Order = 60 = 22.3.5.
Mult = 2.
Out = 2.


Porting notes

Porting incomplete.

Standard generators

Standard generators of A5 = L2(5) = L2(4) are a, b where a has order 2, b has order 3 and ab has order 5.

Standard generators of 2.A5 = SL2(5) are preimages A, B where B has order 3 and AB has order 5.

Standard generators of S5 = A5:2 are c, d where c is in class 2B, d has order 4 and cd has order 5.

Standard generators of 2.S5 are preimages C, D where CD has order 5.

Standard generators of 2.S5i are preimages C, D where CD has order 5.


Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
A5 〈〈 a, b | some conditions 〉〉 Download

Presentations

Group Presentation Link
A5 a, b | a2 = b3 = (ab)5 = 1 〉 Details
2.A5 A, B | A4 = [A2, B] = B3 = (AB)5 = 1 〉 Details
S5 c, d | c2 = d4 = (cd)5 = [c, d]3 = 1 〉 Details
2.S5 C, D | C2 = D8 = [C, D4] = (CD)5 = [C, D]3 = 1 〉 Details
2.S5i C, D | C4 = C−2D4 = (CD)5 = [C, D]3 = 1 〉 Details

Representations

Representations of A5

Representations of 2.A5

Representations of S5

Representations of 2.S5

Representations of 2.S5i


Maximal subgroups

Maximal subgroups of A5

Subgroup Order Index Programs/reps
A4 12 5 Program: Generators
D10 10 6 Program: Generators
S3 6 10 Program: Generators

Maximal subgroups of S5

Subgroup Order Index Programs/reps
A5 60 2 Program: Standard generators
S4 24 5 Program: Generators
5:4 20 6 Program: Generators
S3 × 2 = D12 12 10 Program: Generators