Orientable vertex transitive embeddings of Kp {{\sf K}}_p

In [J. Combin. Theory Ser. B, 99 (2009), 447-454)], Li characterized the classification of vertex-transitive embeddings of complete graphs, and proposed how to enumerate such maps. In this paper, we study the counting problem of orientable vertex-transitive embeddings of ${{\sf K}}_p$, where $p\geq 5$ is a prime. Moreover, we obtain the number of non-isomorphic orientable vertex-transitive complete maps with $p$ vertices