Input Data for the Verification of Atlas Character Tables

• What is an Atlas Character Table?

  The ATLAS of Finite Groups [CCNPW85] shows the ordinary character tables of several simple groups, and of many upwards and downwards extensions of these groups by cyclic groups. The ATLAS calls these groups “bicyclic extensions” of the simple groups in question. Up to isoclinism, these are in total 399 character tables.

  The description of the groups 4.A₆.2₃, 12.A₆.2₃, 4.L₂(25).2₃, and 9.U₃(8).3₃ involves “broken boxes”, see [CCNPW85, p. xxiv]. We may regard their character tables not as ATLAS tables; if we exclude them then 395 tables remain.

• The Names of the Groups

  The list of names of bicyclic extensions of simple groups whose character tables are shown in the ATLAS of Finite Groups can be found in the file ATLASnames.json.

  (The corresponding GAP list can be formed using the functions StringFile and EvalString.)

• The Representations

  A description of the representations that have been used in the verification [BMO17] can be found in the file ATLASrepres.json.

  (The corresponding GAP list can be formed using the functions StringFile and EvalString.)

• Overview of Input Data and Runtimes

  An overview of the group names, the representations used, the MAGMA input files, and the MAGMA runtimes can be found in the files overview.html (without MathJax) and overview_mj.html (with MathJax).

  Note that the generating permutations and matrices are stored in MeatAxe format.

• Source of the Data

  GAP code for creating the files mentioned above, including the MAGMA input files, can be found in the file utils.g.

References

[BMO17] Breuer, T., Malle, G. and O'Brien, E. A., Reliability and reproducibility of Atlas information, in Finite simple groups: thirty years of the Atlas and beyond, Amer. Math. Soc., Contemp. Math., 694, Providence, RI (2017), 21-31. arXiv:1603.08650.

[CP96] Cannon, J. J. and Playoust, C., An introduction to algebraic programming in Magma, School of Mathematics and Statistics, University of Sydney, Sydney, Australia (1996), http://www.math.usyd.edu.au:8000/u/magma.

[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).

[GAP] GAP – Groups, Algorithms, and Programming, Version 4.5.0, The GAP Group (2012), http://www.gap-system.org.

File created: 11th November 2015 by Thomas Breuer.

Last modified: 09th April 2020 by Thomas Breuer.