Order = 504 = 23.32.7.
Mult = 1.
Out = 3.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of L2(8) are a, b where a has order 2, b has order 3 and ab has order 7.

Standard generators of L2(8):3 are c, d where c has order 2, d has order 3, cd has order 9 and cdcdcd−1cdcd−1cd−1 has order 7. Alternatively: c has order 2, d has order 3, cd has order 9 and cdcdcd−1cd−1cdcd−1 has order 2.

## Black box algorithms

### Checking generators (semi-presentations)

Group Semi-presentation File

## Maximal subgroups

### Maximal subgroups of L2(8)

Subgroup Order Index Programs/reps
23:7 = F56
D18
D14

### Maximal subgroups of L2(8):3

Subgroup Order Index Programs/reps
L2(8)
23:7:3 = 23:F21
9:6
7:6 = F42

## Conjugacy classes

### Conjugacy classes of L2(8)

Conjugacy class Centraliser order Power up Class rep(s)
1A 504 (aaa)2
2A 8 aaa
3A 9 (ababb)3
7A 7 ab
7B 7 (ab)2
7C 7 (ab)4
9A 9 ababb
9B 9 (ababb)2
9C 9 (ababb)4

### Conjugacy classes of L2(8):3

Conjugacy class Centraliser order Power up Class rep(s)
1A 1 512 (cdcdcdd)6
2A 24 (cdcdcdd)3
3A 27 (cdcdd)3
7A 7 cdcdcddcdd
9A 9 cdcdd
3B 18 (cdcdcdd)4
3B' 18 (cdcdcdd)2
6A 6 cdcdcdd
6A' 6 (cdcdcdd)5
9D 9 cd
9D' 9 (cd)2