Representing the Sporadic Groups as Noncentral Automorphisms ofp-Groups Original Research Article

In Heineken and Liebeck [Arch. Math.25(1974), 8–16] it is proved that for every finite groupKand odd primep, there exists ap-groupGof nilpotence class 2 and exponentp2on whichKacts as the full group of noncentral automorphisms. The authors investigate this problem under the additional requirement thatG/Z(G) be representation space for thep-modular regular representation ofK. In particular, they prove that every sporadic simple groupKcan be so represented for any odd primep.