Mult = 2.

Out = 2.

The following information is available for A_{18}:

Standard generators of A_{18} are **a** of order 3
(belonging to the smallest conjugacy class of elements of order 3),
**b** of order 17 such that **ab** has order 16 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).

Standard generators of S_{18} are **c** of order 2
(belonging to the smallest conjugacy class of outer involutions),
**d** of order 17 such that **cd** has order 18.

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).

To find standard generators of A_{18}:

- Find an element of order 39, 66 or 120 (probability about 1/24)
and power it up to give an element
*a*in class 3A. - Find an element
*t*of order 17 (probability 2/17, or approximately 1/9). - Find a conjugate
*b*of*t*such that*ab*has order 16 and*[a,b]*has order 2 (probability 1/96). - The elements
*a*and*b*are standard generators of A_{16}.

To find standard generators of S_{18}:

- Find an element of order 78, 110 or 126
(probability 1/34) and power it up to give an element
*c*in class 2A. (If you only look among outer elements, then finding an element of order 26, 78, or 90 would also work, and increases the probability of finding an appropriate element to about 1/9.) - Find an element
*t*of order 17 (probability 1/17). - Find a conjugate
*d*of*t*such that*cd*has order 18 (probability 1/9). - The elements
*c*and*d*are standard generators of S_{18}.

- 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.