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A338883 Orders of elements of the Rubik's Cube group. 1
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)