Order = 168 = 23.3.7.
Mult = 2.
Out = 2.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of L3(2) = L2(7) are a, b where a has order 2, b has order 3 and ab has order 7.

Standard generators of SL2(7) = 2.L2(7) are preimages A, B where B has order 3 and AB has order 7.

Standard generators of L2(7):2 = PGL2(7) = L3(2):2 are c, d where c is in class 2B, d has order 3, cd has order 8 (necessarily in class 8A) and cdcdd has order 4.

Standard generators of 2.PGL2(7) = 2.L2(7).2 are preimages C, D where D has order 3.

Standard generators of 2.L2(7).2i = 2.L2(7):2 are preimages C, D where D has order 3.

## Black box algorithms

### Checking generators (semi-presentations)

Group Semi-presentation File

## Presentations

L3(2) a, b | a2 = b3 = (ab)7 = [a, b]4 = 1 〉 Details
SL2(7) A, B | A4 = [A2,B] = B3 = (AB)7 = B2[A,B]4 = 1 〉 Details
L2(7):2 c, d | c2 = d3 = (cd)8 = [c, d]4 = 1 〉 Details

## Maximal subgroups

### Maximal subgroups of L3(2)

Subgroup Order Index Programs/reps
S4 Program: Generators
Program: Generators
Program: Generators
S4 Program: Generators
Program: Generators
Program: Generators
7:3 = F21 Program: Generators
Program: Generators
Program: Generators

### Maximal subgroups of L2(7):2

Subgroup Order Index Programs/reps
L2(7) Program: Standard generators
7:6 = F42 Program: Generators
D16 Program: Generators
D12 Program: Generators