This is probably going to be a tedious job for someone. I apologize in advance.

I have posted a multiplication table for this group. The group is generated by two elements a, and b, both cyclic and of order 4 and 3 respectively. That is to say that all the group elements are in the form where and . The only other piece of information needed to create the table is that I have set .

The problem I have is finding the center. By my definition, the center of a group G is the set of elements . I have determined the center of this group to be . The center is an Abelian subgroup, so the set I have labeled must be a group.

But it is not closed. In particular and .

What have I done wrong?

-Dan

Edit: That attachment is huge! I'll have to figure out how to reduce the size at some point.