_1_0⁸·c_1_1²·c_1_2⁴·c_1_3
       + c_1_0⁸·c_1_1⁴·c_1_2·c_1_3² + c_1_0⁸·c_1_1⁴·c_1_2²·c_1_3, an element of degree 15

About the group

Ring generators

Ring relations

Completion information

Restriction maps