Geodesic
Orientable and non-orientable Klein surfaces with maximal symmetry
Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 31-34

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Let X be a bordered Klein surface, by which we mean a Klein surface with non-empty boundary. X is characterized topologically by its orientability, the number k of its boundary components and the genus p of the closed surface obtained by filling in all the holes. The algebraic genus g of X is defined by.If g≥2 it is known that if G is a group of automorphisms of X then |G|≤12(g-l) and that the upper bound is attained for infinitely many values of g ([4], [5]). A bordered Klein surface for which this upper bound is attained is said to have maximal symmetry. A group of 12(g-l) automorphisms of a bordered Klein surface of algebraic genus g is called an M*-group and it is known that a finite group G is an M*-group if and only if it is generated by 3 non-trivial elements T1, T2, T3 which obey the relations([4]). 
Singerman, David. Orientable and non-orientable Klein surfaces with maximal symmetry. Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 31-34. doi: 10.1017/S0017089500005747
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