Order = 32537600 = 210.52.31.41.
Mult = 1.
Out = 5.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of Sz(32) are a, b where a has order 2, b has order 4, ab has order 5, ab2 has order 25 and abab2ab3 has order 25. Alternatively: a has order 2, b has order 4, ab has order 5, abab2 has order 25 and ababab2abab2ab2 has order 25.

Standard generators of Sz(32):5 are c, d where c has order 2, d has order 5, cd has order 5, cdcd4 has order 5, cd2cd3 has order 31 and cdcd2cd3 has order 10.

## Maximal subgroups

### Maximal subgroups of Sz(32)

Subgroup Order Index Programs/reps
25+5:31 Program: Generators
41:4 Program: Generators
25:4 Program: Generators
D62 Program: Generators

### Maximal subgroups of Sz(32):5

Subgroup Order Index Programs/reps
Sz(32)
25+5:31:5
41:20
25:20
31:10

## Conjugacy classes

### Conjugacy classes of Sz(32)

Conjugacy class Centraliser order Power up Class rep(s)
1A32 537 600 bbbb
2A1 024 bb
4A64 b
4B64 (b)31
5A25 (abb)5
25A25 abb
25B25 abbabbabbabbabbabbabbabb
25C25 abbabb
25D25 abbabbabbabbabbabbabbabbabbabbabbabbabbabbabbabb
25E25 abbabbabbabb
31A31 (ababbb)5
31B31 (ababbbababbb)5
31C31 (ababbbababbbababbbababbb)5
31D31 (ababbbababbbababbbababbbababbbababbbababbbababbb)5
31E31 Omitted owing to length.
31F31 (ababbb)25
31G31 (ababbbababbb)25
31H31 (ababbbababbbababbbababbb)25
31I31 (ababbbababbbababbbababbbababbbababbbababbbababbb)25
31J31 Omitted owing to length.
31K31 ababbb
31L31 ababbbababbb
31M31 ababbbababbbababbbababbb
31N31 ababbbababbbababbbababbbababbbababbbababbbababbb
31O31 Omitted owing to length.
41A41 (ababbabbababbabbababbabbababbabb)3
41B41 (ababbabbababbabbababbabbababbabb)6
41C41 (ababbabbababbabbababbabbababbabb)12
41D41 (ababbabbababbabbababbabbababbabb)11
41E41 (ababbabbababbabbababbabbababbabb)7
41F41 ababbabbababbabbababbabbababbabb
41G41 Omitted owing to length.
41H41 Omitted owing to length.
41I41 ababbabb
41J41 ababbabbababbabb

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

Conjugacy class Centraliser order Power up Class rep(s)
1A162 688 000
2A5 120
4A320
4B320
5A125
25A25 cddcdcddcdcddcddccdcddcddc
31A31
31B31
31C31
41A41
41B41
5B100
5C100
5D100
5E100
10A20
10B20
10C20
10D20
20A20
20B20
20C20
20D20
20E20
20F20
20G20
20H20
25B25
25C25
25D25
25E25
31A-O cdcddcddc
41A-J cdcddcdd
20A-B'''' cdd
25F-F'''' cdcddcdcddcddc