Witch Week, by Diana Wynne Jones, 1982

Class 6B of Larwood House, a school for witch-orphans and other problem children, is obsessed with discovering which of its students is secretly a witch. If caught, witches are burned to death; if not caught, young witches cause mayhem so thick that only Chrestomanci, a dapper and astute enchanter from a parallel world, can sort it out. A boarding-school take on witch fantasy, Witch Week is a skillful concoction of dark humor, danger, magic, and school-age nastiness with a strong ending. Highly recommended.