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Serre the fact that any curve $\\mathbb{F}$-covered by the Hermitian curve $\\mathcal{H}_{q+1}:\\, y^{q+1}=x^q+x$ is also $\\mathbb{F}$-maximal. Nevertheless, the converse is not true as the Giulietti-Korchm\\'aros example shows provided that $q>8$ and $h\\equiv 0\\pmod{3}$. In this paper, we show that if an $\\mathbb{F}$-maximal curve $\\mathcal{X}$ of genus $g\\geq 2$ where $q=p$ is such that $|Aut(\\mathcal{X})|>84(g-1)$ then $\\mathcal{X}$ is Galois-covered by $\\mathcal{H}_{p+1}$. 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