Mult = 2.

Out = 2.

The following information is available for A_{20}:

Standard generators of A_{20} are **a** of order 3
(belonging to the smallest conjugacy class of elements of order 3),
**b** of order 19 such that **ab** has order 18 and **[a,b]**
has order 2.

In the natural
representation we may take
**a** = (1, 2, 3) and
**b** = (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,19,20).

Standard generators of S_{20} are **c** of order 2
(belonging to the smallest conjugacy class of outer involutions),
**d** of order 19 such that **cd** has order 20.

In the natural
representation we may take
**c** = (1, 2) and
**d** = (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20).

To find standard generators of A_{20}:

- Find an element of order 51, 78, 132, 165 or 168 (probability about 1/14)
and power up to give an element
*a*in class 3A. - Find an element
*t*of order 19 (probability about 1/10). - Find a conjugate
*b*of*t*such that*ab*has order 17 and*a*has order 2 (probability about 1/127).^{-1}b^{-1}ab - The elements
*a*and*b*are standard generators for A_{20}.

To find standard generators of S_{20}:

- Find an element of order 34, 130 or 154 (probability about 1/23) and
power up to give an element
*c*in the class of transpositions. (Alternatively, if you restrict your search to outer elements, then elements of order 120 and 126 also work, and the probability increases to about 1/9.) - Find an element
*t*of order 19 (probability 1/19). - Find an conjugate
*d*of*t*such that*cd*has order 20 (probability 1/10). - The elements
*c*and*d*are standard generators for S_{20}.

- 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 27.02.04 by SN.