Order = 2448 = 24.32.17.
Mult = 2.
Out = 2.

Porting notes

Porting incomplete.

Standard generators

Standard generators of L2(17) are a, b where a has order 2, b has order 3 and ab has order 17.

Standard generators of 2.L2(17) are preimages A, B where B has order 3 and AB has order 17.

Standard generators of L2(17):2 = PGL2(17) are c, d where c is in class 2B, d has order 3, cd has order 16 (necessarily in class 16B) and cdcdd has order 4.

Standard generators of 2.L2(17).2 are preimages C, D where D has order 3.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
L2(17) 〈〈 a, b | some conditions 〉〉 Download


Group Presentation Link
L2(17) a, b | a2 = b3 = (ab)17 = ((ab)5(ab−1)3)2 = 1 〉 Details
L2(17):2 c, d | c2 = d3 = (cd)16 = [c, d]4 = [a, (ab)5]2 = 1 〉 Details


Representations of L2(17)

Representations of 2.L2(17)

Representations of L2(17):2

Representations of 2.L2(17).2

Conjugacy classes

Conjugacy classes of L2(17)

Conjugacy class Centraliser order Power up Class rep(s)
1A2 448 Omitted owing to length.
2A16 ababababbababababbababababbababababb
3A9 (ababb)3
4A8 ababababbababababb
8A8 (ababababb)3
8B8 ababababb
9A9 ababb
9B9 ababbababb
9C9 ababbababbababbababb
17A17 ab
17B17 (ab)3

Download words for class representatives.