Finite and infinite Groups:
If a group contains a finite number of distinct elements, it is called finite group otherwise an infinite group.
In other words, a group is said to be finite or infinite according as the underlying set is finite or infinite.
Order of a Group:
The number of elements in a finite group is called the order of the group. An infinite group is said to be of infinite order.
Note: It should be noted that the smallest group for a given composition is the set consisting of the identity element alone.
Example:

is the example of finite group with order 3.

is the another example of finite group with order 4.