Geodesic
Genus spectra for split metacyclic groups
Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 209-218

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An integer n\geq2 is said to be a genus of a finite group G if there is a compact Riemann surface of genus n on which G acts as a group of automorphisms. In this paper, formulae are given for the minimum genus, minimum stable genus and the gap sequence, i.e., the (finite) set of non-genera, for a split metacyclic group of order pq, where p and q are primes. This information completely determines the genus spectrum for such groups. 
Weaver, A. Genus spectra for split metacyclic groups. Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 209-218. doi: 10.1017/S0017089501020067
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     title = {Genus spectra for split metacyclic groups},
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     year = {2001},
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     doi = {10.1017/S0017089501020067},
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