Is there an article somewhere with an exhaustive study of the Rubik's Cube Group $G$? Such as computing some subgroups of it or exhibiting some elements of its center $Z(G)$? I tried googling it and searching in this page but I could not find any such article.
Thank you very much!
Adventures in Group Theory talks somewhat extensively about the Rubik's Cube.
http://www.amazon.com/dp/0801869471/