  The interplay of symmetry and topological order leads to a variety of
distinct phases of matter, the Symmetry Enriched Topological (SET) phases. Here
we discuss physical observables that distinguish different SETs in the context
of Z$_2$ quantum spin liquids with SU(2) spin rotation invariance. We focus on
the cylinder geometry, and show that ground state quantum numbers for different
topological sectors are robust invariants which can be used to identify the SET
phase. More generally these invariants are related to 1D symmetry protected
topological phases when viewing the cylinder geometry as a 1D spin chain. In
particular we show that the Kagome spin liquid SET can be determined by
measurements on one ground state, by wrapping the Kagome in a few different
ways on the cylinder. In addition to guiding numerical studies, this approach
provides a transparent way to connect bosonic and fermionic mean field theories
of spin liquids. When fusing quasiparticles, it correctly predicts nontrivial
phase factors for combining their space group quantum numbers.
