  We describe two similar but independently-coded computations used to
construct a complete catalogue of the transitive groups of degree less than
$48$, thereby verifying, unifying and extending the catalogues previously
available. From this list, we construct all the vertex-transitive graphs of
order less than $48$. We then present a variety of summary data regarding the
transitive groups and vertex-transitive graphs, focussing on properties that
seem to occur most frequently in the study of groups acting on graphs. We
illustrate how such catalogues can be used, first by finding a complete list of
the elusive groups of order at most $47$ and then by completely determining
which groups of order at most $47$ are CI groups
