  If a finite group of orientation-preserving diffeomorphisms of the
3-dimensional torus leaves invariant an oriented, closed, embedded surface of
genus g>1 and preserves the orientation of the surface, then its order is
bounded from above by 12(g-1). In the present paper we classify (up to
conjugation) all such group actions and surfaces for which the maximal possible
order 12(g-1) is achieved, and note that the unknotted surfaces can be realized
by equivariant minimal surfaces in a 3-torus.
