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.

## 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)
1A5 859 000 000 (abababbabababbabbababbabababbababb)6
2A14 400 (abababbabababbabbababbabababbababb)3
3A378 000 (bababbabababbababbabbababbabababbababb)8
3B720 (abababbabababbabbababbabababbababb)2
4A480 (bababbabababbababbabbababbabababbababb)6
4B480 (abababbabbababbabababbababb)6
5A375 000 (abababbabababbababbabbababbabababbababb)4
5B15 000 (abababbababbabbababbabababbababb)4
5C3 750 (ababbabababbababb)2
5D1 875 (ababbabababbababbabababbabbababbabababbababb)3
5E1 250 (ababababbabababbababbabbababbabababbababb)2
6A720 (bababbabababbababbabbababbabababbababb)4
6B720 (abababbabbababbabababbababb)4
6C36 abababbabababbabbababbabababbababb
7A21 (ababbabababbabbababbabababbababb)3
8A24 (bababbabababbababbabbababbabababbababb)3
8B24 (abababbabbababbabababbababb)3
10A600 (abababbabababbababbabbababbabababbababb)2
10B600 (abababbababbabbababbabababbababb)2
10C50 ababbabababbababb
10D50 ababababbabababbababbabbababbabababbababb
12A24 (bababbabababbababbabbababbabababbababb)2
12B24 (abababbabbababbabababbababb)2
15A750 (abbababbabababbababb)2
15B75 abababbababbabbababbabababbababb
15C75 ababbabababbababbabababbabbababbabababbababb
15D75 (ababbabababbababbabababbabbababbabababbababb)2
15E30 (ababbabababbababbabbababbabababbababb)2
20A20 abababbababbabbababbabababbababb
20B20 abababbabababbababbabbababbabababbababb
21A21 (ababbabababbabbababbabababbababb)2
21B21 ababbabababbabbababbabababbababb
24A24 (bababbabababbababbabbababbabababbababb)7
24B24 bababbabababbababbabbababbabababbababb
24C24 abababbabbababbabababbababb
24D24 (abababbabbababbabababbababb)7
25A25 abbababbabababbababb
30A30 abbababbabababbababb
30B30 ababbabababbababbabbababbabababbababb
31A31 ababababbababb
31B31 (ababababbababb)2
31C31 (ababababbababb)4
31D31 (ababababbababb)8
31E31 (ababababbababb)16