Order = 12180 = 22.3.5.7.29.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of L2(29) are a, b where a has order 2, b has order 3 and ab has order 29.
Standard generators of 2.L2(29) = SL2(29) are preimages A, B where B has order 3 and AB has order 29.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| L2(29) | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of L2(29)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 30 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 C 15 a Std Details 0 C 15 b Std Details 0 Z 28 a Std Details 0 C 28 b Std Details 0 C 28 c Std Details 0 Z 29 Std Details 0 C 30 a Std Details 0 C 30 b Std Details 0 C 30 c Std Details 0 C 30 d Std Details 0 C 30 e Std Details 0 C 30 f Std Details 0 Z 30 g Std Details 0 Z 56 Std Details 0 Z 112 Std Details Char Ring Dimension ID Generators Description Link 2 GF(4) 14 a Std Details 2 GF(4) 14 b Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 28 a Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 28 b Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 29 Std Details Char Ring Dimension ID Generators Description Link 29 GF(29) 3 Std Details 29 GF(29) 5 Std Details 29 GF(29) 7 Std Details 29 GF(29) 9 Std Details 29 GF(29) 11 Std Details 29 GF(29) 13 Std Details 29 GF(29) 15 Std Details 29 GF(29) 17 Std Details 29 GF(29) 19 Std Details 29 GF(29) 21 Std Details 29 GF(29) 23 Std Details 29 GF(29) 25 Std Details 29 GF(29) 27 Std Details 29 GF(29) 29 Std Details
Representations of 2.L2(29)
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 29 GF(29) 2 Std Details
Conjugacy classes
Conjugacy classes of L2(29)
| Conjugacy class | Centraliser order | Power up | Class rep(s) |
|---|---|---|---|
| 1A | 12 180 |
(abababb)15 |
|
| 2A | 28 |
(abababbababb)7 |
|
| 3A | 15 |
(abababb)5 |
|
| 5A | 15 |
(abababbabababb)3 |
|
| 5B | 15 |
(abababb)3 |
|
| 7A | 14 |
Omitted
owing to
length. |
|
| 7B | 14 |
abababbababbabababbababb |
|
| 7C | 14 |
abababbababbabababbababbabababbababbabababbababb |
|
| 14A | 14 |
abababbababb |
|
| 14B | 14 |
(abababbababb)9 |
|
| 14C | 14 |
(abababbababb)3 |
|
| 15A | 15 |
abababbabababbabababbabababb |
|
| 15B | 15 |
abababbabababbabababbabababbabababbabababbabababbabababb |
|
| 15C | 15 |
abababb |
|
| 15D | 15 |
abababbabababb |
|
| 29A | 29 | ab |
|
| 29B | 29 |
abab |
Download words for class representatives.