THE GROUPS OF REAL GENUS ρ ≤ 16

Let G be a finite group. The real genus rho(G) is the minimum algebraic genus of any compact bordered Klein surface on which G acts. Here we classify the groups of real genus rho, for all values of rho such that 9 <= rho <= 16, rho not equal 12, and also for the remaining even values such that rho <= 24. We also determine the real genus of each group G with 32 < vertical bar G vertical bar < 48. in addition, we obtain some general results about the partial presentations that groups acting on bordered surfaces must have.