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Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.

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Does there exist a non-hyperelliptic Riemann surface with automorphism group $C_2\times A_4$?

Does there exist a non-hyperelliptic Riemann surface of genus 5 with automorphism group $C_2\times A_4$?
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