The cross section of the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ 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 $1.2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ 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 $\ensuremath{\omega}$-meson parameters ${m}_{\ensuremath{\omega}}=782.79\ifmmode\pm\else\textpm\fi{}0.08\ifmmode\pm\else\textpm\fi{}0.09\mathrm{MeV},$ ${\ensuremath{\Gamma}}_{\ensuremath{\omega}}=8.68\ifmmode\pm\else\textpm\fi{}0.04\ifmmode\pm\else\textpm\fi{}0.15\mathrm{MeV},$ and $\ensuremath{\sigma}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}3\ensuremath{\pi})=1615\ifmmode\pm\else\textpm\fi{}9\ifmmode\pm\else\textpm\fi{}57\mathrm{nb}$ were obtained. It was found that the experimental data cannot be described by a sum of only $\ensuremath{\omega},$ $\ensuremath{\varphi},$ ${\ensuremath{\omega}}^{\ensuremath{'}},$ and ${\ensuremath{\omega}}^{\ensuremath{''}}$ resonance contributions. This can be interpreted as a manifestation of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\rho}}3\ensuremath{\pi}$ decay, suppressed by G parity, with a relative probability $B(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\rho}}3\ensuremath{\pi}{)=(1.01}_{\ensuremath{-}0.36}^{+0.54}\ifmmode\pm\else\textpm\fi{}0.034)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}.$