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)
1A9 999 360 Omitted owing to length.
2A21 504 abababbababababbababababbababababbab
2B1 536 babababbababababbababbbabababbababababbababb
3A504 Omitted owing to length.
3B180 bbabababbababababbababbbbabababbababababbababb
4A384 (abababbababababbababababbababb)3
4B128 abababbababababbab
4C32 babababbababababbababb
5A15 (abababbababb)3
6A24 abababbababababbababababbababbabababbababababbababababbababb
6B12 bbabababbababababbababb
7A42 abababbababababbababbabababbababababbababb
7B42 (abababbababababbababbabababbababababbababb)3
8A16 abababbab
12A12 abababbababababbababababbababb
14A14 abababbababababbababb
14B14 (abababbababababbababb)3
15A15 abababbababb
15B15 (abababbababb)7
21A21 (ab)5
21B21 ab
31A31 (abb)27
31B31 abb
31C31 (abb)243
31D31 (abb)9
31E31 (abb)3
31F31 (abb)81

Download words for class representatives.