  The cross section is estimated for the $\pi^+\pi^-\pi^0$ invariant mass
distribution in the $\gamma p$ reaction in the GeV region. This reaction is
assumed to proceed through the formation of the $\omega$ meson in the
intermediate state, since the production cross section for this meson in the
$\gamma p$ reaction in GeV region is significant and it has large branching
ratio (88.8%) in the $\pi^+\pi^-\pi^0$ channel. The cross sections for this
reaction have been calculated using the energy dependent reaction amplitude,
i.e., $f_{\gamma p \to \omega p}(0)$, extracted from the latest $\omega$ meson
photoproduction data. We use established procedure to calculate other factors,
like width and propagator of the $\omega$ meson, so that our calculation can
provide reliable cross section. The calculated results reproduce the measured
$\pi^+\pi^-\pi^0$ invariant mass distribution spectra in the $\gamma p$
reaction.
