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.
Representations
Representations of Sz(32)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 1025 Std Details 198400 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z[i, ½] 124 a Std Details 0 Z[i, ½] 124 b Std Details 2 GF(32) 4 a Std Details 5 GF(5) 124 a Std Details 41 GF(41) 124 b Std Details
Representations of Sz(32):5
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 1025 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 20 Std Details 5 GF(5) 124 Std Details 5 GF(5) 248 Std Details 41 GF(41) 124 Std Details
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) |
|---|---|---|---|
| 1A | 32 537 600 |
bbbb |
|
| 2A | 1 024 | bb |
|
| 4A | 64 | b |
|
| 4B | 64 | (b)31 |
|
| 5A | 25 |
(abb)5 |
|
| 25A | 25 | abb |
|
| 25B | 25 |
abbabbabbabbabbabbabbabb |
|
| 25C | 25 |
abbabb |
|
| 25D | 25 |
abbabbabbabbabbabbabbabbabbabbabbabbabbabbabbabb |
|
| 25E | 25 |
abbabbabbabb |
|
| 31A | 31 |
(ababbb)5 |
|
| 31B | 31 |
(ababbbababbb)5 |
|
| 31C | 31 |
(ababbbababbbababbbababbb)5 |
|
| 31D | 31 |
(ababbbababbbababbbababbbababbbababbbababbbababbb)5 |
|
| 31E | 31 |
Omitted
owing to
length. |
|
| 31F | 31 |
(ababbb)25 |
|
| 31G | 31 |
(ababbbababbb)25 |
|
| 31H | 31 |
(ababbbababbbababbbababbb)25 |
|
| 31I | 31 |
(ababbbababbbababbbababbbababbbababbbababbbababbb)25 |
|
| 31J | 31 |
Omitted
owing to
length. |
|
| 31K | 31 |
ababbb |
|
| 31L | 31 |
ababbbababbb |
|
| 31M | 31 |
ababbbababbbababbbababbb |
|
| 31N | 31 |
ababbbababbbababbbababbbababbbababbbababbbababbb |
|
| 31O | 31 |
Omitted
owing to
length. |
|
| 41A | 41 |
(ababbabbababbabbababbabbababbabb)3 |
|
| 41B | 41 |
(ababbabbababbabbababbabbababbabb)6 |
|
| 41C | 41 |
(ababbabbababbabbababbabbababbabb)12 |
|
| 41D | 41 |
(ababbabbababbabbababbabbababbabb)11 |
|
| 41E | 41 |
(ababbabbababbabbababbabbababbabb)7 |
|
| 41F | 41 |
ababbabbababbabbababbabbababbabb |
|
| 41G | 41 |
Omitted
owing to
length. |
|
| 41H | 41 |
Omitted
owing to
length. |
|
| 41I | 41 |
ababbabb |
|
| 41J | 41 |
ababbabbababbabb |
Download words for class representatives.
Conjugacy classes of Sz(32):5
| Conjugacy class | Centraliser order | Power up | Class rep(s) |
|---|---|---|---|
| 1A | 162 688 000 | ||
| 2A | 5 120 | ||
| 4A | 320 | ||
| 4B | 320 | ||
| 5A | 125 | ||
| 25A | 25 |
cddcdcddcdcddcddccdcddcddc |
|
| 31A | 31 | ||
| 31B | 31 | ||
| 31C | 31 | ||
| 41A | 41 | ||
| 41B | 41 | ||
| 5B | 100 | ||
| 5C | 100 | ||
| 5D | 100 | ||
| 5E | 100 | ||
| 10A | 20 | ||
| 10B | 20 | ||
| 10C | 20 | ||
| 10D | 20 | ||
| 20A | 20 | ||
| 20B | 20 | ||
| 20C | 20 | ||
| 20D | 20 | ||
| 20E | 20 | ||
| 20F | 20 | ||
| 20G | 20 | ||
| 20H | 20 | ||
| 25B | 25 | ||
| 25C | 25 | ||
| 25D | 25 | ||
| 25E | 25 | ||
| 31A-O |
cdcddcddc |
||
| 41A-J |
cdcddcdd |
||
| 20A-B'''' | cdd |
||
| 25F-F'''' |
cdcddcdcddcddc |
Download words for class representatives.