A density prebunched electron beam on a Cerenkov free electron laser (CFEL) offers considerable enhancement in gain and efficiency in a dielectric loaded waveguide. The growth rate, efficiency, and gain were evaluated based on experimentally known parameters relevant to the CFEL. It was found that the growth rate, efficiency, and gain of the CFEL increase with the modulation index and has the largest value when the modulation index approaches unity in addition to the frequency and wave number of the prebunched beam are comparable to that of the radiation wave, i.e., when the prebunched beam velocity is comparable to the phase velocity of the radiation wave. The growth rate of the CFEL instability scales as one third power of the beam current. Moreover, the phase velocity of the radiation wave scales as minus one half power of the effective permittivity.