A classification of primer hypermaps with a product of two primes number of hyperfaces

A hypermap is a cellular embedding of a connected bipartite graph G into a compact and connected surface S without border. The vertices of G lie in distinct partitions, colored black and white, and are called respectively the hypervertices and hyperedges of the hypermap, while the connected regions of G∖S are the hyperfaces. A hypermap H is called orientable if the underlying surface S is orientable. An orientable hypermap is called regular if its orientation preserving automorphism group G acts regularly on the flags (hypervertex, hyperedge and hyperface incident triples), and further, it is called (face-)primer if G induces a faithful action on their hyperfaces. In Breda d'Azevedo and Fernandes (2011), a classification of the primer hypermap with a prime number of hyperfaces is given. In this paper, a classification will be given, for all primer hypermaps with a product of two primes hyperfaces, see Theorem 5.1.