For a finite subgroup G of GL(2,C), it is known that the Hilbert scheme G-Hilb(C^2), which parameterizes “G-clusters”, is the minimal resolution of the quotient singularity. Generalizing it, we consider the moduli space of “G-constellations”, which are certain G-equivariant coherent sheaves. The moduli space depends on the choice of a stability parameter. For a generic stability parameter, it is a resolution of the quotient singularity and its derived category can be embedded into that of the quotient stack. The problem we address is to characterize these moduli spaces among resolutions of the quotient singularity.