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Let $F=F|\mathbb{K}$ a be function field over an algebraically closedconstant field $\mathbb{K}$ of positive characteristic $p$. For a$\mathbb{K}$-automorphism group $G$ of $F$, the invariant of $G$ is the fixedfield $F^G$ of $G$. If $F$ has transendency degree $1$ (i.e. $F$ is thefunction field of an irreducible curve) and $F^G$ is rational, then eachgenerator of $F^G$ uniquely determines $F^G$ and it makes sense to call each ofthem the invariant of $G$. In this paper, $F$ is the Hermitian function field$\mathbb{K}(\mathcal{H}_q)=\mathbb{K}(x,y)$ with $y^q+y-x^{q+1}=0$ and $q=p^r$.We determine the invariant of $Aut(\mathbb{K}(\mathcal{H}_q))\cong PGU(3,q)$,and discuss some related questions on Galois subcovers of maximal curves overfinite fields.

The invariant of $PGU(3,q)$ in the Hermitian function field