We have observed the Crab pulsar with the Deep Space Network Goldstone 70 m antenna at 1664 MHz during three observing epochs for a total of 4 hr. Our data analysis has detected more than 2500 giant pulses, with flux densities ranging from 0.1 kJy to 150 kJy and pulse widths from 125 ns (limited by our bandwidth) to as long as 100 μs, with median power amplitudes and widths of 1 kJy and 2 μs, respectively. The most energetic pulses in our sample have energy fluxes of approximately 100 kJy μs. We have used this large sample to investigate a number of giant pulse emission properties in the Crab pulsar, including correlations among pulse flux density, width, energy flux, phase, and time of arrival. We present a consistent accounting of the probability distributions and threshold cuts in order to reduce pulse-width biases. The excellent sensitivity obtained has allowed us to probe further into the population of giant pulses. We find that a significant portion, no less than 50%, of the overall pulsed energy flux at our observing frequency is emitted in the form of giant pulses.