  In this paper, the equations governing the unsteady flow of a perfect
polytropic gas in three space dimensions are considered. The basic similarity
reductions for this system are performed. Reduced equations and exact solutions
associated with the symmetries are obtained. This results is used to give the
invariance of system up to Galilean motions of space-times $\RR^4$. Then, an
optimal system of one-dimensional sub-algebras for symmetry algebra of this
system is given.
