Order = 660 = 22.3.5.11.
Mult = 2.
Out = 2.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of L2(11) are a, b where a has order 2, b has order 3 and ab has order 11.

Standard generators of 2.L2(11) = SL2(11) are preimages A, B where B has order 3 and AB has order 11.

Standard generators of L2(11):2 = PGL2(11) are c, d where c is in class 2B, d has order 3, cd has order 10 (necessarily in class 10A) and cdcdd has order 11.

Standard generators of 2.L2(11).2 = 2.PGL2(11) are preimages C, D where D has order 3.

## Black box algorithms

### Checking generators (semi-presentations)

Group Semi-presentation File
L2(11) 〈〈 a, b | o(a) = 2, o(b) = 3, o(ab) = 11 〉〉 Download
L2(11):2 〈〈 c, d | o(c) = 2, o(d) = 3, o(cd) = 10, o(cdcd2) = 11 〉〉 Download

## Presentations

L2(11) a, b | a2 = b3 = (ab)11 = [a, babab]2 = 1 〉 Details
L2(11):2 c, d | c2 = d3 = (cd)10 = (cdcdcd−1)4 = [c, dcdcd−1cd−1cd−1cdcd] = 1 〉 Details

## Maximal subgroups

### Maximal subgroups of L2(11)

Subgroup Order Index Programs/reps
A5 Program: Generators
A5 Program: Generators
F55 = 11:5 Program: Generators
D12 Program: Generators

### Maximal subgroups of L2(11):2

Subgroup Order Index Programs/reps
L2(11) Program: Generators
F110 = 11:10 Program: Generators
S4 Program: Generators
D24 Program: Generators
D20 Program: Generators

## Conjugacy classes

### Conjugacy classes of L2(11)

Conjugacy class Centraliser order Power up Class rep(s)
1A660 (ababababbababababb)3
2A12 (ababababb)3
3A6 ababababbababababb
5A5 abababb
5B5 abababbabababb
6A6 ababababb
11A11 ab
11B11 abab

### Conjugacy classes of L2(11):2

Conjugacy class Centraliser order Power up Class rep(s)
1A1 320 (cdcdcddcdcdd)12
2A24 (cdcdcddcdcdd)6
3A12 (cdcdcddcdcdd)4
5A10 (cd)4
5B10 (cd)2
6A12 (cdcdcddcdcdd)2
11A11 cdcdd
2B20 (cd)5
4A12 (cdcdcddcdcdd)3
10A10 cd
10B10 (cd)3
12A12 cdcdcddcdcdd
12B12 (cdcdcddcdcdd)5