  We show that a rank two finite group G admits a finite G-CW-complex X
homotopy equivalent to a sphere, with rank one prime power isotropy, if and
only if G does not p'-involve Qd(p) for any odd prime p. This follows from a
more general theorem which allows us to construct a finite G-CW-complex by
gluing together a given G-invariant family of representations defined on the
Sylow subgroups of G.
