The number of elements in a group G, denoted left bracketing bar G right bracketing bar . If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite group G is the smallest power of n such that g^n = I, where I is the identity element. In general, finding the order of the element of a group is at least as hard as factoring. However, the problem becomes significantly easier if left bracketing bar G right bracketing bar and the factorization of left bracketing bar G right bracketing bar are known. Under these circumstances, efficient algorithms are known. The group order can be computed in the Wolfram Language using the function GroupOrder[n].

Abelian group | finite group

GroupOrder