Rubik's Cube Group
From Speedsolving.com Wiki
The Rubik's Cube group is a group of order 43,252,003,274,489,856,000, and represents the states of the 3x3x3 Rubik's Cube.
As every group can be represented as a subgroup of a permutation group, the Rubik's Cube group can be represented as a subgroup of the permutations of its stickers.
The diameter of the Rubik's Cube group is known as God's Number for 3x3x3.
