Order = 32736 = 25.3.11.31.
Mult = 1.
Out = 5.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of L2(32) are a, b where a has order 2, b has order 3 and ab is in class 31A/B/C/D/E. Alternatively: a has order 2, b has order 3, ab has order 31 and ababb has order 11.

Standard generators of L2(32):5 are c, d where c has order 2, d has order 5, cd has order 15, cdd has order 15, cdcdd has order 15, cdcdcdd has order 15 and cdcdcdcddcdcddcdd has order 11.

### Notes

• (L2(32):5) The conditions ensure that d is conjugate to the field automorphism x -> x16.

## Black box algorithms

### Checking generators (semi-presentations)

Group Semi-presentation File

## Presentations

L2(32) a, b | a2 = b3 = (ab)31 = (ab)4(ab−1abab−1)3(ab)4(ab−1)2 = 1 〉 Details
L2(32):5 c, d | c2 = d5 = cdcdcd−2cd−1cd−2cdcd−2cd−1 cd2cd−2 = (cd)4cd−2(cd2)3cd−2cd2cd−1cdcd2 = 1 〉 Details

## Conjugacy classes

### Conjugacy classes of L2(32)

Conjugacy class Centraliser order Power up Class rep(s)
1A32 736 aa
2A32 a
3A33 (ababababb)11
11A33 (ababababbababababbababababbababababb)3
11B33 Omitted owing to length.
11C33 Omitted owing to length.
11D33 (ababababb)3
11E33 (ababababbababababb)3
31A31 ab
31B31 abab
31C31 abababab
31D31 abababababababab
31E31 abababababababababababababababab
31F31 (abababab)9
31G31 (abababababababab)9
31H31 (abababababababababababababababab)9
31I31 (ab)9
31J31 (abab)9
31K31 (abab)3
31L31 (abababab)3
31M31 (abababababababab)3
31N31 (abababababababababababababababab)3
31O31 (ab)3
33A33 (ababababb)10
33B33 (ababababb)13
33C33 (ababababb)7
33D33 (ababababb)14
33E33 (ababababb)5
33F33 ababababb
33G33 ababababbababababb
33H33 ababababbababababbababababbababababb
33I33 Omitted owing to length.
33J33 Omitted owing to length.

### Conjugacy classes of L2(32):5

Conjugacy class Centraliser order Power up Class rep(s)
1A163 680 (cdcddcddd)10
2A160 (cdcddcddd)5
3A165 (cd)5
11A33 (cdcdcddd)3
31A31 (cdcddcdd)3
31F31 cdcddcdd
31K31 (cdcddcdd)9
33A33 cdcdcddd
33F33 (cdcdcddd)5
5A30 (cdcddcddd)16
5A'30 (cdcddcddd)2
5A''30 (cdcddcddd)8
5A'''30 (cdcddcddd)4
10A10 cdcddcddd
10A'10 (cdcddcddd)27
10A''10 (cdcddcddd)3
10A'''10 (cdcddcddd)9
15A15 cd
15A'15 (cd)2
15A''15 (cd)8
15A'''15 (cd)4