Order = 14880 =
Mult = 2.
Out = 2.

Porting notes

Porting incomplete.

Standard generators

Standard generators of L2(31) are a, b where a has order 2, b has order 3 and ab has order 31.

Standard generators of 2.L2(31) are preimages A, B where B has order 3 and AB has order 31.

Standard generators of L2(31):2 = PGL2(31) are c, d where c has order 2, d has order 3, cd has order 10 and cdcdd has order 8.

Standard generators of 2.L2(31).2 are C, D where D has order 3.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
L2(31) 〈〈 a, b | some conditions 〉〉 Download


Group Presentation Link
L2(31) a, b | a2 = b3 = [a,b]3ab[a,b][a,bab][a,b−1abab] = 1 〉 Details
L2(31):2 c, d | c2 = d3 = (cd)10 = [c, d]8 = (cd(cdcdcd−1)3)2 = 1 〉 Details


Representations of L2(31)

Representations of 2.L2(31)

Representations of L2(31):2

Conjugacy classes

Conjugacy classes of L2(31)

Conjugacy class Centraliser order Power up Class rep(s)
1A14 880 Omitted owing to length.
2A32 abababbabababbabababbabababbabababbabababbabababbabababb
3A15 (ababb)5
4A16 abababbabababbabababbabababb
5A15 (ababb)3
5B15 (ababbababb)3
8A16 (abababbabababb)3
8B16 abababbabababb
15A15 ababbababbababbababbababbababbababbababb
15B15 ababb
15C15 ababbababb
15D15 ababbababbababbababb
16A16 (abababb)27
16B16 abababb
16C16 (abababb)3
16D16 (abababb)9
31A31 ab
31B31 (ab)3

Download words for class representatives.