Order = 9999360 = 210.32.5.7.31.
Mult = 1.
Out = 2.

Porting notes

Porting incomplete. Comment in stdgens.

Standard generators

Standard generators of L5(2) are a, b where a is in class 2A, b has order 5 and ab has order 21.

Standard generators of L5(2):2 are c, d where c is in class 2C, d is in class 8B, cd has order 21 and cdcdd has order 8.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
L5(2) 〈〈 a, b | some conditions 〉〉 Download

Representations

Representations of L5(2)

Representations of L5(2):2

Maximal subgroups

Maximal subgroups of L5(2)

Subgroup Order Index Programs/reps
24:L4(2)
24:L4(2)
26:(S3 × L3(2))
26:(S3 × L3(2))
31:5

Maximal subgroups of L5(2):2

Subgroup Order Index Programs/reps
L5(2) Program: Standard generators
21+6:L3(2):2
L4(2):2 = S8
24+4:(S3 × S3):2
S3 × L3(2):2
31:10

Conjugacy classes

Conjugacy classes of L5(2)

Conjugacy class Centraliser order Power up Class rep(s)
1A 9 999 360 Omitted owing to length.
2A 21 504 abababbababababbababababbababababbab
2B 1 536 babababbababababbababbbabababbababababbababb
3A 504 Omitted owing to length.
3B 180 bbabababbababababbababbbbabababbababababbababb
4A 384 (abababbababababbababababbababb)3
4B 128 abababbababababbab
4C 32 babababbababababbababb
5A 15 (abababbababb)3
6A 24 abababbababababbababababbababbabababbababababbababababbababb
6B 12 bbabababbababababbababb
7A 42 abababbababababbababbabababbababababbababb
7B 42 (abababbababababbababbabababbababababbababb)3
8A 16 abababbab
12A 12 abababbababababbababababbababb
14A 14 abababbababababbababb
14B 14 (abababbababababbababb)3
15A 15 abababbababb
15B 15 (abababbababb)7
21A 21 (ab)5
21B 21 ab
31A 31 (abb)27
31B 31 abb
31C 31 (abb)243
31D 31 (abb)9
31E 31 (abb)3
31F 31 (abb)81

Download words for class representatives.