The USS John C. Stennis (CVN 74) conducting flight operations in the Atlantic. The Stennis, when fully crewed, has a capacity of more than 6,000 officers and crew.
The Stennis is powered by two nuclear reactors, so it can run for decades without needing to be refueled. The only limitation on its range is the need for other supplies. Otherwise it can travel the globe at more than 30 knots continuously if needed.