A338883 Orders of elements of the Rubik's Cube group.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 33, 35, 36, 40, 42, 44, 45, 48, 55, 56, 60, 63, 66, 70, 72, 77, 80, 84, 90, 99, 105, 110, 112, 120, 126, 132, 140, 144, 154, 165, 168, 180, 198, 210, 231, 240, 252, 280, 315, 330, 336, 360, 420, 462, 495, 504, 630, 720, 840, 990, 1260

Offset

1,2

Comments

The Rubik's Cube group G is a subgroup of the symmetric group S_48 of order |G| = 43252003274489856000 = 2^27 * 3^14 * 5^3 * 7^2 * 11, generated by the six face twists of the cube. The elements of G have 73 distinct orders. The exponent of G, given by the least common multiple of the orders of the elements, is 55440.

Links

Table of n, a(n) for n=1..73.

Jaap's Puzzle Page, Order of elements, Cubic Circular, Issue 3 & 4, Spring & Summer 1982, p 34.

Example

10 is in the sequence because the algorithm U R U' F2 (in Singmaster notation) has order 10.
13 is not in the sequence because 13 is a prime not dividing the order of the group.

Crossrefs

Cf. A075152, A330389.

Number of elements of order a(n): A339122.

Sequence in context: A096076 A108864 A334140 * A055722 A028830 A327749

Adjacent sequences: A338880 A338881 A338882 * A338884 A338885 A338886

Keyword

nonn,fini,full

Author

Ben Whitmore, Nov 13 2020

Status

approved