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In this paper we compute the automorphism group of the curves$\mathcal{X}_{a,b,n,s}$ and $\mathcal{Y}_{n,s}$ introduced in Tafazolian et al.in 2016 as new examples of maximal curves which cannot be covered by theHermitian curve. They arise as subcovers of the first generalized GK curve (GGScurve). As a result, a new characterization of the GK curve, as a member ofthis family, is obtained.

On the automorphism group of a family of maximal curves not covered by the Hermitian curve