We study the existence of symplectic resolutions of quotient singularities
V /G, where V is a symplectic vector space and G acts symplectically.
Namely, we classify the symplectically irreducible and
imprimitive groups, excluding those of the form K S2 where K <
SL2(C), for which the corresponding quotient singularity admits a
projective symplectic resolution. As a consequence, for dim V = 4,
we classify all symplectically irreducible quotient singularities V /G
admitting a projective symplectic resolution, except for at most
four explicit singularities, that occur in dimensions at most 10, for
which the question of existence remains open.