Mult = 2.

Out = 2.

The following information is available for A_{23}:

Standard generators of A_{23} 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 S_{23} 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).

To find standard generators of A_{23}:

- Find an element of order 57, 195, 231, 273 or 330
(probability about 1/19)
and power up to give an element
*s*in class 3A. - Find an element
*t*of order 23 (probability about 1/12). - Find a conjugate
*u*of*t*such that*su*has order 21 (probability 1/140). - Let
*a = s*and^{-1}*b = su* - The elements
*a*and*b*are standard generators for A_{23}.

To find standard generators of S_{23}:

- Find an element of order 182, 198, 390, 462 or 630 (probability about
1/59)
and power up to give an element
*c*in the class of transpositions. (Alternatively, if you restrict your search to outer elements then an element of order 38 or 154 would also work, and would increase the probability at each attempt to about 1/13. - Find an element
*t*of order 23 (probability 1/23). - Find an conjugate
*u*of*t*such that*cu*has order 22 (probability 1/11). - The elements
*c*and*d = cu*are standard generators for S_{23}.

- Some primitive permutation representations
- Some integer matrix representations

- Some primitive permutation representations
- Some integer matrix representations

Go to main ATLAS (version 2.0) page.

Go to alternating groups page.

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.