  We have studied, with the KLOE detector at the DA$\Phi$NE $\Phi$-Factory, the
dynamics of the decay $\eta\to\pi^+\pi^-\pi^0$ using $\eta$ mesons from the
decay $\phi\to\eta\gamma$ for an integrated luminosity ${\mathcal L}$ = 450
pb$^{-1}$. From a fit to the Dalitz plot density distribution we obtain a
precise measurement of the slope parameters. An alternative parametrization
relates the $\pi^+\pi^-\pi^0$ slopes to that for $\eta\to 3\pi^0$ showing the
consistency of KLOE results for both channels. We also obtain the best
confirmation of the $C$-invariance in the $\eta\to\pi^+\pi^-\pi^0$ decay.
