ATLAS: Linear group L3(7)

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

The following information is available for L3(7):


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.

Conjugacy classes

A set of generators for the maximal cyclic subgroups of L3(7) can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements.

A set of generators for the maximal cyclic subgroups of L3(7):2 can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements.


Main ATLAS page Go to main ATLAS (version 2.0) page.
Linear groups page Go to linear groups page.
Old L3(7) page Go to old L3(7) page - ATLAS version 1.
ftp access Anonymous ftp access is also available on for.mat.bham.ac.uk.

Version 2.0 created on 22nd March 2001.
Last updated 14.12.01 by RAW.
Information checked to Level 0 on 14.12.01 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.