  Quantum computations that involve only Clifford operations are classically
simulable despite the fact that they generate highly entangled states; this is
the content of the Gottesman-Knill theorem. Here we isolate the ingredients of
the theorem and provide generalisations of some of them with the aim of
identifying new classes of simulable quantum computations. In the usual
construction, Clifford operations arise as projective normalisers of the first
and second tensor powers of the Pauli group. We consider replacing the Pauli
group by an arbitrary finite subgroup G of U(d). In particular we seek G such
that G tensor G has an entangling normaliser. Via a generalisation of the
Gottesman-Knill theorem the resulting normalisers lead to classes of quantum
circuits that can be classically efficiently simulated. For the qubit case d=2
we exhaustively treat all finite subgroups of U(2) and find that the only ones
(up to unitary equivalence and trivial phase extensions) with entangling
normalisers are the groups G_n generated by X and the n^th root of Z.
