Real genus of minimal nonnilpotent groups

The real genus ρ(G) of a finite group G is the minimum algebraic genus of compact bordered Klein surfaces on which G can act. A group G is minimal nonnilpotent if each of its maximal subgroups is nilpotent but G itself is not. In this paper, we obtain a lower bound for the real genus of a minimal nonnilpotent group with an exact value in a special case.