Mult = 2.

Out = 2.

Standard generators of A_{15} are **a** in class 3A,
**b** of order 13 such that **ab** has order 15 and **abb**
has order 15. In the natural
representation we may take
**a** = (1, 2, 3) and
**b** = (3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15).

Standard generators of S_{15} are **c** in class 2D,
**d** in class 14E such that **cd** has order 15. 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).

- Find an element of order 33 or 105 (probability 92/1155, or approximately 1/13) and power it up to give an element
*a*in class 3A. - Find an element
*t*of order 13 (probability 1/13). - Find a conjugate
*b*of t such that*ab*has order 15 and*abb*has order 15 (probability 1/35). - The elements
*a*and*b*are standard generators of A_{15}.

- Find an element of order 26 or 70 (probability 24/455, or approximately 1/18) and power it up to give an element
*c*in class 2D. There are other possibilities if you are able to distinguish outer and inner elements (such as powering up an outer 22 or 42 element). - Find an element
*t*of order 14 (probability approximately 1/14). This is probably in class 14E. - Find a conjugate
*c*of*t*such that*cd*has order 15 (probability 2/15, or about 1/7). If you cannot find such a*d*after several attempts, then*t*was probably in the wrong class, so go back to the second step. - The elements
*c*and*d*are standard generators of S_{15}.

- 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.