The Gap condition for S5 and GAP Programs

In transformation groups on manifolds, it has been an interesting problem to ask whether for a given finite group G, there exists a real G-module V such that dim VP >2dimV>P for all subgroups P of prime power order and such that VH=0 for certain large subgroups H of G. This paper provides GAP programs to show that S5 does not admit such a real S5-module V.