For all g greater than or equal to 2, there is a Riemann surface of genus g whose automorphism group has order 8g+8, establishing a lower bound for the possible orders of automorphism groups of Riemann surfaces. Accola and MacLachlan established the existence of such surfaces; we shall call them Accola-MacLachlan surfaces. In this paper we determine the symmetries of surfaces with genus g = 3(mod 4), computing the number of ovals and the separability of the symmetries. The results are then applied to classify the real forms of these complex algebraic curves.
Broughton, Sean A.; Bujalance, E; Costa, A F.; Gamboa, J M.; and Gromadzki, G, "Symmetries of Accola-MacLachlan and Kulkarni Surfaces" (1995). Mathematical Sciences Technical Reports (MSTR). 64.