  We investigate the existence of action for both the electric and magnetic
sectors of Galilean Electrodynamics using Helmholtz conditions. We prove the
existence of unique action in magnetic limit with the addition of a scalar
field in the system. The check also implies the non existence of action in the
electric sector of Galilean electrodynamics. Dirac constraint analysis of the
theory reveals that there are no local degrees of freedom in the system.
Further, the theory enjoys a reduced but an infinite dimensional subalgebra of
Galilean conformal symmetry algebra as global symmetries. The full Galilean
conformal algebra however is realized as canonical symmetries on the phase
space. The corresponding algebra of Hamilton functions acquire a state
dependent central charge.
