  We study in general spacetime dimension the symmetry of the theory obtained
by gauging a non-anomalous finite normal Abelian subgroup $A$ of a
$\Gamma$-symmetric theory. Depending on how anomalous $\Gamma$ is, we find that
the symmetry of the gauged theory can be i) a direct product of $G=\Gamma/A$
and a higher-form symmetry $\hat A$ with a mixed anomaly, where $\hat A$ is the
Pontryagin dual of $A$; ii) an extension of the ordinary symmetry group $G$ by
the higher-form symmetry $\hat A$; iii) or even more esoteric types of
symmetries which are no longer groups.
  We also discuss the relations to the effect called the $H^3(G,\hat A)$
symmetry localization obstruction in the condensed-matter theory and to some of
the constructions in the works of Kapustin-Thorngren and Wang-Wen-Witten.
