The group of Rubik's Cube (TM) is a group of cube transformations of the popular Rubik's Cube (TM) puzzle game.

The RubiksCubeGroup() command returns a permutation group isomorphic to the Rubik's Cube (TM) group.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$R≔\mathrm{RubiksCubeGroup}\left(\right)$

$R≔\mathrm{<\; a\; permutation\; group\; on\; 48\; letters\; with\; 6\; generators\; >}$

$\mathrm{GroupOrder}\left(R\right)$

$43252003274489856000$

$\mathrm{IsSimple}\left(R\right)$

$\mathrm{false}$

$\mathrm{Degree}\left(R\right)$

$48$

$\mathrm{IsTransitive}\left(R\right)$

$\mathrm{false}$

$\mathrm{numelems}\left(\mathrm{Orbits}\left(R\right)\right)$

$2$

$\mathrm{map}\left(\mathrm{numelems}\&comma;\mathrm{Orbits}\left(R\right)\right)$

$\left[24\&comma;24\right]$

$\mathrm{Labels}\left(R\right)$

$\left[\mathrm{front}\&comma;\mathrm{back}\&comma;\mathrm{left}\&comma;\mathrm{right}\&comma;\mathrm{up}\&comma;\mathrm{down}\right]$

$\mathrm{zip}\left(\mathrm{assign}\&comma;\mathrm{Labels}\left(R\right)\&comma;\mathrm{Generators}\left(R\right)\right)\&colon;$

$\mathrm{SS}≔\mathrm{Subgroup}\left(\left\{\mathrm{`.`}\left({\mathrm{right}}^2\&comma;{\mathrm{left}}^2\right)\&comma;\mathrm{`.`}\left({\mathrm{up}}^2\&comma;{\mathrm{down}}^2\right)\&comma;\mathrm{`.`}\left({\mathrm{front}}^2\&comma;{\mathrm{back}}^2\right)\right\}\&comma;R\right)$

$\mathrm{SS}≔⟨\left(1\&comma;48\right)\left(2\&comma;47\right)\left(3\&comma;46\right)\left(6\&comma;43\right)\left(7\&comma;42\right)\left(8\&comma;41\right)\left(9\&comma;32\right)\left(11\&comma;30\right)\left(12\&comma;29\right)\left(13\&comma;28\right)\left(14\&comma;27\right)\left(16\&comma;25\right)\left(17\&comma;24\right)\left(18\&comma;23\right)\left(19\&comma;22\right)\left(20\&comma;21\right)\left(33\&comma;40\right)\left(34\&comma;39\right)\left(35\&comma;38\right)\left(36\&comma;37\right)\&comma;\left(1\&comma;41\right)\left(3\&comma;43\right)\left(4\&comma;44\right)\left(5\&comma;45\right)\left(6\&comma;46\right)\left(8\&comma;48\right)\left(9\&comma;16\right)\left(10\&comma;15\right)\left(11\&comma;14\right)\left(12\&comma;13\right)\left(17\&comma;40\right)\left(19\&comma;38\right)\left(20\&comma;37\right)\left(21\&comma;36\right)\left(22\&comma;35\right)\left(24\&comma;33\right)\left(25\&comma;32\right)\left(26\&comma;31\right)\left(27\&comma;30\right)\left(28\&comma;29\right)\&comma;\left(1\&comma;8\right)\left(2\&comma;7\right)\left(3\&comma;6\right)\left(4\&comma;5\right)\left(9\&comma;25\right)\left(10\&comma;26\right)\left(11\&comma;27\right)\left(14\&comma;30\right)\left(15\&comma;31\right)\left(16\&comma;32\right)\left(17\&comma;33\right)\left(18\&comma;34\right)\left(19\&comma;35\right)\left(22\&comma;38\right)\left(23\&comma;39\right)\left(24\&comma;40\right)\left(41\&comma;48\right)\left(42\&comma;47\right)\left(43\&comma;46\right)\left(44\&comma;45\right)⟩$

$\mathrm{IsAbelian}\left(\mathrm{SS}\right)$

$\mathrm{true}$

$\mathrm{GroupOrder}\left(\mathrm{SS}\right)$

$8$

The GroupTheory[RubiksCubeGroup] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.