Minimal Degrees of Faithful Representations for Sporadic Simple Groups and their Covering Groups

The files mindeg.dvi and contain a DVI and PostScript version, respectively, of a list of the minimal faithful Brauer character degrees for all the sporadic simple groups and their covering groups. The last open cases, the minimal degrees of the double cover 2.B of the Baby Monster in characteristics 3, 5, 7, and 13, have been settled by Richard Parker (September 4, 2001).

This list is due to Christoph.Jansen@Math.RWTH-Aachen.De ; a paper of these results together with proofs has now appeared. (C. JANSEN, The minimal degrees of faithful representations of the sporadic simple groups and their covering groups, LMS J. Comput. Math. 8 (2005), 122 - 144.) Part of the data is already contained in the Atlas of Brauer Characters, in the book Brauer Trees of Sporadic Groups by Gerhard Hiß and Klaus Lux, or in the results to be found in the database of decomposition matrices. The minimal faithful ordinary character degrees, as can be found in the Atlas Of Finite Groups, are given as well.

There was an error in an earlier list, concerning the minimal degree of the simple Fischer group Fi24' in characteristic 2. Until October 23, 2001, the value stated for this minimal degree was 8,670. Jürgen Müller has now constructed an irreducible, selfdual representation for Fi24' of degree 3,774 over the field with two elements. We believe that this is the smallest possible degree for Fi24' in even characteristic.

Following the original arguments by Christoph Jansen, it has now (October 29, 2001) been proved by Gerhard Hiss, that 3,774 is indeed the smallest degree of a faithful 2-modular character of Fi24'.

File created on 23th July 1999 by Thomas Breuer
Last modified: 4th September 2001 by Gerhard Hiss
Last modified: 26th October 2001 by Gerhard Hiss
Last modified: 31st October 2001 by Gerhard Hiss
Last modified: 29th June 2005 by Gerhard Hiss