The $e^+e^-\to\eta\gamma$ cross section has been measured in the center-of-mass energy range 1.07--2.00 GeV using the decay mode $\eta\to 3\pi^0$, $\pi^0\to \gamma\gamma$. The analysis is based on 36 pb$^{-1}$ of integrated luminosity collected with the SND detector at the VEPP-2000 $e^+e^-$ collider. The measured cross section of about 35 pb at 1.5 GeV is explained by decays of the $\rho(1450)$ and $\phi(1680)$ resonances.
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