  We show that the topological rank of an orbit full group generated by an
ergodic, probability measure-preserving free action of a non-discrete
unimodular locally compact Polish group is two. For this, we use the existence
of a cross section and show that for a locally compact Polish group, the full
group generated by any dense subgroup is dense in the orbit full group of the
action of the group.
  We prove that the orbit full group of a free action of a locally compact
Polish group is extremely amenable if and only if the acting group is amenable,
using the fact that the full group generates the von Neumann algebra of the
action.
