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
L3(8) 〈〈 a, b | some conditions 〉〉 Download

Representations

Representations of L3(8)

Representations of L3(8).2

Representations of L3(8).3

Representations of L3(8).6

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)
1A16 482 816
2A3 584
3A63
4A64 abbabababbababbabbabababbabbabbabbabababbababb
7A3 528
7B3 528
7C3 528
7D3 528
7E3 528
7F3 528
7G49 abbabababbabbabbabbabababbababb
7H49
7I49 (ababb)4
7J49
7K49
9A63
9B63
9C63
14A56 (abbabbabbabababbababb)9
14B56
14C56
14D56
14E56
14F56
21A63
21B63
21C63
21D63
21E63
21F63
63A63 (ababababbabb)43
63B63
63C63
63D63
63E63
63F63
63G63
63H63
63I63
63J63
63K63
63L63
63M63
63N63
63O63
63P63
63Q63
63R63
73A73 (abababbab)12
73B73
73C73
73D73
73E73
73F73
73G73
73H73
73I73
73J73
73K73
73L73
73M73
73N73
73O73
73P73
73Q73
73R73
73S73
73T73
73U73
73V73
73W73
73X73

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Conjugacy classes of L3(8).2

Conjugacy class Centraliser order Power up Class rep(s)
1A32 965 632
2A7 168
3A126
4A128
7A3 528
7B3 528
7C3 528
7D49
7E98
7F98
7G98 cdcdcdcddcdcdcddcddcdcdd
9A126
9B126
9C126
14A56 (cdcdcddcddcdcdcddcdcddcdd)3
14B56
14C56
21A63
21B63
21C63
63A63 (cdcdd)10
63B63
63C63
63D63
63E63
63F63
63G63
63H63
63I63
73A73 (cdcdcddcdcddcdd)7
73B73
73C73
73D73
73E73
73F73
73G73
73H73
73I73
73J73
73K73
73L73
2B1 008
6A18
8A32
8B32
14D14
14E14
14F14
18A18
18B18
18C18
8A-B cd
14G-I cdcdcddcdcddcddcdd
18A-C cdcdcdcddcdd

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Conjugacy classes of L3(8).3

Conjugacy class Centraliser order Power up Class rep(s)
1A49 448 448
2A10 752
3A189
4A192
7A3 528
7D3 528
7G147
7H147
7I49 efefefeffeffefefefeffeffefefeff
9A63
14A56 efefeffeffefefefefeffeffeffeff
14B56
21A63
21D63
63A63 (efefefefeffeffeffeff)23
63B63
63C63
63D63
63E63
63F63
73A73 (efefefeffefeffeffeff)9
73B73
73C73
73D73
73E73
73F73
73G73
73H73
3B504
3C504
6A24
6B24
9D9 efefefefeffeff
9D'9
12A12 f
12B12
21G21 ef
21G'21
21H21
21H'21

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Conjugacy classes of L3(8).6

Conjugacy class Centraliser order Power up Class rep(s)
1A98 896 896
2A21 504
3A378
4A384
7A3 528
7B147
7C98
9A126
14A56 ghghghghhghhghhghghh
21A63
63A63 (ghghghghhghghhghhghh)5
63B63
63C63
73A73 (ghghghhghh)3
73B73
73C73
73D73
2B3 024
6A54
8A96
8B96
14G14 ghghh
18A18 ghghghghhghhghh
3B1 008
3C1 008
6B48
6C48 ghghghghghhghghhghh
9B18
9C18
12A24
12B24
21G21 ghghhghghghhghhghhghghh
21C21
6D36
6E36
18D18 h
18D'18
24A24
24A'24
24B24
24B'24
24A-B gh

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