ATLAS: Alternating group A21

Order = 25545471085854720000
Mult = 2.
Out = 2.

The following information is available for A21:


Standard generators

Standard generators of A21 are a of order 3 (in the smallest conjugacy class of elements of elements of order 3), b of order 19 such that ab has order 21.
In the natural representation we may take a = (1,2,3) and b = (3,4,5,6,7,8, ... ,21).

Standard generators of S21 are c of order 2 (belonging to the smallest conjugacy class of outer involutions), d of order 20 such that cd has order 21.
In the natural representation we may take c = (1, 2) and d = (2, 3, 4, 5, 6, 7, 8, ..., 21).


Black box algorithms

To find standard generators of A21: To find standard generators of S21

Representations

The representations of A21 available are: The representations of S21 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 24th February 2004.
Last updated 01.03.04 by SN.