Mult = 2.

Out = 2.

The following information is available for A_{16}:

Standard generators of A_{16} are **a** in class 3A,
**b** in class 15F/G such that **ab** has order 14 and
**abb** has order 63. This last condition can be replaced
with **[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).

Standard generators of the double cover 2.A_{16} are
not yet defined.

Standard generators of S_{16} are **c** in class 2E,
**d** in class 15FG such that **cd** has order 16.

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).

Standard generators of the double covers 2.S_{16} are
not yet defined.

To find standard generators of A_{16}:

- Find an element of order 33, 39, 84 or 105 (probability about 1/9)
and power it up to give an element
*a*in class 3A. - Find an element
*t*of order 15 (probability about 1/15). It is probably in class 15F or 15G. - Find a conjugate
*b*of*t*such that*ab*has order 14 and*abb*has order 63 (probability about 1/6). If you cannot find such a conjugate, then*t*was probably in the wrong class, so go back to step 2. - The elements
*a*and*b*are standard generators of A_{16}.

To find standard generators of S_{16}:

- Find an element of order 26, 66 or 90 (probability about 1/15)
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 22 or 70 would also work, and increases the probability of finding an appropriate element to about 1/6.) - Find an element
*t*of order 15 (probability about 1/15). It is probably in class 15FG. - Find a conjugate
*d*of*t*such that*cd*has order 16 (probability 1/8). If you cannot find such a conjugate after several attempts, then*t*was probably in the wrong class, so go back to step 2. - The elements
*c*and*d*are standard generators of S_{16}.

- 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 18th February 2004.

Last updated 27.02.04 by SN.