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 The representations of L3(7):2 available are The representations of SL3(7) = 3.L3(7) available are The representations of 3.L3(7):2 available are

Maximal subgroups

The maximal subgroups of L3(7) are as follows. The maximal subgroups of L3(7):2 are as follows.
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- R.A.Wilson@bham.ac.uk
- richard@ukonline.co.uk