FRW spacetime is characterized by symmetries of isotropy and homogeneity, represented by its six Killing vectors corresponding to three translations and three rotations. While Lorentz symmetry applies locally, it does not extend globally in FRW metrics due to the universe's preferred rest frame. The FRW metric is conformally flat, which implies that it can be derived from the Minkowski metric through angle-preserving transformations, but this does not directly relate to Lorentz transformations. The discussion emphasizes that time symmetry is absent, as it would hinder the universe's evolution. Overall, the properties of FRW spacetime are crucial for understanding the dynamics of expanding universes, including effects like cosmological redshift.