  In this work, for a finite group $G$ and a 4-cocycle $\omega \in Z^4(G,
\mathbf{k}^\times)$, we compute explicitly the center of the monoidal
2-category $\operatorname{2Vec}_G^{\omega}$ of $\omega$-twisted $G$-graded
1-categories of finite dimensional $\mathbf{k}$-vector spaces. This center
gives a precise mathematical description of the topological defects in the
associated 3+1D Dijkgraaf-Witten TQFT. We prove that this center is a braided
monoidal 2-category with a trivial sylleptic center.
