  We extend the 5-dimensional Galilean space-time to a (5+1) Galilean
space-time in order to define a parity transformation in a covariant manner.
This allows us to discuss the discrete symmetries in the Galilean space-time,
which is embedded in the (5+1) Minkowski space-time. We discuss the Dirac-type
field, for which we give the 8\times 8 gamma matrices explicitly. We
demonstrate that the CPT theorem holds in the (5+1) Galilean space-time.
