compute the order of a group
GroupOrder( G )
a permutation group
The order of a group is the cardinality of its underlying set.
The GroupOrder( G ) command computes the order of the group G, if possible. (Note that the order of a finitely presented group cannot be determined, in general.)
In most cases, it is much more efficient to use the GroupOrder command to determine the order of a group than to list its elements with the Elements command and then count them. In the case of a symbolic group, this is the only way to compute the group order.
G ≔ SymmetricGroup⁡5
G ≔ BabyMonster⁡
G ≔ a,b|a2,b3,`.`⁡a,b5=1
The GroupTheory[GroupOrder] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
Download Help Document