  We study category O for the (centrally extended) Schr\"odinger algebra. We
determine the quivers for all blocks and relations for blocks of nonzero
central charge. We also describe the quiver and relations for the finite
dimensional part of O. We use this to determine the center of the universal
enveloping algebra and annihilators of Verma modules. Finally, we classify
primitive ideals with nonzero central charge.
