  We study the Newman--Unti (NU) group from the viewpoint of
infinite-dimensional geometry. The NU group is a topological group in a natural
coarse topology, but it does not become a manifold and hence a Lie group in
this topology. To obtain a manifold structure we consider a finer Whitney-type
topology. This turns the unit component of the NU group into an
infinite-dimensional Lie group. We then study the Lie theoretic properties of
this group. Surprisingly, the group operations of the full NU group become
discontinuous, whence the NU group does not support a Lie group structure. The
NU group contains the Bondi--Metzner--Sachs (BMS) group as a subgroup, whose
Lie group structure was constructed in a previous article. It is well known
that the NU Lie algebra splits into a direct sum of Lie ideals of the Lie
algebras of the BMS group and conformal rescalings of scri. However, the lack
of a Lie group structure on the NU group implies that the BMS group cannot be
embedded as a Lie subgroup therein.
