Let G be a finiteg oroup. We denote BG a classifying space of G, which a contractible universal principal G bundle EG. The stable type of BG does not determine G up to isomorphism. A simple example [due to N. Minami]is given by $Q_{4p} imes Z/2$ and $D_{2p} imes Z/4$ where ps is an odd prime, $Q_{4p} is the generalized quarternion group of order 4p and $D_{2p}$ is the dihedral group of order 2p. However the paper [6] gives us a necessary and sufficient condition for $BG_1$ and $BG_2$ to be stably equivalent localized et pp. The local stable type of BG depends on the conjegacy classes of homomorphisms from the p-groups Q into G. This classification theorem simplifies if G has a normal sylow p-subgroup. Then the stable homotopy type depends on the Weyl group of the sylow p-subgroup.