The files mindeg.dvi and mindeg.ps 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 Fi_{24}' 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 Fi_{24}' of
degree 3,774 over the field with two elements. We believe that
this is the smallest possible degree for Fi_{24}'
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 Fi_{24}'.

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