The mod-2 cohomology ring of the third Conway group is Cohen-Macaulay
Simon A. King, David J. Green and Graham Ellis

Abstract. By explicit machine computation we obtain the
mod 2 cohomology of the third Conway group Co3 and show 
that it is Cohen-Macaulay. Moreover, the maximal elementary
abelian 2-subgroups detect the mod-2 cohomology of Co3.