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 (20), the Rubik's Domino (18) and, to some extent, the Pocket Cube (11). The table also shows that there is only one combination that is exactly 8 moves away from the solved state; this is the combination in which all the corners are in their correct places but all the edges are flipped, analogous to the "superflip" on the Rubik's Cube, which requires 20 moves to solve. The Super Floppy Cube (often shortened to "Super Floppy") is a common variant of the Floppy Cube. It was also invented by Katsuhiko Okamoto but several versions have also been produced by other