Order = 25920 = 26.34.5.
Mult = 2.
Out = 2.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of U4(2) = S4(3) are a, b where a is in class 2A, b has order 5 and ab has order 9.

Standard generators of 2.U4(2) = Sp4(3) are preimages A, B where B has order 5 and AB has order 9.

Standard generators of U4(2):2 = S4(3):2 are c, d where c is in class 2C, d has order 9 and cd has order 10.

Standard generators of 2.U4(2):2 are preimages C, D where D has order 9.

## Black box algorithms

### Checking generators (semi-presentations)

Group Semi-presentation File
U4(2) 〈〈 a, b | some conditions 〉〉 Download

## Presentations

U4(2) a, b | a2 = b5 = (ab)9 = [a, b]3 = [a, bab]2 = 1 〉 Details

## Representations

### Representations of 2.U4(2):2

• View detailed report.
• Permutation representations:
Number of points ID Generators Description Link
240 Std Details
• Matrix representations
Char Ring Dimension ID Generators Description Link
3 GF(3) 4 Std Details

## Conjugacy classes

### Conjugacy classes of U4(2)

Conjugacy class Centraliser order Power up Class rep(s)
1A 25 920 abaababbababbabaababbababbabaababbababbabaababbababb
2A 576 (ababb)3
2B 96 abaababbababbabaababbababb
3A 648 abbabbabbabbabbabbabbabb
3B 648 abbabbabbabb
3C 108 ababbababb
3D 54 bababaababbababbbababaababbababb
4A 48 (abb)3
4B 8 abaababbababb
5A 5 b
6A 72 abbabb
6B 72 (abbabb)5
6C 36 (ababb)5
6D 36 ababb
6E 18 bababaababbababb
6F 12 aababbababb
9A 9 ab
9B 9 abab
12A 12 (abb)5
12B 12 abb

### Conjugacy classes of U4(2):2

Conjugacy class Centraliser order Power up Class rep(s)
1A 51 840 (cdcdcddcdcdddcdd)4
2A 1 152 (cdd)4
2B 192 (cdcdcddcdcdddcdd)2
3A 648 (cdcdd)4
3C 216 (ccdcdddcddd)2
3D 108 (cddcdcdddcdd)2
4A 96 (cdd)2
4B 16 cdcdcddcdcdddcdd
5A 10 (cd)2
6A 72 (cdcdd)2
6C 36 ccdcdddcddd
6E 36 cddcdcdddcdd
6F 24 (cdcdcdd)2
9A 9 d
12A 12 cdcdd
2C 1 440 (ccdcdcddcdcdddcddcddcdcdddcdd)3
2D 96 (cdcdddcdd)3
4C 96 (cdcdcdd)3
4D 32 dcdcdcdd
6G 36 ccdcdcddcdcdddcddcddcdcdddcdd
6H 36 dcdd
6I 12 cdcdddcdd
8A 8 cdd
10A 10 cd
12C 12 cdcdcdd