Order = 17971200 = 211.33.52.13.
Mult = 1.
Out = 2.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of 2F4(2)' = T are a, b where a is in class 2A, b has order 3 and ab has order 13.

Standard generators of 2F4(2)'.2 = 2F4(2) are c, d where c is in class 2A, d is in class 4F, cd has order 12 and cdcd2cd3 has order 4.

## Presentations

2F4(2)' a, b | a2 = b3 = (ab)13 = [a, b]5 = [a, bab]4 = ((ab)4ab−1)6 = 1 〉 Details
2F4(2)'.2 c, d | c2 = d4 = (cd)12 = (cd2)8 = [c, d]5 = (cdcd2cd3)4 = (cdcd2cd2cd2)3cd−1(cd2)3 = [c, (dc)3(d−1c)2dcd−1cd−2] = [c, dcdcd−1cd2]2 = [c, d2cd]4 = (cd)4cd2cd(cd−1)4cd(cd2cd−1)2cdcd2cdcdcd−1cd−1cdcd2 = 1 〉 Details

## Representations

### Representations of 2F4(2)'.2

• View detailed report.
• Permutation representations:
Number of points ID Generators Description Link
1755 Std Details
2304 Std Details
• Matrix representations
Char Ring Dimension ID Generators Description Link
2 GF(2) 26 Std Details
2 GF(2) 246 Std Details
Char Ring Dimension ID Generators Description Link
3 GF(3) 52 Std Details
3 GF(3) 54 Std Details
3 GF(3) 77 Std Details
Char Ring Dimension ID Generators Description Link
5 GF(5) 27 Std Details
5 GF(5) 52 Std Details
5 GF(5) 78 Std Details
5 GF(5) 218 Std Details
Char Ring Dimension ID Generators Description Link
13 GF(13) 27 a Std Details
13 GF(13) 27 b Std Details
13 GF(13) 78 Std Details
13 GF(13) 1374 Std Details

## Maximal subgroups

### Maximal subgroups of 2F4(2)'

Subgroup Order Index Programs/reps
L3(3):2 Program: Generators
L3(3):2 Program: Generators
2.[28].5.4 Program: Generators
L2(25) Program: Generators
22.[28].S3 Program: Generators
A6.22 Program: Generators
A6.22 Program: Generators
52:4A4 Program: Generators

### Maximal subgroups of 2F4(2)'.2

Subgroup Order Index Programs/reps
2F4(2)' Program: Standard generators
13:12 = F156
31+2:SD16
2.[29].5.4
L2(25).23
22.[29].S3
52:4S4

## Conjugacy classes

### Conjugacy classes of 2F4(2)'

Conjugacy class Centraliser order Power up Class rep(s)
1A 17 971 200 Omitted owing to length.
2A 10 240 Omitted owing to length.
2B 1 536 abababbababababbababababbababababbab
3A 108 abababbabababbabababbabababb
4A 192 (abababb)3
4B 128 Omitted owing to length.
4C 64 abababbababababbab
5A 50 aabababbababababbabaabababbababababbab
6A 12 abababbabababb
8A 32 Omitted owing to length.
8B 32 Omitted owing to length.
8C 16 abababbab
8D 16 aabababbababababbabaabababbab
10A 10 aabababbababababbab
12A 12 abababb
12B 12 (abababb)5
13A 13 ab
13B 13 abab
16A 16 (abbaabababbababababbabaabababbab)5
16B 16 (abbaabababbababababbabaabababbab)3
16C 16 abbaabababbababababbabaabababbab
16D 16 (abbaabababbababababbabaabababbab)15