Normalisers of primitive permutation groups in quasipolynomial time

We show that given generators for subgroups $G$ and $H$ of ${\mathrm{S}}_n$, if $G$ is primitive then generators for ${\mathrm{N}}_H(G)$ may be computed in quasipolynomial time, namely $2^{O({\log }^{3}n)}$. The previous best known bound was simply exponential.