  Based on a sample of $1.31$ billion $J/\psi$ events collected with the BESIII
detector, we report the study of the doubly radiative decay $\eta^\prime\to
\gamma\gamma\pi^0$ for the first time, where the $\eta^\prime$ meson is
produced via the $J/\psi\to \gamma\eta^\prime$ decay. The branching fraction of
$\eta^\prime\to \gamma\gamma\pi^0$ inclusive decay is measured to be ${\cal
B}(\eta^\prime\to \gamma\gamma\pi^0)_{\text{Incl.}}$ =
$(3.20\pm0.07\mbox{(stat)}\pm0.23\mbox{(sys)})\times 10^{-3}$, while the
branching fractions of the dominant process
$\eta^\prime\rightarrow\gamma\omega$ and the non-resonant component are
determined to be ${\cal B}(\eta^\prime\to \gamma\omega)\times {\cal
B}(\omega\to \gamma\pi^0) = (23.7 \pm1.4\mbox{(stat)}\pm1.8\mbox{(sys)})\times
10^{-4}$ and ${\cal B}(\eta^\prime\to \gamma\gamma\pi^0)_{\text{NR}} =
(6.16\pm0.64\mbox{(stat)} \pm0.67\mbox{(sys)})\times 10^{-4}$, respectively. In
addition, the $M^2_{\gamma\gamma}$-dependent partial widths of the inclusive
decay are also presented.
