you're right. if n is odd, the center is e.
now, if n is even, the center is . this should be easy to prove.
Thanks for taking the time to answer my question. I just have a question on the notation that you used, what is ? does this represent a "flip" or a rotation. Also how would I begin to prove that this is abelian to every element in where n is even? Should i use a multiplication table?