On the Cayley Isomorphism Problem for a Digraph with 24 Vertices

Abstract

In this paper we are mainly concerned with the Cayley isomorphism problem for groups containing $Q_8$. We prove that the group $Q_8\times C_3$ is not a CI-group with respect to colour ternary relational structures. Further, we prove that the non-nilpotent group $Q_8\rtimes C_3$ is not a CI-group with respect to graphs.