G is simply the number of elements in G .
Unfortunately, the word order is also associated with an element of a group and while there is a connection, it tends to be confusing in a first time meeting. The order of an element g in a group is the least positive integer k such that is the identity. If no such integer k exists, then g has infinite order. For example, in the real numbers under addition, the element 1 has infinite order. For the same reason, the number -1 has infinite order.