Order = 4585351680 = 29.39.5.7.13.
Mult = 2.
Out = 2.


Porting notes

Porting complete except note about some representatios not necessarily in standard generators. Check your representation carefully!

Standard generators

Standard generators of S6(3) are a, b where a is in class 2A, b has order 5, ab has order 13 and abb has order 14.

Standard generators of 2.S6(3) are preimages A, B where B has order 5 and AB has order 13.

Standard generators of S6(3):2 are c, d where c is in class 2A, d is in class 4F, cd has order 20 and cdd has order 8.

Standard generators of 2.S6(3).2 are preimages C, D where CDCDCDCDDCDDD has order 13.

Standard generators of 2.S6(3).2 (isoclinic) are preimages C, D where CDCDCDCDDCDDD has order 13.


Representations

Representations of S6(3)

Representations of 2.S6(3)

Representations of S6(3):2

Representations of 2.S6(3).2


Maximal subgroups

Maximal subgroups of S6(3)

Subgroup Order Index Programs/reps
31+4:2.U4(2) Program: Generators
36:L3(3) Program: Generators
2.(A4 × U4(2)) Program: Generators
22+6:33:S3 Program: Generators
L2(27):3 Program: Generators
U3(3):2 × 2 Program: Generators
L3(3):2 Program: Generators
L2(13) Program: Generators
L2(13) Program: Generators
A5 Program: Generators
31+4:2.(S4 × A4)

Maximal subgroups of S6(3):2

Subgroup Order Index Programs/reps
31+4:2.U4(2):2
36:(L3(3) × 2)
31+4:2.(S4 × S4)
2.(A4 × U4(2)).2
22+6:33:D12
L2(27):6
(U3(3) × 4):2
L3(3):2 × 2
S5