  We investigate the magnetic field inversion symmetry of the pumped currents
in quantum pumps with various discrete symmetries using Floquet scattering
matrix approach. We found the pumped currents can have symmetries $I(B,\phi) =
-I(-B,-\phi)$ and $I(B,\phi) = I(-B,-\phi)$, where $\phi$ is the phase
difference of two time dependent perturbations, depending on the discrete
symmetry considered. The results in the adiabatic limit for each discrete
symmetry are compared with those of Brouwer's formula.
