Order = 244823040 = 210.33.5.7.11.23.
Mult = 1.
Out = 1.


Porting notes

Porting incomplete.

Standard generators

Standard generators of M24 are a, b where a is in class 2B, b is in class 3A, ab has order 23 and abababbababbabb has order 4.


Black box algorithms

Finding generators

Group Algorithm File
M24
Download

Checking generators (semi-presentations)

Group Semi-presentation File
M24 〈〈 a, b | o(a) = 2, o(b) = 3, o(ab) = 23, o(abababbababbabb) = 4, o(abababb) = 12 〉〉 Download

Presentations

Group Presentation Link
M24 a, b | a2 = b3 = (ab)23 = [a, b]12 = [a, bab]5 = (ababab−1)3(abab−1ab−1)3 = (ab(abab−1)3)4 = 1 〉 Details

Representations

Representations of M24


Maximal subgroups

Maximal subgroups of M24

Subgroup Order Index Programs/reps
M23 10 200 960 24Program: Standard generators
Program: Generators
M22:2 887 040 276Program: Generators
24:A8 322 560 759Program: Generators
M12:2 190 080 1 288Program: Generators
26:3.S6 138 240 1 771Program: Generators
L3(4):S3 120 960 2 024Program: Generators
26:(L3(2) S3) 64 512 3 795Program: Generators
L2(23) 6 072 40 320Program: Generators
L2(7) 168 1 457 280Program: Generators

Conjugacy classes

Notes

(M24) Problems of algebraic conjugacy are not yet dealt with.

Conjugacy classes of M24

Conjugacy class Centraliser order Power up Class rep(s)
1A244 823 040 Omitted owing to length.
2A21 504 4A 4B 6A 8A 12A 14A 14B ababababbababababbababababbababababb
2B7 680 4C 6B 10A 12B (ababbababb)3
3A1 080 6A 12A 15A 15B abababbabababbabababbabababb
3B504 6B 12B 21A 21B ababbababbababbababb
4A384 12A (abababb)3
4B128 8A ababababbababababb
4C96 12B (ababb)3
5A60 10A 15A 15B abababbababbabababbababb
6A24 12A abababbabababb
6B24 12B ababbababb
7A42 7B3 14A 14B 21A 21B (ababababbabbababababbabb)3
7B42 7A3 14A 14B 21A 21B ababababbabbababababbabb
8A16 ababababb
10A20 abababbababb
11A11 ababababbabbabb
12A12 abababb
12B12 ababb
14A14 14B3 (ababababbabb)3
14B14 14A3 ababababbabb
15A15 15B7 abababababb
15B15 15A7 (abababababb)7
21A21 21B5 ababababababb
21B21 21A5 (ababababababb)5
23A23 23B5 ab
23B23 23A5 (ab)5

Download words for class representatives.