  We compute the modular data (that is, the $S$ and $T$ matrices) for the
centre of the extended Haagerup subfactor. The full structure (i.e. the
associativity data, also known as 6-$j$ symbols or $F$ matrices) still appears
to be inaccessible. Nevertheless, starting with just the number of simple
objects and their dimensions (obtained by a combinatorial argument in
arXiv:1404.3955) we find that it is surprisingly easy to leverage knowledge of
the representation theory of $SL (2, \mathbb Z)$ into a complete description of
the modular data. We also investigate the possible character vectors associated
with this modular data.
