Author: David J Green 
Title : The 3-local cohomology of the Mathieu group M_24
Date  : Submitted 8th August 1994.  Resubmitted 11th November 1994.
Status: Glasgow Math. J. 38 (1996), 69-75.
        MR 96j:20075

Abstract:
The localisation at the prime 3 of the integral cohomology ring of the
Mathieu group $M_{24}$ is calculated.  The Chern classes of the Todd
representation in $GL_{11} (F_2)$ generate the even-degree part
of this ring.  The mod-3 cohomology ring is also calculated.
  [These results have been used by C. B. Thomas to prove that the elliptic
cohomology of the classifying space $BM_{24}$ is generated by Chern classes,
and is therefore concentrated in even dimensions.]

1991 Mathematics Subject Classification: 20J06 (primary),  20C34 20D08