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Gareth Jones asked during the 2014 SIGMAP conference for examples of regulardessins with nonabelian fields of moduli. In this paper, we first constructdessins whose moduli fields are nonabelian Galois extensions of the form$\mathbb{Q}(\zeta_p,\sqrt[p]{q})$, where $p$ is an odd prime and $\zeta_p$ is a$p$th root of unity and $q\in\mathbb{Q}$ is not a $p$th power, and we then showthat their regular closures have the same moduli fields. Finally, in thespecial case $p=q=3$ we give another example of a regular dessin with modulifield $\mathbb{Q}(\zeta_3,\sqrt[3]{3})$ of degree $2^{19}\cdot3^4$ and genus$14155777$.

Regular dessins with moduli fields of the form $\mathbb{Q}(\zeta_p,\sqrt[p]{q})$