  Gravity coupled three--dimensional $\sigma$--model describing the stationary
Einstein--Maxwell--dilaton system with general dilaton coupling is studied.
Killing equations for the corresponding five--dimensional target space are
integrated. It is shown that for general coupling constant $\alpha$ the
symmetry algebra is isomorphic to the maximal solvable subalgebra of $sl(3,R)$.
For two critical values $\alpha =0$ and $\alpha =\sqrt{3}$, Killing algebra
enlarges to the full $sl(3,R)$ and $su(2,1)\times R$ algebras respectively,
which correspond to five--dimensional Kaluza--Klein and four--dimensional
Brans--Dicke--Maxwell theories. These two models are analyzed in terms of the
unique real variables. Relation to the description in terms of complex Ernst
potentials is discussed. Non--trivial discrete maps between different subspaces
of the target space are found and used to generate new arbitrary--$\alpha$
solutions to dilaton gravity.
