The GAP Character Table Library

This is the first release (Version 1.0) of the GAP Character Table Library as an add-on package for both GAP 3 and GAP 4. Up to GAP 4.2, the library of character tables had been distributed as an inseparable part of the GAP distribution. The aims of the restructuring are the following.

• Upgrades of the GAP Character Table Library are possible, independent of GAP releases, via the mechanism that has been used already for installing or upgrading GAP packages; each such upgrade will get a version number.
• The new directory structure provides an environment that is more suitable for the further development of the GAP library of character tables.
• It is easy to omit the character table library from the GAP 4 installation if one is not interested in it.

There is a manual (available here in HTML, DVI, and PostScript format) that describes the available functions in detail.

The manual of the new character table library is intended for GAP 4.3, in particular the cross-references refer to the GAP 4.3 Reference Manual. So when using the new character table library with GAP 3.4 or GAP 4.2, one should still consult the documentation of the character table library contained in the Reference Manual of GAP 3.4 or GAP 4.2, respectively.

The data contained in the GAP Character Table Library have been contributed by various people. Important sources of the ordinary character tables are

• the famous Atlas of Finite Groups (see Chapter 8, paragraph 5 of this book for a list of contributors),
• the character table library of the CAS system, see the article

  Joachim Neubüser, Herbert Pahlings, and Wilhelm Plesken, CAS; Design and use of a system for the handling of characters of finite groups, pages 195-247 in Computational Group Theory, Proceedings LMS Symposium on Computational Group Theory, Durham 1982, ed. by Michael D. Atkinson, Academic Press, 1984.

• and the character tables published in the book

  Derek F. Holt and Wilhelm Plesken, Perfect Groups, Oxford Math. Monographs, Oxford University Press, 1989.

For the origin of the Brauer tables in the GAP Character Table Library, see the homepage of the Atlas of Brauer Characters.

The GAP interface and the data format used were developed by Thomas Breuer.

The following files show a few applications of the GAP Character Table Library.

• Computations of permutation characters (in DVI and HTML format),
• Ordinary character tables, Brauer tables, and decomposition matrices (in DVI and HTML format),
• Multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups (in DVI and HTML format).

Any comments are very welcome. If you have found important features missing or if there is a bug, let us know and we will try to address it in the next version of the GAP Character Table Library. Please send a short email to Thomas Breuer about it. This holds in particular if you have used the GAP Character Table Library to solve a problem.

You can also reach the GAP developers by sending an email to the general GAP email address for problems with GAP.

If you want to get Version 1.0 of the GAP Character Table Library then download the most appropriate of a gzipped tar archive (ca. 3.0 MB) or zoo archive (ca. 3.2 MB). Further information is contained in the README file.

(The README file and the zoo archive are available also on the GAP servers.)

File created on 19th May 2001 by Thomas Breuer.
Last modified on 16th November 2001 by Thomas Breuer.