  Lie symmetry algebra of the dispersionless Davey-Stewartson (dDS) system is
shown to be infinite-dimensional. The structure of the algebra turns out to be
Kac-Moody-Virasoro one, which is typical for integrable evolution equations in
$2+1$-dimensions. Symmetry group transformations are constructed using a direct
(global) approach. They are split into both connected and discrete ones.
Several exact solutions are obtained as an application of the symmetry
properties.
