Order = 7920 = 24.32.5.11.
Mult = 1.
Out = 1.
Porting notes
Porting incomplete.Standard generators
Standard generators of M11 are a, b where a has order 2, b has order 4, ab has order 11 and ababababbababbabb has order 4. Alternatively: a has order 2, b has order 4, ab has order 11 and ababbabbb has order 5 or a has order 2, b has order 4, ab has order 11 and ababbbabb has order 3.
Black box algorithms
Finding generators
| Group | Algorithm | File |
|---|---|---|
| M11 |
| Download |
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| M11 | 〈〈 a, b | o(a) = 2, o(b) = 4, o(ab) = 11, o(abab2ab3) = 5 〉〉 | Download |
Presentations
| Group | Presentation | Link |
|---|---|---|
| M11 | 〈 a, b | a2 = b4 = (ab)11 = (ab2)6 = ababab−1abab2ab−1abab−1ab−1 = 1 〉 | Details |
Representations
Representations of M11
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 11 Std Details 12 Std Details 55 Std Details 66 Std Details 165 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 10 a Std Details 0 Z[i2] 10 b Std Details 0 Z[i2] 10 c Std Details 0 Z 11 Std Details 0 Z 20 Std Details 0 Z 32 Std Details 0 Z 44 Std Details 0 Z 45 Std Details 0 Z 55 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 10 Std Details 2 GF(4) 16 a Std Details 2 GF(4) 16 b Std Details 2 GF(2) 32 Std Details 2 GF(2) 44 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 5 a Std The “cocode” representation Details 3 GF(3) 5 b Std The “code” representation Details 3 GF(3) 10 a Std Details 3 GF(3) 10 b Std Details 3 GF(3) 10 c Std Details 3 GF(3) 24 Std Details 3 GF(3) 45 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 10 a Std Details 5 GF(25) 10 b Std Details 5 GF(25) 10 c Std Details 5 GF(5) 11 Std Details 5 GF(5) 16 a Std Details 5 GF(5) 16 b Std Details 5 GF(5) 20 Std Details 5 GF(5) 45 Std Details 5 GF(5) 55 Std Details Char Ring Dimension ID Generators Description Link 11 GF(11) 9 Std Details 11 GF(11) 10 a Std Details 11 GF(11) 10 b Std Details 11 GF(11) 11 Std Details 11 GF(11) 16 Std Details 11 GF(11) 44 Std Details 11 GF(11) 55 Std Details
Maximal subgroups
Maximal subgroups of M11
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| M10 = A6.23 | 720 | 11 | Program: Standard generators |
| L2(11) | 660 | 12 | Program: Standard generators |
| M9:2 | 144 | 55 | Program: Generators |
| S5 | 120 | 66 | Program: Standard generators |
| 2S4 | 48 | 165 | Program: Generators |
Conjugacy classes
Conjugacy classes of M11
| Conjugacy class | Centraliser order | Power up | Class rep(s) |
|---|---|---|---|
| 1A | 7 920 |
ababbabbababbabbababbabbababbabbababbabbababbabbababbabbababbabb | |
| 2A | 48 | 4A 6A 8A 8B |
ababbabbababbabbababbabbababbabb |
| 3A | 18 | 6A |
abbabb |
| 4A | 8 | 8A 8B |
ababbabbababbabb |
| 5A | 5 |
ababbabbb | |
| 6A | 6 |
abb | |
| 8A | 8 | 8B5 |
ababbabb |
| 8B | 8 | 8A5 |
(ababbabb)5 |
| 11A | 11 | 11B2 |
ab |
| 11B | 11 | 11A2 |
abab |
Download words for class representatives.