The number of elements in a group 
, denoted 
. If the order of a group is a
finite number, the group is said to be a finite group.
The order of an element 
of a finite group 
is the smallest power of 
such that 
, where 
is the identity element.
In general, finding the order of the element of a group is at least as hard as factoring
(Meijer 1996). However, the problem becomes significantly easier if 
and the factorization of 
are known. Under these circumstances, efficient algorithms
are known (Cohen 1993).
The group order can be computed in the Wolfram Language using the function GroupOrder[n].
