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The $e^+e^-\to\eta\gamma$ cross section is measured in the center-of-massenergy range from 1.07 to 2.00 GeV in the decay channel $\eta\to 3\pi^0$,$\pi^0\to\gamma\gamma$. The data set with an integrated luminosity of 242pb$^{-1}$ accumulated in the experiment with the SND detector at the VEPP-2000$e^+e^-$ collider is analyzed.

Study of the process $e^+e^-\to\eta\gamma\to 7\gamma$ in the energy range $\sqrt{s}$ = 1.07 -- 2 GeV