Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects. Symmetry groups are thus Brauer–Picard groups. We present a gauge theoretic realization of all symmetries of abelian Dijkgraaf–Witten theories. The symmetry group for a Dijkgraaf–Witten theory with gauge group a finite abelian group A, and with vanishing 3-cocycle, is generated by group automorphisms of A, by automorphisms of the trivial Chern–Simons 2-gerbe on the stack of A-bundles, and by partial e-m dualities. We show that transmission functors naturally extracted from extended topological field theories with surface defects give a physical realization of the bijection between invertible bimodule categories of a fusion category A A and braided auto-equivalences of its Drinfeld center Z(A) Z(A) . The latter provides the labels for bulk Wilson lines; it follows that a symmetry is completely characterized by its action on bulk Wilson lines.