Order = 51765179004000000 = 28.37.56.7.11.31.37.67.
Mult = 1.
Out = 1.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of Ly are a, b where a has order 2, b is in class 5A, ab has order 14 and abababb has order 67.

## Black box algorithms

### Checking generators (semi-presentations)

Group Semi-presentation File
Ly 〈〈 a, b | o(a) = 2, o(b) = 5, o(ab) = 14, o(abababb) = 67, o(z) = 42, o(rs) = 14, o(rsrss) = 30; z = (ab)5(abb)2, r = z14, s = bababbabababb 〉〉 Download

## Maximal subgroups

### Maximal subgroups of Ly

Subgroup Order Index Programs/reps
G2(5) Program: Standard generators
3.McL:2 Program: Standard generators
53.L3(5) Program: Generators
2.A11 Program: Generators
51+4:4.S6 Program: Generators
35:(2 × M11) Program: Generators
32+4:2.A5.D8 Program: Generators
67:22 = F1474 1 474 35 118 846 000 000 Program: Generators
37:18 666 77 725 494 000 000 Program: Generators

## Conjugacy classes

### Conjugacy classes of Ly

Conjugacy class Centraliser order Power up Class rep(s)
1A 51 765 179 004 000 000 Omitted owing to length.
2A 39 916 800 4A 6A 6B 6C 8A 8B 10A 10B 12A 12B 14A 18A 20A 22A 22B 24A 24B 24C 28A 30A 30B 40A 40B 42A 42B (ababbababbbababbababbbababbababbbababbababbb)3
3A 2 694 384 000 6A 12A 15A 15C 21A 21B 24A 30A 33A 33B 42A 42B Omitted owing to length.
3B 174 960 6B 6C 9A 12B 15B 18A 24B 24C 30B Omitted owing to length.
4A 20 160 8A 8B 12A 12B 20A 24A 24B 24C 28A 40A 40B (ababbababbbababbababbb)3
5A 2 250 000 10A 15A 15B 20A 25A 30A 30B 40A 40B Omitted owing to length.
5B 3 750 10B 15C aababbababbbababbbaababbababbbababbb
6A 120 960 12A 24A 30A 42A 42B ababbababbbababbababbbababbababbbababbababbb
6B 2 160 12B 24B 24C 30B Omitted owing to length.
6C 324 18A (abababbababbbabbabababbb)3
7A 168 14A 21A 21B 28A 42A 42B Omitted owing to length.
8A 480 24A 40A 40B (ababbababbb)3
8B 96 24B 24C (abbababbababbababbb)3
9A 54 18A abababbababbbabbabababbbabababbababbbabbabababbb
10A 3 600 20A 30A 30B 40A 40B abababbbabababbbabababbbabababbb
10B 50 aababbababbbababbb
11A 66 11B2 22A 22B 33A 33B abbabababbbabbabababbbabbabababbbabbabababbb
11B 66 11A2 22A 22B 33A 33B abbabababbbabbabababbb
12A 288 24A ababbababbbababbababbb
12B 72 24B 24C abbababbababbababbbabbababbababbababbb
14A 168 28A 42A 42B abababbbababbababbbabababbbababbababbb
15A 2 250 30A abbabb
15B 90 30B aababbababbbaababbababbb
15C 75 babababbb
18A 18 abababbababbbabbabababbb
20A 40 40A 40B abababbbabababbb
21A 42 21B2 42A 42B ababbababbababbbababbababbababbb
21B 42 21A2 42A 42B Omitted owing to length.
22A 22 22B7 abbabababbb
22B 22 22A7 (abbabababbb)7
24A 24 ababbababbb
24B 24 24C7 (abbababbababbababbb)7
24C 24 24B7 abbababbababbababbb
25A 25 ababb
28A 28 abababbbababbababbb
30A 90 abb
30B 90 aababbababbb
31A 31 31B3 31C8 31D4 31E2 abbababbababbbabbababbababbbabbababbababbbabbababbababbb
31B 31 31A2 31C3 31D8 31E4 Omitted owing to length.
31C 31 31A4 31B2 31D3 31E8 Omitted owing to length.
31D 31 31A8 31B4 31C2 31E3 abbababbababbb
31E 31 31A3 31B8 31C4 31D2 abbababbababbbabbababbababbb
33A 33 33B2 babababbababbbbabababbababbb
33B 33 33A2 babababbababbb
37A 37 37B2 abababbababbb
37B 37 37A2 abababbababbbabababbababbb
40A 40 40B7 (abababbb)7
40B 40 40A7 abababbb
42A 42 42B11 (ababbababbababbb)11
42B 42 42A11 ababbababbababbb
67A 67 67B4 67C2 ababbb
67B 67 67A2 67C4 ababbbababbb
67C 67 67A4 67B2 ababbbababbbababbbababbb