Alligators are not mammals, they are reptiles. Alligators do not have hair or fur like mammals, but are instead covered in scales, nor do they nurse their young with milk. Additionally alligators are cold-blooded, rather than warm-blooded like mammals.
Most reptiles like the alligator do not give live birth like mammals, but instead lay eggs. Alligators lay approximately 35 eggs at a time, however less than half that number will actually hatch, and less than half again will survive into adulthood.
Because they are cold-blooded, alligators have to put extra effort into regulating their body temperature. To help heat up their bodies they have to rely on outside heat sources, which is why they can often be found basking in the sun. When they need to cool off, they move to cooler/shadier spots, such as the water.