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The general solution for non-rotating perfect-fluid spacetimes admitting oneKilling vector and two conformal (non-isometric) Killing vectors spanning anabelian three-dimensional conformal algebra (C_3) acting on spacelikehypersurfaces is presented. It is of Petrov type D; some properties of thefamily such as matter contents are given. This family turns out to be anextension of a solution recently given in \cite{SeS} using completely differentmethods. The family contains Friedman-Lema\^{\i}tre-Robertson-Walker particularcases and could be useful as a test for the different FLRW perturbationschemes. There are two very interesting limiting cases, one with a non-abelianG_2 and another with an abelian G_2 acting non-orthogonally transitively onspacelike surfaces and with the fluid velocity non-orthogonal to the grouporbits. No examples are known to the authors in these classes.Comment: Submitted to GRG, Latex fil

LETTER TO THE EDITOR: General Non-Rotating Perfect-Fluid Solution with an Abelian Spacelike C3 Including Only One Isometry