Here's some notes from Harvard on how to count Rubik's Cube positions with Group Theory
The number is: 2^(12)3^88!*12!
http://www.math.harvard.edu/~jjchen/docs/Group%20Theory%20an...
The number is: 2^(12)3^88!*12!
http://www.math.harvard.edu/~jjchen/docs/Group%20Theory%20an...
Foo*barOr ~520 exapositions, if you want to say it in a way that upsets people.
https://en.wikipedia.org/wiki/Binary_prefix#exbi
BTW don't bother Googling for exaposition or exbiposition. :-)