Order = 9196830720 = 215.36.5.7.11.
Mult = 22 × 3.
Out = S3.

## Porting notes

Porting incomplete. This needs a lot of work. Some of the reps may be under the wrong group. The names seem to have been copied very badly. Meaning of U62S3 stdgens?

## Standard generators

Standard generators of U6(2) = Fi21 are a, b where a is in class 2A, b has order 7, ab has order 11 and abb has order 18.

Standard generators of 2.U6(2) are preimages A, B where B has order 7, AB has order 11 and ABBB has order 11.

Standard generators of 3.U6(2) are preimages A, B where A has order 2 and B has order 7.

Standard generators of 6.U6(2) are preimages A, B where A has order 2, B has order 7, AB has order 33 and ABBB has order 11.

Standard generators of 22.U6(2) are preimages A, B where B has order 7 and AB has order 11.

Standard generators of (22 × 3).U6(2) are preimages A, B where A has order 2, B has order 7 and AB has order 33.

Standard generators of U6(2):2 are c, d where c is in class 2D, d is in class 6J and cd has order 11.

Standard generators of 2.U6(2).2 are preimages C, D where CD has order 11.

Standard generators of 3.U6(2):2 are preimages C, D where CD has order 11.

Standard generators of 6.U6(2).2 are preimages C, D where CD has order 11.

Standard generators of 22.U6(2):2 are preimages C, D where C has order 2, D has order 6 and (CD)3(CDCDD)2(CDD)2 has order 7.

Standard generators of U6(2):3 are e, f where e is in class 3D, f has order 11, ef has order 21 and eff has order 18.

Standard generators of 3.U6(2):3 are preimages E, F where F has order 11.

Standard generators of 22.U6(2):3 are preimages E, F where F has order 11.

Standard generators of U6(2):S3 are g, h where g is in class 2D, h is in class 6J [6J'/6J'' from the point of view of U6(2)] and gh has order 21.

Standard generators of 3.U6(2):S3 are preimages G, H.

## Representations

### Representations of (22 × 3).U6(2)

• View detailed report.
• Permutation representations:
Number of points ID Generators Description Link
4704StdDetails
8064StdDetails
• Matrix representations
Char Ring Dimension ID Generators Description Link
2GF(4)27aStdDetails

### Representations of U6(2):S3

• View detailed report.
• Permutation representations:
Number of points ID Generators Description Link
693StdDetails
891StdDetails
• Matrix representations
Char Ring Dimension ID Generators Description Link
2GF(2)20StdDetails
2GF(2)34StdDetails
2GF(2)140a0StdDetails
2GF(2)140a1StdDetails
2GF(2)140a2StdDetails
2GF(2)154StdDetails
2GF(2)400StdDetails
Char Ring Dimension ID Generators Description Link
3GF(3)21aStdDetails
3GF(3)210aStdDetails
3GF(3)229aStdDetails
3GF(3)364aStdDetails
Char Ring Dimension ID Generators Description Link
5GF(5)22aStdDetails
Char Ring Dimension ID Generators Description Link
7GF(7)22aStdDetails
Char Ring Dimension ID Generators Description Link
11GF(11)22aStdDetails

## Maximal subgroups

### Maximal subgroups of U6(2)

Subgroup Order Index Programs/reps
U5(2) 13 685 760 672Program: Generators
Program: Standard generators
21+8:U4(2) 13 271 040 693Program: Generators
29:L3(4) 10 321 920 891Program: Generators
U4(3):22 6 531 840 1 408Program: Generators
Program: Standard generators
U4(3):22 6 531 840 1 408Program: Generators
U4(3):22 6 531 840 1 408Program: Generators
24+8:(S3 × A5) 1 474 560 6 237Program: Generators
S6(2) 1 451 520 6 336Program: Generators
Program: Standard generators
S6(2) 1 451 520 6 336Program: Generators
S6(2) 1 451 520 6 336Program: Generators
M22 443 520 20 736Program: Standard generators
Program: Generators
M22 443 520 20 736Program: Generators
M22 443 520 20 736Program: Generators
U4(2) × S3 155 520 59 136Program: Generators
31+4:(Q8 × Q8):S3 93 312 98 560Program: Generators
L3(4):21 40 320 228 096Program: Generators

### Maximal subgroups of U6(2):2

Subgroup Order Index Programs/reps
U6(2)
U5(2):2
21+8:U4(2):2
29:L3(4).2
U4(3):(22)122
24+8:(S3 × S5)
S6(2) × 2
M22:2
U4(2):2 × S3
31+4:(Q8 × Q8):S3.2
L3(4):22

### Maximal subgroups of U6(2):3

Subgroup Order Index Programs/reps
U6(2)
U5(2) × 3
21+8:(U4(2) × 3)
29:L3(4):3
24+8:(S3 × A5).3
U4(2) × S3 × 3
31+4:(Q8 × Q8):S3.3
35:S6
L3(4):6
L2(8):3 × 3

### Maximal subgroups of U6(2):S3

Subgroup Order Index Programs/reps
U6(2):3
U6(2):2
(U5(2) × 3):2
21+8:(U4(2) × 3):2
29:L3(4).S3
24+8:(S3 × A5).S3
(U4(2) × S3 × 3).2
31+4:(Q8 × Q8):S3.S3
35:(S6 × 2)
L3(4):D12
L2(8):3 × S3