Order = 5859000000 =
26.33.56.7.31.
Mult = 1.
Out = 1.
Porting notes
Porting incomplete.Standard generators
Standard generators of G2(5) are a, b where a is in class 2A, b is in class 3B, ab has order 7 and ababb has order 15.
Representations
Representations of G2(5)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 3906 a Std Cosets of N(5A) Details 3906 b Std Cosets of N(5A2) Details 7750 Std Details 7875 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 124 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 124 Std Details 3 GF(3) 651 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 7 Std Natural representation Details 5 GF(5) 14 Std Lie algebra Details 5 GF(5) 27 Std Details 5 GF(5) 64 Std Details 5 GF(5) 77 a Std Details 5 GF(5) 77 b Std Details 5 GF(5) 97 Std Details 5 GF(5) 182 Std Details 5 GF(5) 189 Std Details 5 GF(5) 196 Std Details 5 GF(5) 371 Std Details 5 GF(5) 469 Std Details 5 GF(5) 483 Std Details 5 GF(5) 721 Std Details 5 GF(5) 792 Std Details
Maximal subgroups
Maximal subgroups of G2(5)
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 51+4:GL2(5) | Program: Generators |
||
| 52+1+2:GL2(5) = 53+2:GL2(5) = N(5A2) | Program: Generators |
||
| 3.U3(5):2 | Program: Generators |
||
| L3(5):2 | Program: Generators |
||
| 2.(A5×A5).2 | Program: Generators |
||
| U3(3):2 | Program: Generators |
||
| 23.L3(2) | Program: Generators |
Conjugacy classes
Conjugacy classes of G2(5)
| Conjugacy class | Centraliser order | Power up | Class rep(s) |
|---|---|---|---|
| 1A | 5 859 000 000 |
(abababbabababbabbababbabababbababb)6 |
|
| 2A | 14 400 |
(abababbabababbabbababbabababbababb)3 |
|
| 3A | 378 000 |
(bababbabababbababbabbababbabababbababb)8 |
|
| 3B | 720 |
(abababbabababbabbababbabababbababb)2 |
|
| 4A | 480 |
(bababbabababbababbabbababbabababbababb)6 |
|
| 4B | 480 |
(abababbabbababbabababbababb)6 |
|
| 5A | 375 000 |
(abababbabababbababbabbababbabababbababb)4 |
|
| 5B | 15 000 |
(abababbababbabbababbabababbababb)4 |
|
| 5C | 3 750 |
(ababbabababbababb)2 |
|
| 5D | 1 875 |
(ababbabababbababbabababbabbababbabababbababb)3 |
|
| 5E | 1 250 |
(ababababbabababbababbabbababbabababbababb)2 |
|
| 6A | 720 |
(bababbabababbababbabbababbabababbababb)4 |
|
| 6B | 720 |
(abababbabbababbabababbababb)4 |
|
| 6C | 36 |
abababbabababbabbababbabababbababb |
|
| 7A | 21 |
(ababbabababbabbababbabababbababb)3 |
|
| 8A | 24 |
(bababbabababbababbabbababbabababbababb)3 |
|
| 8B | 24 |
(abababbabbababbabababbababb)3 |
|
| 10A | 600 |
(abababbabababbababbabbababbabababbababb)2 |
|
| 10B | 600 |
(abababbababbabbababbabababbababb)2 |
|
| 10C | 50 |
ababbabababbababb |
|
| 10D | 50 |
ababababbabababbababbabbababbabababbababb |
|
| 12A | 24 |
(bababbabababbababbabbababbabababbababb)2 |
|
| 12B | 24 |
(abababbabbababbabababbababb)2 |
|
| 15A | 750 |
(abbababbabababbababb)2 |
|
| 15B | 75 |
abababbababbabbababbabababbababb |
|
| 15C | 75 |
ababbabababbababbabababbabbababbabababbababb |
|
| 15D | 75 |
(ababbabababbababbabababbabbababbabababbababb)2 |
|
| 15E | 30 |
(ababbabababbababbabbababbabababbababb)2 |
|
| 20A | 20 |
abababbababbabbababbabababbababb |
|
| 20B | 20 |
abababbabababbababbabbababbabababbababb |
|
| 21A | 21 |
(ababbabababbabbababbabababbababb)2 |
|
| 21B | 21 |
ababbabababbabbababbabababbababb |
|
| 24A | 24 |
(bababbabababbababbabbababbabababbababb)7 |
|
| 24B | 24 |
bababbabababbababbabbababbabababbababb |
|
| 24C | 24 |
abababbabbababbabababbababb |
|
| 24D | 24 |
(abababbabbababbabababbababb)7 |
|
| 25A | 25 |
abbababbabababbababb |
|
| 30A | 30 |
abbababbabababbababb |
|
| 30B | 30 |
ababbabababbababbabbababbabababbababb |
|
| 31A | 31 |
ababababbababb |
|
| 31B | 31 |
(ababababbababb)2 |
|
| 31C | 31 |
(ababababbababb)4 |
|
| 31D | 31 |
(ababababbababb)8 |
|
| 31E | 31 |
(ababababbababb)16 |
Download words for class representatives.