Order = 4680000 = 26.32.54.13.
Mult = 2.
Out = 2.


Porting notes

Fully copied from version 2. 29/7/06.

Standard generators

Standard generators of S4(5) are a, b where a is in class 2B, b is in class 3B and ab is in class 13C. Alternatively: a is in class 2B, b is in class 3B, ab has order 13 and ababb has order 12.

Standard generators of 2.S4(5) are preimages A, B where B has order 3 and AB has order 13.

Standard generators of S4(5):2 are c, d where c is in class 2D, d is in class 3B and cd is in class 26A. Alternatively: c is in class 2D, d is in class 3B, cd has order 26 and cdcdd has order 10.

Standard generators of 2.S4(5):2 are preimages C, D where D has order 3.

Standard generators of 2.S4(5).2 (isoclinic) are preimages C, D where D has order 3.


Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
S4(5) 〈〈 a, b | some conditions 〉〉 Download

Representations

Representations of S4(5)

Representations of 2.S4(5)

Representations of S4(5):2


Maximal subgroups

Maximal subgroups of S4(5)

Subgroup Order Index Programs/reps
51+2:4A5 Program: Generators
53:(2 × A5).2 Program: Generators
L2(25):22 Program: Generators
2.(A5 × A5).2 Program: Generators
24:A5 Program: Generators
S3 × S5 Program: Generators
(2 × 2 × A5):2 Program: Generators
A6 Program: Generators