Title: Arc-transitive maps with coprime Euler characteristic and edge number

Abstract: This is one of a series of papers which aim towards a classification of edge-transitive maps of which the Euler characteristic and the edge number are coprime. This one carries out the classification work for arc-transitive maps with nonsolvable automorphism groups, which illustrates how the edge number impacts on the Euler characteristic for maps. The classification is involved with the construction of some new and interesting arc-regular maps.