Order = 43589145600 = 210.35.52.72.11.13.
Mult = 2.
Out = 2.

Porting notes

Porting incomplete.

Standard generators

Standard generators of A14 are a, b where a is in class 3A, b has order 13, ab has order 12, abb has order 24 and ababb has order 20. Alternatively: a is in class 3A, b has order 13, ab has order 12 and [a,b] has order 2.

Standard generators of 2.A14 are preimages A, B where A has order 3 and B has order 13.

Standard generators of S14 = A14:2 are c, d where c is in class 2D, d has order 13 and ab has order 14.

Standard generators of 2.S14 are preimages C, D where D has order 13.

Standard generators of 2.S14 (isoclinic) are preimages C, D where D has order 13.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
A14 〈〈 a, b | some conditions 〉〉 Download

Presentations

Group Presentation Link
A14 〈 a, b | a3 = b13 = (ab)12 = [a,b]2 = (aabab)2 = [a,babab]2 = (aabababab)2 = (aabababababab)2 = [a,babababab]2 = 1 〉 Details
2.A14 〈 A, B | some relations 〉 Details
S14 〈 c, d | some relations 〉 Details
2.S14 〈 C, D | some relations 〉 Details
2.S14 (isoclinic) 〈 C, D | some relations 〉 Details

Representations

Representations of A14

Representations of 2.A14

Representations of S14

Representations of 2.S14

Representations of 2.S14 (isoclinic)