  It is shown that the supersymmetry-preserving automorphisms of any non-linear
sigma-model on K3 generate a subgroup of the Conway group Co_1. This is the
stringy generalisation of the classical theorem, due to Mukai and Kondo,
showing that the symplectic automorphisms of any K3 manifold form a subgroup of
the Mathieu group M_{23}. The Conway group Co_1 contains the Mathieu group
M_{24} (and therefore in particular M_{23}) as a subgroup. We confirm the
predictions of the Theorem with three explicit CFT realisations of K3: the
T^4/Z_2 orbifold at the self-dual point, and the two Gepner models (2)^4 and
(1)^6. In each case we demonstrate that their symmetries do not form a subgroup
of M_{24}, but lie inside Co_1 as predicted by our Theorem.
