Order = 372000 = 25.3.53.31.
Mult = 1.
Out = 2.

## Porting notes

Porting incomplete.

## Standard generators

Type I generators of L3(5) are a, b where a has order 3, b is in class 5A and has order 20.

Type II generators of L3(5) are x, y where x has order 2, y has order 3, xy has order 31 and xyxyy has order 5.

Standard generators of L3(5):2 are c, d where c is in class 2B, d is in class 4D and cd has order 12.

## Black box algorithms

### Checking generators (semi-presentations)

Group Semi-presentation File
L3(5) 〈〈 a, b | o(a) = 3, o(b) = 5, o(ab) = 20, o(a2babab) = 10 〉〉 Download

## Presentations

L3(5) a, b | a3 = b5 = aba−1baba−1b2ab−2a−1b2 = abab−2(a−1b2a−1b−2)3 = 1 〉 Details
L3(5) x, y | x2 = y3 = (xy)31 = [x, y]5 = ((xy)5(xy−1)4)2 = 1 〉 Details
L3(5):2 c, d | c2 = d4 = (cd)12 = (cdcd2cd2)3 = [d2, cdc]3 = [c, dcdcd−1cdcdcd−1cdcd] = 1 〉 Details

## Maximal subgroups

### Maximal subgroups of L3(5)

Subgroup Order Index Programs/reps
52:GL2(5) 12 000 31
52:GL2(5) 12 000 31
S5 120 3 100
42:S3 96 3 875
F93 = 31:3 93 4 000

### Maximal subgroups of L3(5):2

Subgroup Order Index Programs/reps
L3(5) 372 000 2Program: Standard generators
51+2. 4 000 186Program: Generators
GL2(5).2 960 775Program: Generators
S5 × 2 240 3 100Program: Standard generators
42:D12 192 3 875Program: Generators
F186 = 31:6 186 4 000Program: Generators