Let be a number field and let be an order in . Then the set of equivalence classes of invertible fractional ideals of forms a multiplicative Abelian group called the Picard group of .

If is a maximal order, i.e., the ring of integers of , then every fractional ideal of is invertible and the Picard group of is the class group of . The order of the Picard group of is sometimes called the class number of . If is maximal, then the order of the Picard group is equal to the class number of .