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

### 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

M11 a, b | a2 = b4 = (ab)11 = (ab2)6 = ababab−1abab2ab−1abab−1ab−1 = 1 〉 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