Some groups are infinite. The group of integers under addition is an infinite group. There are an infinite number of integers so the addition group of integers has an infinite number of elements.
Some groups are finite.
The main diagonal is the one from the upper left corner to the lower right corner. Similarly the binary operation for a group can be represented in a square array just as the multiplication table was. Again by noticing the symmetry about the main diagonal we can see that this is an abelian group. This means that each element has an inverse. For each element there is something that combines with it according to the group operation to produce the identity.