  The cross section of the process $e^+e^-\to \pi^+\pi^-\pi^0$ was measured in
the Spherical Neutral Detector (SND) experiment at the VEPP-2M collider in the
energy region $\sqrt[]{s}$ below 980 MeV. This measurement was based on about
$1.2 \times 10^6$ selected events. The obtained cross section was analyzed
together with the SND and DM2 data in the energy region $\sqrt[]{s}$ up to 2
GeV. The $\omega$-meson parameters: $m_\omega=782.79\pm 0.08\pm 0.09$ MeV,
$\Gamma_\omega=8.68\pm 0.04\pm 0.15$ MeV and $\sigma(\omega\to 3\pi)=1615\pm
9\pm 57$ nb were obtained. It was found that the experimental data cannot be
described by a sum of only $\omega$, $\phi$, $\omega^\prime$ and
$\omega^{\prime\prime}$ resonances contributions. This can be interpreted as a
manifestation of $\rho\to 3\pi$ decay, suppressed by $G$-parity, with relative
probability $B(\rho\to 3\pi) = (1.01\pm^{0.54}_{0.36}\pm 0.034) \times
10^{-4}$.
