ATLAS: Linear group L3(3)

Order = 5616 = 24.33.13.
Mult = 1.
Out = 2.

Standard generators

Standard generators of L3(3) are a and b where a has order 2, b is in class 3B and ab is in class 13A/B. The last condition is equivalent to: ab has order 13 and ababb has order 4.
Wlog define 13A to be the class containing ab, and then 8B is the class containing abababb.

Standard generators of L3(3):2 are c and d where c is in class 2B, d is in class 4B and cd is in class 13AB. The last condition is equivalent to: cd has order 13 and cdcdcdd has order 12.


The representations of L3(3) available are The representations of L3(3):2 available are

Maximal subgroups

The maximal subgroups of L3(3) are as follows. The maximal subgroups of L3(3):2 are as follows.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Linear groups page Go to linear groups page.
Old L3(3) page Go to old L3(3) page - ATLAS version 1.
ftp access Anonymous ftp access is also available on

Version 2.0 created on 13th December 2001.
Last updated 13.12.01 by RAW.
Information checked to Level 0 on 13.12.01 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.