  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 and
braided auto-equivalences of its Drinfeld center. The latter provides the
labels for bulk Wilson lines; it follows that a symmetry is completely
characterized by its action on bulk Wilson lines.
