  Symmetry acting on a (2+1)$D$ topological order can be anomalous in the sense
that they possess an obstruction to being realized as a purely (2+1)$D$ on-site
symmetry. In this paper, we develop a (3+1)$D$ topological quantum field theory
to calculate the anomaly indicators of a (2+1)$D$ topological order with a
general symmetry group $G$, which may be discrete or continuous, Abelian or
non-Abelian, contain anti-unitary elements or not, and permute anyons or not.
These anomaly indicators are partition functions of the (3+1)$D$ topological
quantum field theory on a specific manifold equipped with some $G$-bundle, and
they are expressed using the data characterizing the topological order and the
symmetry actions. Our framework is applied to derive the anomaly indicators for
various symmetry groups, including $\mathbb{Z}_2\times\mathbb{Z}_2$,
$\mathbb{Z}_2^T\times\mathbb{Z}_2^T$, $SO(N)$, $O(N)^T$, $SO(N)\times
\mathbb{Z}_2^T$, etc, where $\mathbb{Z}_2$ and $\mathbb{Z}_2^T$ denote a
unitary and anti-unitary order-2 group, respectively, and $O(N)^T$ denotes a
symmetry group $O(N)$ such that elements in $O(N)$ with determinant $-1$ are
anti-unitary. In particular, we demonstrate that some anomaly of $O(N)^T$ and
$SO(N)\times \mathbb{Z}_2^T$ exhibit symmetry-enforced gaplessness, i.e., they
cannot be realized by any symmetry-enriched topological order. As a byproduct,
for $SO(N)$ symmetric topological orders, we derive their $SO(N)$ Hall
conductance.
