Galois subcovers of the Hermitian curve in characteristic p with respect to subgroups of order p^2

A (projective, geometrically irreducible, non-singular) curve X defined over a finite field Fq2 is maximal if the number Nq2 of its Fq2-rational points attains the Hasse-Weil upper bound, that is Nq2 =q2+2gq+1where g is the genus of X. An important question, also motivated by applications to algebraic-geometry codes, is to find explicit equations for maximal curves. For a few curves which are Galois covered of the Hermitian curve, this has been done so far ad hoc, in particular in the cases where the Galois group has prime order. In this paper we obtain explicit equations of all Galois covers of the Hermitian curve with Galois group of order p2where pis the characteristic of Fq2. Doing so we also determine the Fq2-isomorphism classes of such curves and describe their full Fq2-automorphism groups.