Order = 979200 =
Mult = 1.
Out = 4.

Porting notes

Porting incomplete. Standard generators have some comments

Standard generators

Standard generators of S4(4) are a, b where a is in class 2A/2B, b is in class 5E, ab has order 17 and ababb has order 15.

Standard generators of S4(4):2 are c, d where c is in class 2D, d is in class 4C/4D, cd has order 17 and cdd has order 4.

Standard generators of S4(4):4 are e, f where e is in class 2AB, f is in class 4F/4F', ef has order 16, eff has order 6, efeff has order 8 and efeffefff has order 6.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
S4(4) 〈〈 a, b | some conditions 〉〉 Download


Representations of S4(4)

Representations of S4(4):2

Representations of S4(4):4

Maximal subgroups

Maximal subgroups of S4(4)

Subgroup Order Index Programs/reps
26:(3 × A5) Program: Generators
26:(3 × A5) Program: Generators
L2(16):2 Program: Generators
L2(16):2 Program: Generators
(A5 × A5):2 Program: Generators
(A5 × A5):2 Program: Generators
S6 = A6:2 Program: Generators