Let p be a prime and G a subgroup of the general linear group GL(d,p) acting transitively on the nonzero vectors of the d-dimensional vector space (F(p))^d over the finite field F(p) with p elements. Assume that G contains a sharply transitive set. Then p^d is in the sequence and G is one of the seven finite sharply transitive linear groups of Zassenhaus (see "Sporadic finite transitive linear groups" in Wikipedia link).