Order = 175560 = 23.3.5.7.11.19.
Mult = 1.
Out = 1.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of J1 are a, b where a has order 2, b has order 3, ab has order 7 and ababb has order 19.

## Black box algorithms

### Finding generators

Group Algorithm File

### Checking generators (semi-presentations)

Group Semi-presentation File
J1 〈〈 a, b | o(a) = 2, o(b) = 3, o(ab) = 7, o(abab2) = 19 〉〉 Download

## Presentations

J1 a, b | a2 = b3 = (ab)7 = (ab(abab−1)3)5 = (ab(abab−1)6abab(ab−1)2)2 = 1 〉 Details

## Maximal subgroups

### Maximal subgroups of J1

Subgroup Order Index Programs/reps
L2(11) Program: Standard generators
23:7:3 = F168 Program: Generators
2 × A5 Program: Generators
19:6 = F114 Program: Generators
11:10 = F110 Program: Generators
D6 × D10 Program: Generators
7:6 = F42 Program: Generators

## Conjugacy classes

### Conjugacy classes of J1

Conjugacy class Centraliser order Power up Class rep(s)
1A 175 560 (ababbababbabababbabbababbababbabababbabb)3
2A 120 6A 10A 10B (ababbababbabababbabb)3
3A 30 6A 15A 15B ababbababbabababbabbababbababbabababbabb
5A 30 5B2 10A 10B 15A 15B ababbabababbabbababbabababbabb
ababbabababbabbababbabababbabb
5B 30 5A2 10A 10B 15A 15B ababbabababbabbababbabababbabbababbabababbabbababbabababbabb
6A 6 ababbababbabababbabb
ababbababbabababbabb
7A 7 ab
ab
10A 10 10B3 (ababbabababbabb)3
10B 10 10A3 ababbabababbabb
ababbabababbabb
ababbabababbabb
11A 11 abababbabbababbabababbabbababbabababbabb
abababbabbababbabababbabbababbabababbabb
15A 15 15B2 abababbabbabababbabb
15B 15 15A2 abababbabb
abababbabb
abababbabb
19A 19 19B4 19C2 ababb
ababb
ababb
19B 19 19A2 19C4 ababbababb
19C 19 19A4 19B2 ababbababbababbababb