  The study of spatial symmetries was accomplished during the last century, and
had greatly improved our understanding of the properties of solids. Nowadays,
the symmetry data of any crystal can be readily extracted from standard
first-principles calculation. On the other hand, the topological data
(topological invariants), the defining quantities of nontrivial topological
states, are in general considerably difficult to obtain, and this difficulty
has critically slowed down the search for topological materials. Here, we
provide explicit and exhaustive mappings from symmetry data to topological data
for arbitrary gapped band structure in the presence of time-reversal symmetry
and any one of the 230 space groups. The mappings are completed using the
theoretical tools of layer construction and symmetry-based indicators. With
these results, finding topological invariants in any given gapped band
structure reduces to a simple search in the mapping tables provided.
