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A finite group is a finite set of elements with an associated group operation. The set is a group if it is closed and associative with respect to the operation on the set, and the set contains the identity and the inverse of every element in the set. Finite groups can be classified using a variety of properties, such as simple, complex, cyclic and Abelian. The study of groups is called group theory.

Find information about a finite group of a given order or type.

Find information and perform operations on permutations.