  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 when the system is of type dDS-I. For the type dDS-II
system this rare structure is spoilt. Symmetry group transformations are
constructed using a global approach. They are split into both connected and
discrete ones. Several exact solutions are obtained as an application of the
symmetry properties.
