  Let G be a finite group given in one of the forms listed in the title with
period 2d and X(n) an n-dimensional CW-complex with the homotopy type of an
n-sphere. We study the automorphism group Aut(G) to compute the number of
distinct homotopy types of orbit spaces X(2dn-1)/\mu with respect to free and
cellular G-actions \mu on all CW-complexes X(2dn-1). At the end, the groups
E(X(2dn-1)/\mu) of self homotopy equivalences of orbit spaces X(2dn-1)/\mu
associated with free and cellular G-actions \mu on X(2dn-1) are determined.
