  Let Y be a complex Enriques surface whose universal cover X is birational to
a general quartic Hessian surface. Using the result on the automorphism group
of X due to Dolgachev and Keum, we obtain a finite presentation of the
automorphism group of Y. A fundamental domain of the action of the automorphism
group on the nef cone of Y is described explicitly. The list of elliptic
fibrations on Y and the list of combinations of rational double points that can
appear on a surface birational to Y are presented. As an application, a set of
generators of the automorphism group of the generic Enriques surface is
calculated explicitly.
