Order = 2520 = 23.32.5.7.
Mult = 6.
Out = 2.


Porting notes

Porting incomplete.

Standard generators

Standard generators of A7 are a, b where a is in class 3A, b has order 5 and ab has order 7.

Standard generators of 2.A7 are preimages A, B where A has order 3 and B has order 5. Alternatively: A has order 3 and AB has order 7 or A has order 5 and AB has order 7.

Standard generators of 3.A7 are preimages A, B where B has order 5 and AB has order 7.

Standard generators of 6.A7 are preimages A, B where B has order 5 and AB has order 7.

Standard generators of S7 are c, d where c is in class 2B, d is in class 6C and cd has order 7.

Standard generators of 2.S7 are preimages C, D where CD has order 7.

Standard generators of 3.S7 are preimages C, D where CD has order 7.

Standard generators of 6.S7 are preimages C, D where CD has order 7.

Standard generators of 2.S7 (isoclinic) are preimages C, D where CD has order 7.

Standard generators of 6.S7 (isoclinic) are preimages C, D where CD has order 7.


Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
A7 〈〈 a, b | some conditions 〉〉 Download

Representations

Representations of A7

Representations of 2.A7

Representations of 3.A7

Representations of 6.A7

Representations of S7

Representations of 2.S7

Representations of 3.S7

Representations of 6.S7

Representations of 2.S7 (isoclinic)


Maximal subgroups

Maximal subgroups of A7

Subgroup Order Index Programs/reps
A6 360 7Program: Generators
L2(7) 168 15Program: Generators
L2(7) 168 15
S5 120 21
(A4 × 3):2 72 35

Maximal subgroups of S7

Subgroup Order Index Programs/reps
A7 2 520 2Program: Generators
S6 720 7Program: Generators
S5 2 240 21Program: Generators
S4 S3 144 35Program: Generators
7:6 42 120Program: Generators