The Degree of a p-group G with | G' | = p

Let G be a finite group andδ(G) denote the least n ∈ N such that G is isomorphic to a subgroup of the symmetric group Sn. The numberδ(G) is called the degree of G. This paper is a note on δ(G) for a finite p-group G with derived subgroup of order p. Our method is based on quasi-permutation representations of a finite group.