  We exploit null vectors of the fractional Virasoro algebra of the symmetric
product orbifold to compute correlation functions of twist fields in the large
$N$ limit. This yields a new method to derive correlation functions in these
orbifold CFTs that is purely based on the symmetry algebra. We explore various
generalisations, such as subleading (torus) contributions or correlation
functions of other fields than the bare twist fields. We comment on the
consequences of our computation for the $\text{AdS}_3/\text{CFT}_2$
correspondence.
