Single frequency- phase and group velocity?

Let's consider a single frequency signal of frequency say 'f'. If the wave is propagating through a medium (EM wave with a velocity of 'c') then what will be the phase and group velocity? I believe that we can't find out the phase velocity and that the group velocity should be equal to the velocity of light 'c'.

Can you tell me a specific example where these phase and group velocities are really useful?

Thanks in advance.