A class of orientably‐regular embeddings of graphs of order [formula omitted

Abstract

Let G be the automorphism group of an orientably regular embedding of a connected simple graph of order p3, where p is a prime. It was shown in [19] that except for the case when p=2 and G=S4, G contains a normal Sylow p-subgroup P of order pk where k∈{3,4,5}, while such embeddings with k=5 were determined. In this paper, a further classification is achieved for all such embeddings with k=3.