Rubik's Cube group by rotations of the centre pieces, the second solely by symmetries of the corners, and the third solely by symmetries of the edges. The latter two factors are examples of wreath products. The simple groups that occur as quotients in the composition series of the standard cube group (i.e. ignoring centre piece rotations) are formula_37, formula_38, formula_30 (7 times), and formula_31 (12 times). Rubik's Cube group The Rubik’s Cube group is a group formula_1 that represents the structure of the Rubik's Cube mechanical puzzle. Each element of the set formula_2 corresponds to a cube move, which is the effect of
Professor's Cube of the puzzle uses a different mechanism. The fixed centers hold the centers next to the central edges in place, which in turn hold the outer edges. The non-central edges hold the corners in place, and the internal sections of the corner pieces do not reach the center of the cube. The V-Cube 5 mechanism, designed by Panagiotis Verdes, has elements in common with both. The corners reach to the center of the puzzle (like the original mechanism) and the center pieces hold the central edges in place (like the Eastsheen mechanism). The middle edges and center pieces adjacent to