The GAP Character Table Library

Description

This is Version 1.2 of the GAP Character Table Library, which is an add-on package for both GAP 3.4 and GAP 4.

There is a manual (available in HTML and PDF format) that describes the available functions in detail.

The manual of the GAP Character Table Library is intended for GAP 4.5, in particular the cross-references refer to the GAP 4.5 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 (a list of contributors is in Chapter 8, paragraph 5 of this book), see

  [CCNPW85] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups, Oxford University Press, Eynsham (1985), xxxiv+252 pages
  (Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray).

• the character table library of the CAS system, see the article

  [NPP84] Neubüser, J., Pahlings, H. and Plesken, W. (Atkinson, M. D., Ed.), CAS; design and use of a system for the handling of characters of finite groups, in Computational group theory (Durham, 1982), Academic Press, London (1984), 195-247.

• and the character tables published in the book

  [HP89] Holt, D. F. and Plesken, W., Perfect groups, The Clarendon Press Oxford University Press, Oxford Mathematical Monographs, New York (1989), xii+364 pages
  (With an appendix by W. Hanrath, Oxford Science Publications).

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 2-modular character table of 3.(2×2¹⁺⁸):(U₄(2):2×2) is not correct, due to an error in the function that constructs the table from the ordinary one. No other library tables are affected by this bug.

  (Thanks to Jürgen Müller for reporting this bug.)

• The 2- and 19-modular Brauer tables of J₃, J₃.2, 3.J₃, and 3.J₃.2 shown in the ATLAS of Brauer Characters are not consistent. Therefore, the 19-modular tables of these groups will be changed in the forthcoming version of the library, by swapping the columns of the classes of element order divisible by 17. The details can be found here.

  The bug and its fix are mentioned also in the list of improvements to the ATLAS of Brauer Characters.

  The decomposition matrices of J₃ and its extensions had to be adjusted as well.

  (Thanks to Klaus Lux for reporting this bug.)

• The character table of E₆(2) is not correct, as follows. The irrationalities on classes of element order 91 are wrong, and consequently the coprime power maps are wrong on these classes.

  One can confirm the bug by looking at the 11th power map. The wrong character table claims that all elements of order 91 are conjugate to their 11th powers, but the smallest matrix representations of E₆(2) that are available in the ATLAS of Group Representations –of dimension 27 over the field with two elements– suffice to show that this cannot be correct, since the characteristic polynomials of elements of order 91 and their 11th powers are different.

  (Thanks to Bill Unger for reporting this bug.)

• The character tables of the groups 12₁.U₄(3).2₂^' and 12₂.U₄(3).2₃^' are missing from the character table library, despite the claim in the package manual that the library covers all character tables of bicyclic extensions of simple groups that are shown in the ATLAS of Finite Groups. As a consequence, also the corresponding Brauer tables are not available in GAP's character table library.

Accompanying Material

The package manual lists several files showing character theoretic computations in the context of the GAP Character Table Library.

Some of these files have meanwhile been turned into a GAPDoc book.

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 1.2 of the GAP Character Table Library then download the gzipped tar archive (ca. 11 MB). Further information is contained in the README file.

(The README file and the 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 19-May-2001 by Thomas Breuer.
Last modified on 11-Mar-2016 by Thomas Breuer.