1. The alternating group A6 acting on genus 10. 

Here we work out one of the curves known as "Wiman sextic". This example was partially included in [2], here we compute the hyperbolic polygon uniformizing the action, among other results, following [1].

References

[1] Behn, Antonio; Rodríguez, Rubí E.; Rojas, Anita M. Adapted hyperbolic polygons and symplectic representations for group actions on Riemann surfaces. J. Pure Appl. Algebra 217 (2013), no. 3, 409–426.

[2]  Behn, Antonio; Rojas, Anita M.; Tello-Carrera, Miguel; A SAGE Package for n-Gonal Equisymmetric Stratification of Mg. Exp. Math. 32 (2023), no. 1, 54–69. https://doi.org/10.1080/10586458.2020.1763872 

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