The real genus of the groups of order 48

Abstract

Every finite group acts as an automorphism group of several bordered compact Klein surfaces. The minimal genus of these surfaces is called the real genus of and it is denoted The systematical study of this parameter was begun by May and continued by him in several papers about the topic. As a consequence of these works, he and other authors obtained the groups such that On the other hand, the real genus of the groups of order less than 64, excepting 48, is already known. The orders 48 and 64 are just the first obstructions in the search of the groups of real genus greater than 16. In this work we complete the calculation of the real genus of all the fifty two groups of order 48.