  We address the nature of the $X(2370)$ resonance observed in the $J/\psi$
radiative decays, $J/\psi\rightarrow\gamma K^{+} K^{-}\eta'$,
$J/\psi\rightarrow\gamma K_S K_S\eta'$ and $J/\psi\rightarrow\gamma
\pi^{+}\pi^{-}\eta'$. By studying the invariant mass spectra we confirm that
decays of the $X(2370)$ into three pseudo-scalars are well described by an
effective chiral Lagrangian. We extract the branching ratio of $J/\psi\to
X(2370)\gamma$ and show that it is an order of magnitude larger compared to the
glueball production rate predicted by lattice QCD. This indicates that
$X(2370)$ is not likely to be a glueball candidate.
