  The general solution for non-rotating perfect-fluid spacetimes admitting one
Killing vector and two conformal (non-isometric) Killing vectors spanning an
abelian three-dimensional conformal algebra (C_3) acting on spacelike
hypersurfaces is presented. It is of Petrov type D; some properties of the
family such as matter contents are given. This family turns out to be an
extension of a solution recently given in \cite{SeS} using completely different
methods. The family contains Friedman-Lema\^{\i}tre-Robertson-Walker particular
cases and could be useful as a test for the different FLRW perturbation
schemes. There are two very interesting limiting cases, one with a non-abelian
G_2 and another with an abelian G_2 acting non-orthogonally transitively on
spacelike surfaces and with the fluid velocity non-orthogonal to the group
orbits. No examples are known to the authors in these classes.
