  A coupled-channel analysis of BESIII data on radiative $J/\psi$ decays into
$\pi\pi$, $K\bar K$, $\eta\eta$ and $\omega\phi$ has been performed. The
partial-wave amplitude is constrained by a large number of further data. The
analysis finds ten isoscalar scalar mesons. Their masses, widths and decay
modes are determined. The scalar mesons are interpreted as mainly SU(3)-singlet
and mainly octet states. Octet isoscalar scalar states are observed with
significant yields only in the 1500-2100\,MeV mass region. Singlet scalar
mesons are produced over a wide mass range but their yield peaks in the same
mass region. The peak is interpreted as scalar glueball. Its mass and width are
determined to $M=1865$\er25$^{+10}_{-30}$ {\rm MeV} and $\Gamma=
370$\er$50^{+30}_{-20}$ {\rm MeV}, its yield in radiative $J/\psi$ decays to
($5.8\pm 1.0)\,10^{-3}$.
