  Given a 3-cocycle $\psi$ in the cohomology of a finite group $G$, we can
define the Dijkgraaf-Witten invariant of closed 3-manifolds. In this paper, we
focus on the case where $\psi$ is a 3-cocycle canonically obtained from the
second Chern class of a representation of $G$, and show some procedures for
computing the invariant, and clarify its topological interpretation under some
conditions.
