Order = 1876896 = 25.32.73.19.
Mult = 3.
Out = S3.

Porting notes

Porting incomplete.

Standard generators

Standard generators of L3(7) are a, b where a has order 2, b has order 3, ab has order 19 and ababb has order 6.

Standard generators of 3.L3(7) are preimages A, B where A has order 2 and AB has order 19.

Standard generators of L3(7).2 are c, d where c is in class 2B, d is in class 4B, cd has order 19 and cdcdd has order 8.

Standard generators of 3.L3(7).2 are preimages C, D where CD has order 19.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File

Maximal subgroups

Maximal subgroups of L3(7)

Subgroup Order Index Programs/reps
72:2.L2(7):2
72:2.L2(7):2
L2(7).2
L2(7).2
L2(7).2
(3 x A4)2
32:Q8
19:3

Maximal subgroups of L3(7).2

Subgroup Order Index Programs/reps
L3(7) Program: Generators
71+2:(3 x D8) Program: Generators
2.(2 x L2(7)).2
L2(7)×2
S3 x S4
32:SD16
19:6

Conjugacy classes

Conjugacy classes of L3(7)

Conjugacy class Centraliser order Power up Class rep(s)
1A1 876 896 Omitted owing to length.
2A672 abababbabababbabababbabababbabababbabababbabababbabababb
3A36 ababbababb
4A16 abababbabababbabababbabababb
6A12 ababb
7A686 abbabababbababbabbabababbababb
7B49 aabababbabbabababbababb
7C49 abbabababbababbabababbababbabbabababbababb
7D49 baabababbabbabababbababbaabababbabbabababbababb
8A16 (abababbabababb)3
8B16 abababbabababb
14A14 abbabababbababb
16A16 (abababb)27
16B16 (abababb)3
16C16 abababb
16D16 (abababb)9
19A19 abababab
19B19 Omitted owing to length.
19C19 ab
19D19 abababababababab
19E19 abababababababababababababababab
19F19 abab

Conjugacy classes of L3(7).2

Conjugacy class Centraliser order Power up Class rep(s)
1A3 753 792 (cdcdd)8
2A1 344 (cdcdd)4
3A72 (cccdcddcdcdcddcdcdcdd)2
4A32 (cdcdd)2
6A24 (cccdcddcdcdcddcdd)2
7A1 372 (cdcdcdd)4
7B98 (ccdcddcdcdcdd)2
7C49 ccdcddcdcdcddcdcdcddcccdcddcdcdcdd
8A32 (cdd)2
8B32 (ccdcddcdcdcddcdd)2
14A28 (cdcdcdd)2
16A16 (ccdcddcdcdcddcdd)3
16C16 ccdcddcdcdcddcdd
19A19 cd
19C19 (cd)2
19E19 (cd)4
2B672 (cccdcddcdcdcddcdcdcdd)3
4B672 (cccdcddcdcdcddcdd)3
6D12 cccdcddcdcdcddcdcdcdd
8C16 cdcdd
12B12 cccdcddcdcdcddcdd
14B14 ccdcddcdcdcdd
16E16 cdd
16F16 (cdd)3
28A28 cdcdcdd
28B28 (cdcdcdd)5