The GAP Character Table Library

Description

This is Version 1.1 of the GAP Character Table Library, which is an add-on package for both GAP 3.4 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 and PDF format) that describes the available functions in detail.

The manual of the GAP Character Table Library is intended for GAP 4.4, in particular the cross-references refer to the GAP 4.4 Reference Manual. So when using the new character table library with GAP 3.4, one should still consult the documentation of the character table library contained in the Reference Manual of GAP 3.4.

Authors

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.

Individual contributions are often listed in the ``InfoText´´s of the GAP library tables.

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.

Contents

The differences w.r.t. the Character Table Library in earlier releases of GAP are listed here in HTML and PDF format.

A preliminary version of a ``WWW table of contents´´ of the GAP Character Table Library can be found here.

Known Bugs

The following bugs have been found in the current version of the GAP Character Table Library.

• The character table with the name P12/G1/L2/V1/ext2 is not correct, some of its class multiplication coefficients are not integral. (This problem occurs already in the microfiches that are contained in the book ``Perfect Groups´´.)
• The second power map in the character table with the name 13^1+2.2A4 is not correct.
• The character table with the name P41/G1/L1/V4/ext2 is not correct, this table is not the character table of a finite group. (This problem occurs already in the microfiches that are contained in the book ``Perfect Groups´´.)
• The name 2G2(3) is erroneously associated with the character table of L2(8); the correct table would be that of L2(3).3. (This error has been communicated by Felix Noeske.)
• The 21th and 22th maximal subgroup of the table with the name Co1 must be swapped, that is, the names Co1M21 and Co1M22 are not correct, according to the ordering w.r.t. increasing index.
• The 19th and 20th maximal subgroup of the table with the name F3+ must be swapped, that is, the names F3+M19 and F3+M20 are not correct, according to the ordering w.r.t. increasing index.

Applications

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

• Ambiguous class fusions (in PDF and HTML format),
• Ordinary character tables, Brauer tables, and decomposition matrices (in PDF and HTML format),
• Computations of possible permutation characters (in PDF and HTML format),
• Construction of character tables using table automorphisms (in PDF and HTML format),
• Computations of common central extensions (in PDF and HTML format),
• Multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups (in PDF and HTML format),
• Multiplicity-free permutation characters of central extensions of the sporadic simple groups, and their automorphic extensions (in PDF and HTML format).
• Probabilistic generation of finite simple groups (in PDF and HTML format).
• A question about the group PSO⁺(8,5).S₃ (in PDF and HTML format).
• Maintenance issues for the GAP Character Table Library (in PDF and HTML format).
• Hamiltonian cycles in the generating graphs of finite groups (in PDF and HTML format).

Feedback

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 support group by sending an email to the general email address for problems with GAP.

Download

If you want to get Version 1.1 of the GAP Character Table Library then download the most appropriate of a gzipped tar archive (ca. 4.6 MB) or zoo archive (ca. 4.9 MB). Further information is contained in the README file.

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

Related Links

[GAP Home] [The Modular Atlas Homepage]

The material presented on the following pages has been computed mainly from the data of the GAP Character Table Library and a few small GAP functions.

[Common Irrationalities] [Decomposition Matrices]

File created on 19th May 2001 by Thomas Breuer.
Last modified on 10-Oct-2007 by Thomas Breuer.