#
ATLAS of Finite Group Representations

## Format information

As a general rule, matrices and permutations are stored in
**Meataxe** format, which is fully explained in
the Meataxe manuals. Here we give a brief description which should be
sufficient for a beginner to get started.

- Each file starts with a
**header line** which contains some
information about the content of the file. This can be ignored if you are
not using the Meataxe.
- A
**permutation** *p* is stored in image format, which means
that the file consists of a list of the images *p*(1), *p*(2), ... of
the points 1, 2, ...
- A
**matrix** is written in the usual way, reading across
each row in turn. There are line breaks at the end of each row, and after each
80 characters (usually) in each row. There may or may not be space(s) between
the individual entries.
- The
**entries** in a matrix come from a finite field,
of order *p*^{n} say. If this is a **prime field**, then
the elements are just the integers 0, 1, 2, ...*p*-1.
- If the field is
**not prime**, then the labelling of the elements is
done by reference to the so-called **Conway polynomials**
*C*_{n}(X).
Among other things, these polynomials are irreducible of degree *n*,
so by taking the polynomial ring modulo *C*_{n}(X)
we obtain the field of order *p*^{n}. A polynomial
*a*_{n-1}*X*^{n-1} + ... is then stored as the
non-negative integer *a*_{n-1}*p*^{n-1} + ... .

Other representations are stored in **GAP** or **MAGMA**
format. It is hoped eventually to provide automatic translation between various
different formats, but this has not yet been implemented.

## For advanced users only

Most representations are stored not only as ASCII files, but also as
Meataxe binaries. These can be accessed by replacing the directory
/atlasreps/ in the URL by /atlasbin/. They are frequently significantly smaller
than the ASCII files, but as they may be machine- and meataxe-version-
dependent, we cannot guarantee that you will be able to read them.

Last updated
20th July 1998.

R.A.Wilson (R.A.Wilson@bham.ac.uk)

R.A.Parker (richard@ukonline.co.uk)

J.N.Bray (jnb@for.mat.bham.ac.uk)