I have the answer to your question. The class is mammalia and the order is cetacea. The characteristics of the order are: they are permanently aquatic, have fish like bodies, have flippers, no hind limbs, and broad flat tails called flukes for swimming, breathe through blowholes, and have a thick layer of blubber under the skin for insulation.
Answer provided by Paige Helterbran, Billings West High School.