Mult = 2.

Out = 2.

The following information is available for A_{19}:

Standard generators of A_{19} are **a** of order 3
(in the smallest conjugacy class of elements of elements of order 3),
**b** of order 17 such that **ab** has order 19.

In the natural representation we may take
**a** = (1,2,3) and
**b** = (3,4,5,6,7,8, ... ,19).

Standard generators of S_{19} are **c** of order 2
(belonging to the smallest conjugacy class of outer involutions),
**d** of order 18 such that **cd** has order 19. This
forces **d** to belong to the conjugacy class of 18-cycles.

In the natural
representation we may take
**c** = (1, 2) and
**d** = (2, 3, 4, 5, 6, 7, 8, ..., 19).

To find standard generators of A_{19}:

- Find an element of order 165 or 210 (probability about 1/69)
and power up to give an element
*a*in class 3A. - Find an element
*t*of order 17 (probability about 1/17). - Find a conjugate
*b*of*t*such that*ab*has order 19 (probability about 1/114). - The elements
*a*and*b*are standard generators for A_{19}.

To find standard generators of S_{19}:

- Find an element of order 33, 110 or 126 (probability 1/22) and
power up to give an element
*c*in the class of transpositions. - Find an element
*t*of order 19 (probability 1/19). - Find an conjugate
*u*of*t*such that*cu*has order 18 (probability 1/9). - The elements
*c*and*d = cu*are standard generators for S_{19}.

- 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 18.02.04 by SN.