  The purpose of this paper is to investigate the global categorical symmetries
that arise when gauging finite higher groups in three or more dimensions. The
motivation is to provide a common perspective on constructions of
non-invertible global symmetries in higher dimensions and a precise description
of the associated symmetry categories. This paper focusses on gauging finite
groups and split 2-groups in three dimensions. In addition to topological
Wilson lines, we show that this generates a rich spectrum of topological
surface defects labelled by 2-representations and explain their connection to
condensation defects for Wilson lines. We derive various properties of the
topological defects and show that the associated symmetry category is the
fusion 2-category of 2-representations. This allows us to determine the full
symmetry categories of certain gauge theories with disconnected gauge groups. A
subsequent paper will examine gauging more general higher groups in higher
dimensions.
