The Dijkgraaf-Witten invariants from second Chern classes

Given a 3-cocycle ψ 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 ψ is a 3-cocycle systematically transferred from the second Chern class of a complex representation of G, and show some procedures for computing the invariant, and clarify its topological interpretation under some conditions.