  Perfect fluid space-times admitting a three-dimensional Lie group of
conformal motions containing a two-dimensional Abelian Lie subgroup of
isometries are studied. Demanding that the conformal Killing vector be proper
(i.e., not homothetic nor Killing), all such space-times are classified
according to the structure of their corresponding three-dimensional conformal
Lie group and the nature of their corresponding orbits (that are assumed to be
non-null). Each metric is then explicitly displayed in coordinates adapted to
the symmetry vectors. Attention is then restricted to the diagonal case, and
exact perfect fluid solutions are obtained in both the cases in which the fluid
four-velocity is tangential or orthogonal to the conformal orbits, as well as
in the more general "tilting" case.
