ATLAS: Alternating group A23

Order = 12926008369442488320000
Mult = 2.
Out = 2.

The following information is available for A23:


Standard generators

Standard generators of A23 are a of order 3 (in the smallest conjugacy class of elements of elements of order 3), b of order 21 such that ab has order 23. This forces b to be in the conjugacy class of 21-cycles.
In the natural representation we may take a = (1,2,3) and b = (3,4,5,6,7,8, ... ,23).

Standard generators of S23 are c of order 2 (belonging to the smallest conjugacy class of outer involutions), d of order 22 such that cd has order 23. This forces d to be in the conjugacy class of 22-cycles.
In the natural representation we may take c = (1, 2) and d = (2, 3, 4, 5, 6, 7, 8, ..., 23).


Black box algorithms

To find standard generators of A23:

To find standard generators of S23:


Representations

The representations of A23 available are: The representations of S23 available are:
Main ATLAS page Go to main ATLAS (version 2.0) page.
Alternating groups page Go to alternating groups page.
ftp access Anonymous ftp access is also available on sylow.mat.bham.ac.uk.

Version 2.0 created on 17th February 2004.
Last updated 01.03.04 by SN.