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
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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


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)
1A7 920 ababbabbababbabbababbabbababbabbababbabbababbabbababbabbababbabb
2A48 4A 6A 8A 8B ababbabbababbabbababbabbababbabb
3A18 6A abbabb
4A8 8A 8B ababbabbababbabb
5A5 ababbabbb
6A6 abb
8A8 8B5 ababbabb
8B8 8A5 (ababbabb)5
11A11 11B2 ab
11B11 11A2 abab

Download words for class representatives.