TITLE: Presentation of Rubik's Cube group
QUESTION [15 upvotes]: The Rubik's Cube group is the group of permutations of the 20 cubes at the edges and vertices of a Rubik's group (taking into account their specific rotation) which are attainable by succesive rotations of its sides (the cubes in the middle of the sides are considered as fixed). Wikipedia says that this group is given as $(\mathbb Z_3^7 \times \mathbb Z_2^{11}) \rtimes \,((A_8 \times A_{12}) \rtimes \mathbb Z_2)$.
Is there also a nice presentation of this group in terms of generators and relations (i. e. at most as many relations as one can write down on a single sheet of paper)? In particular, are 6 generators (e. g.  the six standard rotations) the minimum number needed for a presentation or is it even possible to obtain a rotation around one side as a composition of rotations around the other five faces?

REPLY [5 votes]: This belongs as a comment, but due to being new here I can't comment yet. The link Dominik mentioned (129.81.170.14/~erowland/courses/2009-2/projects/Cordell.pdf) is indeed an interesting paper, but I noticed several things wrong, and would advise skepticism. For example, I don't know if the two elements mentioned are indeed generators, but I do know that the orders he claims they have (253 and 60) are wrong; they are in fact 77 and 12. In another section, he claims that "Any permutation of two adjacent sides (for example, F R) has order 105." This is a false generalization. F R does in fact have order 105, but F R' has order 63.
Nevertheless I was quite impressed with the paper; I just felt like mentioning that not everything there is accurate. I have very little understanding of the group theory of the Rubik's Cube, and it's possible there are many more errors I didn't recognize.