ATLAS: Linear group L2(3)

Order = 1092.
Mult = 2.
Out = 2.

The following information is available for L2(13):


Standard generators

Standard generators of L2(13) are a and b where a has order 2, b has order 3 and ab has order 13.
Standard generators of the double cover 2.L2(13) = SL2(13) are pre-images A and B where B has order 3 and AB has order 13.

Standard generators of L2(13).2 are c and d where c has order 2 (necessarily class 2B), d has order 4 and cd has order 13.
Standard generators of the double cover 2.L2(13).2 are pre-images C and D where CD has order 13.

Automorphisms

The outer automorphism of L2(13) may be achieved by applying this program to the standard generators.

Representations

The representations available are The representations of 2.L2(13) available are The representations of L2(13).2 available are The representations of 2L2(13).2 available are

Maximal subgroups

The maximal subgroups of L2(13) are as follows. The maximal subgroups of L2(13):2 are as follows.

Conjugacy classes

A set of generators for the maximal cyclic subgroups of L2(13) can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements.
In the double cover, the element ABABABB is in class +6A, for compatibility with the ABC.

A set of generators for the maximal cyclic subgroups of L2(13):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 L2(13) page Go to old L2(13) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 file created on 21st January 2002, from Version 1 file last updated on 13.03.96.
Last updated 29.01.02 by RAW.
Information checked to Level 0 on 21.01.02 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.