Order = 14880 = 25.3.5.31.
Mult = 2.
Out = 2.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of L2(31) are a, b where a has order 2, b has order 3 and ab has order 31.

Standard generators of 2.L2(31) are preimages A, B where B has order 3 and AB has order 31.

Standard generators of L2(31):2 = PGL2(31) are c, d where c has order 2, d has order 3, cd has order 10 and cdcdd has order 8.

Standard generators of 2.L2(31).2 are C, D where D has order 3.

## Black box algorithms

### Checking generators (semi-presentations)

Group Semi-presentation File

## Presentations

L2(31) a, b | a2 = b3 = [a,b]3ab[a,b][a,bab][a,b−1abab] = 1 〉 Details
L2(31):2 c, d | c2 = d3 = (cd)10 = [c, d]8 = (cd(cdcdcd−1)3)2 = 1 〉 Details

## Conjugacy classes

### Conjugacy classes of L2(31)

Conjugacy class Centraliser order Power up Class rep(s)
1A 14 880 Omitted owing to length.
2A 32 abababbabababbabababbabababbabababbabababbabababbabababb
3A 15 (ababb)5
4A 16 abababbabababbabababbabababb
5A 15 (ababb)3
5B 15 (ababbababb)3
8A 16 (abababbabababb)3
8B 16 abababbabababb
15A 15 ababbababbababbababbababbababbababbababb
15B 15 ababb
15C 15 ababbababb
15D 15 ababbababbababbababb
16A 16 (abababb)27
16B 16 abababb
16C 16 (abababb)3
16D 16 (abababb)9
31A 31 ab
31B 31 (ab)3