Mult = 2.

Out = 2.

The following information is available for A_{17}:

Standard generators of A_{17} are **a** in class 3A,
**b** of order 15 such that **ab** has order 17 (so we must
have **b** in class 15G).

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, 16, 17).

Standard generators of S_{17} are **c** in class 2E,
**d** of order 16 such that **cd** has order 17 (so we must
have **b** in class 16A).

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).

- Find an element of order 39 or 105 (probability about 1/16) and
power up to give an element
*s*in class 3A. - Find an element
*t*of order 17 (probability about 1/9). - Find a conjugate
*u*of*t*such that*su*has order 15 (probability about 1/40). Then*u*is in class 15G. - Let
*a*be the inverse of*s*and*b*be*su*. Then*a*and*b*are standard generators for A_{17}.

- Find an element of order 90 or 210 (probability 1/63) and
power up to give an element
*c*in class 2E. Alternatively, if you look among outer elements only, then elements of order 26 and 70 also work, and the probability rises to about 1/13. - Find an element
*t*of order 16 (probability 1/16). - Find an conjugate
*d*of*t*such that*cd*has order 17 (probability about 1/9). - The elements
*c*and*d*are standard generators for S_{17}.

- 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.