Geodesic
The symmetric genus of 2-groups
Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 115-124

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A finite group G can be represented as a group of automorphisms of a compact Riemann surface, that is, G acts on a Riemann surface. The symmetric genus σ(G) is the minimum genus of any Riemann surface on which G acts (possibly reversing orientation). 
ZIMMERMAN, JAY. The symmetric genus of 2-groups. Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 115-124. doi: 10.1017/S001708959997057X
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