Order = 2448 = 24.32.17.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of L2(17) are a, b where a has order 2, b has order 3 and ab has order 17.
Standard generators of 2.L2(17) are preimages A, B where B has order 3 and AB has order 17.
Standard generators of L2(17):2 = PGL2(17) are c, d where c is in class 2B, d has order 3, cd has order 16 (necessarily in class 16B) and cdcdd has order 4.
Standard generators of 2.L2(17).2 are preimages C, D where D has order 3.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| L2(17) | 〈〈 a, b | some conditions 〉〉 | Download |
Presentations
| Group | Presentation | Link |
|---|---|---|
| L2(17) | 〈 a, b | a2 = b3 = (ab)17 = ((ab)5(ab−1)3)2 = 1 〉 | Details |
| L2(17):2 | 〈 c, d | c2 = d3 = (cd)16 = [c, d]4 = [a, (ab)5]2 = 1 〉 | Details |
Representations
Representations of L2(17)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 18 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 C 9 a Std Details 0 C 9 b Std Details 0 Z 16 a Std Details 0 Z 17 Std Details 0 Z 18 a Std Details 0 Z 18 d Std Details 0 Z 48 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 8 a Std Details 2 GF(2) 8 b Std Details 2 GF(2) 16 a Std Details 2 GF(8) 16 b Std Details 2 GF(8) 16 c Std Details 2 GF(8) 16 d Std Details 2 GF(2) 48 Std Details Char Ring Dimension ID Generators Description Link 3 GF(9) 9 a Std Details 3 GF(9) 9 b Std Details 3 GF(3) 16 Std Details 3 GF(3) 18 a Std Details 3 GF(9) 18 b Std Details 3 GF(9) 18 c Std Details Char Ring Dimension ID Generators Description Link 17 GF(17) 3 Std Details 17 GF(17) 5 Std Details 17 GF(17) 7 Std Details 17 GF(17) 9 Std Details 17 GF(17) 11 Std Details 17 GF(17) 13 Std Details 17 GF(17) 15 Std Details 17 GF(17) 17 Std Details
Representations of 2.L2(17)
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(9) 8 a Std Details 3 GF(9) 8 b Std Details 17 GF(17) 2 Std Details 17 GF(17) 4 Std Details 17 GF(17) 6 Std Details 17 GF(17) 8 Std Details 17 GF(17) 10 Std Details 17 GF(17) 12 Std Details 17 GF(17) 14 Std Details 17 GF(17) 16 Std Details
Representations of L2(17):2
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 18 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 17 GF(17) 3 Std Details
Representations of 2.L2(17).2
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 16 Std Details
Conjugacy classes
Conjugacy classes of L2(17)
| Conjugacy class | Centraliser order | Power up | Class rep(s) |
|---|---|---|---|
| 1A | 2 448 |
Omitted
owing to
length. |
|
| 2A | 16 |
ababababbababababbababababbababababb |
|
| 3A | 9 |
(ababb)3 |
|
| 4A | 8 |
ababababbababababb |
|
| 8A | 8 |
(ababababb)3 |
|
| 8B | 8 |
ababababb |
|
| 9A | 9 |
ababb |
|
| 9B | 9 |
ababbababb |
|
| 9C | 9 |
ababbababbababbababb |
|
| 17A | 17 | ab |
|
| 17B | 17 |
(ab)3 |
Download words for class representatives.