The Cayley isomorphism property for the group C25 × Cp

Abstract

A finite group G is called a DCI-group if two Cayley digraphs over G are isomorphic if and only if their connection sets are conjugate by a group automorphism. We prove that the group C₂⁵ × C_p, where p is a prime, is a DCI-group if and only if p ≠ 2. Together with the previously obtained results, this implies that a group G of order 32p, where p is a prime, is a DCI-group if and only if p ≠ 2 and G ≅ C₂⁵ × C_p.