The Subgroups of M24 or
How to Compute the Table of Marks of a Finite Group.
Experiment. Math. 6 (1997), 247-270.
Let be a finite group. The table of marks of arises from a
characterization of the permutation representations of by certain
numbers of fixed points. It provides a compact description of the subgroup
lattice of and enables explicit calculations in the Burnside ring of
. In this article we introduce a method for constructing the table of
marks of from tables of marks of proper subgroups of . An
implementation of this method is available in the GAP language. These
computer programs are used to construct the
table of marks of the sporadic
simple Mathieu group . The final section describes how to derive
information about the structure of from its table of marks via the
investigation of certain Möbius functions and the idempotents of the
Burnside ring of . The appendix contains tables with detailed
information about and other groups.
DVI (147 kB) and as gzip'ed
PostScript file (164 kB).
The actual table of all 1529 conjugacy classes
of subgroups of is available as a separate document.