ATLAS: Alternating group A22

Order = 562000363888803840000
Mult = 2.
Out = 2.

The following information is available for A22:


Standard generators

Standard generators of A22 are a of order 3 (belonging to the smallest conjugacy class of elements of order 3), b of order 21 such that ab has order 20 and [a,b] has order 2. 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 = (2, 3, 4, 5, 6, 7, 8, ..., 22).

Standard generators of S22 are c of order 2 (belonging to the smallest conjugacy class of outer involutions), d of order 21 such that cd has order 22. This forces d to be in the conjugacy class of 21-cycles.
In the natural representation we may take c = (1, 2) and d = (2, 3, 4, 5, 6, 7, 8, ..., 22).


Black box algorithms

To find standard generators of A22:

To find standard generators of S22:


Representations

The representations of A22 available are: The representations of S22 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.