  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 the
Hermitian curve. They arise as subcovers of the first generalized GK curve (GGS
curve). As a result, a new characterization of the GK curve, as a member of
this family, is obtained.
