# All equivalent moves on a rubik's cube

Call the primitive moves on the rubik's cube "R,L,U,D,F,B" for right, left, up, down, front, and back respectively.

Let us say that I have a permutation of the stickers on the cube written as a word in the primitive moves, e.g. RUDU.

Is there a way to find the set of all equivalent words in the primitive moves (under a certain length)?

I imagine that it would be something like $\sigma H$ where $\sigma$ is the word you start with and $H$ is a subgroup of $\langle R,L,U,D,F,B\rangle$.

Unfortunately, it's been awhile since I've done anything with group theory, so any help would be much appreciated.