  We study the space-time symmetries of the actions obtained by expanding the
action for a massive free relativistic particle around the Galilean action. We
obtain all the point space-time symmetries of the post-Galilean actions by
working in canonical space. We also construct an infinite collection of
generalized Schr\"odinger algebras parameterized by an integer $M$, with $M=0$
corresponding to the standard Schr\"odinger algebra. We discuss the
Schr\"odinger equations associated to these algebras, their solutions and
projective phases.
