# ATLAS: Linear group L3(7)

Order = 1876896.
Mult = 3.
Out = S3.

### Standard generators

Standard generators of L3(7) are a and b where a has order 2, b has order 3, ab has order 19, and ababb has order 6.
Standard generators of 3.L3(7) are preimages A and B where A has order 2 and AB has order 19.

Standard generators of L3(7).2 are c and d where c is in class 2B, d is in class 4B, cd has order 19, and cdcdd has order 8.
Standard generators of 3.L3(7).2 are preimages C and D where CD has order 19.

### Representations

The representations of L3(7) available are
• a and b as permutations on 57 points.
• a and b as 152 x 152 matrices over GF(2).
• a and b as 55 x 55 matrices over GF(3).
• a and b as 57 x 57 matrices over GF(3).
• a and b as 96 x 96 matrices over GF(3).
• a and b as 96 x 96 matrices over GF(3).
• a and b as 96 x 96 matrices over GF(3).
• a and b as 342 x 342 matrices over GF(3).
• a and b as 399 x 399 matrices over GF(3).
• a and b as 8 x 8 matrices over GF(7).
• a and b as 10 x 10 matrices over GF(7).
• a and b as 10 x 10 matrices over GF(7).
• a and b as 27 x 27 matrices over GF(7).
The representations of L3(7):2 available are
• c and d as 152 x 152 matrices over GF(2).
• c and d as 57 x 57 matrices over GF(3).
• c and d as 96 x 96 matrices over GF(3).
• c and d as 8 x 8 matrices over GF(7).
• c and d as 20 x 20 matrices over GF(7).
The representations of SL3(7) = 3.L3(7) available are
• A and B as 3 x 3 matrices over GF(7) - the natural representation.
The representations of 3.L3(7):2 available are
• C and D as 6 x 6 matrices over GF(7).

### Maximal subgroups

The maximal subgroups of L3(7) are as follows.
• 7^2:2.L2(7):2.
• 7^2:2.L2(7):2.
• L2(7):2.
• L2(7):2.
• L2(7):2.
• (3 x A4)2.
• 3^2:Q8.
• 19:3
The maximal subgroups of L3(7):2 are as follows.
• L3(7).
• 7^1+2:(3 x D8).
• 2.(2 x L2(7)).2
• L2(7):2 x2.
• S3 x S4.
• 3^2:SD16.
• 19:6.