  It is shown how to generate three-dimensional Einstein-Maxwell fields from
known ones in the presence of a hypersurface-orthogonal non-null Killing vector
field. The continuous symmetry group is isomorphic to the Heisenberg group
including the Harrison-type transformation. The symmetry of the
Einstein-Maxwell-dilaton system is also studied and it is shown that there is
the $SL(2,{\bf R})$ transformation between the Maxwell and the dilaton fields.
This $SL(2,{\bf R})$ transformation is identified with the Geroch
transformation of the four-dimensional vacuum Einstein equation in terms of the
Ka{\l}uza-Klein mechanism.
