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
Floppy Cube companies. The key difference between this puzzle and the Floppy Cube is that the Floppy Cube is restricted to only 180° rotations (i.e. an edge piece cannot be twisted 90°), while the Super Floppy Cube does allow edges to rotate 90°. This in turn allows the corner pieces to move to locations "above" and "below" the edge pieces and thus change the shape of the puzzle. There is also a subtle difference between the original version of the puzzle and the version mass-produced by other companies. The original puzzle has an internal mechanism which prevents an isolated edge piece from