Order = 16482816 = 29.32.72.73.
Mult = 1.
Out = 6.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of L3(8) are a, b where a has order 2, b has order 3 and ab has order 21.

Standard generators of L3(8).2 are c, d where c is in class 2B, d has order 3, cd has order 8, cdcdd has order 63 and cdcdcdd has order 8.

Standard generators of L3(8).3 are e, f where e has order 2, f has order 12, ef has order 21, efeff has order 7, efefeff has order 12, efefefeff has order 12 and efefeffefeffeffeff has order 9.

Standard generators of L3(8).6 are g, h where g is in class 2A, h is in class 18D, gh has order 24, ghghh has order 14, ghghghh has order 3 and ghghghghghhghghhghh has order 6.

## Black box algorithms

### Checking generators (semi-presentations)

Group Semi-presentation File

## Maximal subgroups

### Maximal subgroups of L3(8)

Subgroup Order Index Programs/reps
26:(7xL2(8)) Program: Generators
26:(7xL2(8)) Program: Generators
72:S3 Program: Generators
73:3 Program: Generators
L2(7) Program: Generators

### Maximal subgroups of L3(8).2

Subgroup Order Index Programs/reps
L3(8) Program: Generators
2(3+6):72:2 Program: Generators
D14xL2(8) Program: Generators
72:D12 Program: Generators
73:6 Program: Generators
L2(7):2 Program: Generators

### Maximal subgroups of L3(8).3

Subgroup Order Index Programs/reps
L3(8) Program: Generators
26:(7xL2(8)):3 Program: Generators
26:(7xL2(8)):3 Program: Generators
72:(3xS3) Program: Generators
73:9 Program: Generators
L2(7)x3 Program: Generators

### Maximal subgroups of L3(8).6

Subgroup Order Index Programs/reps
L3(8).3 Program: Generators
L3(8).2 Program: Generators
2(3+6):72:6 Program: Generators
(D14xL2(8)):3 Program: Generators
72:(6xS3) Program: Generators
73:18 Program: Generators
L2(7):2x3 Program: Generators

## Conjugacy classes

### Conjugacy classes of L3(8)

Conjugacy class Centraliser order Power up Class rep(s)
1A 16 482 816
2A 3 584
3A 63
4A 64 abbabababbababbabbabababbabbabbabbabababbababb
7A 3 528
7B 3 528
7C 3 528
7D 3 528
7E 3 528
7F 3 528
7G 49 abbabababbabbabbabbabababbababb
7H 49
7I 49 (ababb)4
7J 49
7K 49
9A 63
9B 63
9C 63
14A 56 (abbabbabbabababbababb)9
14B 56
14C 56
14D 56
14E 56
14F 56
21A 63
21B 63
21C 63
21D 63
21E 63
21F 63
63A 63 (ababababbabb)43
63B 63
63C 63
63D 63
63E 63
63F 63
63G 63
63H 63
63I 63
63J 63
63K 63
63L 63
63M 63
63N 63
63O 63
63P 63
63Q 63
63R 63
73A 73 (abababbab)12
73B 73
73C 73
73D 73
73E 73
73F 73
73G 73
73H 73
73I 73
73J 73
73K 73
73L 73
73M 73
73N 73
73O 73
73P 73
73Q 73
73R 73
73S 73
73T 73
73U 73
73V 73
73W 73
73X 73

### Conjugacy classes of L3(8).2

Conjugacy class Centraliser order Power up Class rep(s)
1A 32 965 632
2A 7 168
3A 126
4A 128
7A 3 528
7B 3 528
7C 3 528
7D 49
7E 98
7F 98
7G 98 cdcdcdcddcdcdcddcddcdcdd
9A 126
9B 126
9C 126
14A 56 (cdcdcddcddcdcdcddcdcddcdd)3
14B 56
14C 56
21A 63
21B 63
21C 63
63A 63 (cdcdd)10
63B 63
63C 63
63D 63
63E 63
63F 63
63G 63
63H 63
63I 63
73A 73 (cdcdcddcdcddcdd)7
73B 73
73C 73
73D 73
73E 73
73F 73
73G 73
73H 73
73I 73
73J 73
73K 73
73L 73
2B 1 008
6A 18
8A 32
8B 32
14D 14
14E 14
14F 14
18A 18
18B 18
18C 18
8A-B cd
14G-I cdcdcddcdcddcddcdd
18A-C cdcdcdcddcdd

### Conjugacy classes of L3(8).3

Conjugacy class Centraliser order Power up Class rep(s)
1A 49 448 448
2A 10 752
3A 189
4A 192
7A 3 528
7D 3 528
7G 147
7H 147
7I 49 efefefeffeffefefefeffeffefefeff
9A 63
14A 56 efefeffeffefefefefeffeffeffeff
14B 56
21A 63
21D 63
63A 63 (efefefefeffeffeffeff)23
63B 63
63C 63
63D 63
63E 63
63F 63
73A 73 (efefefeffefeffeffeff)9
73B 73
73C 73
73D 73
73E 73
73F 73
73G 73
73H 73
3B 504
3C 504
6A 24
6B 24
9D 9 efefefefeffeff
9D' 9
12A 12 f
12B 12
21G 21 ef
21G' 21
21H 21
21H' 21

### Conjugacy classes of L3(8).6

Conjugacy class Centraliser order Power up Class rep(s)
1A 98 896 896
2A 21 504
3A 378
4A 384
7A 3 528
7B 147
7C 98
9A 126
14A 56 ghghghghhghhghhghghh
21A 63
63A 63 (ghghghghhghghhghhghh)5
63B 63
63C 63
73A 73 (ghghghhghh)3
73B 73
73C 73
73D 73
2B 3 024
6A 54
8A 96
8B 96
14G 14 ghghh
18A 18 ghghghghhghhghh
3B 1 008
3C 1 008
6B 48
6C 48 ghghghghghhghghhghh
9B 18
9C 18
12A 24
12B 24
21G 21 ghghhghghghhghhghhghghh
21C 21
6D 36
6E 36
18D 18 h
18D' 18
24A 24
24A' 24
24B 24
24B' 24
24A-B gh