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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
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
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
Number of elements of order a(n): A339122.
Sequence in context: A096076 A108864 A334140 * A055722 A028830 A327749
KEYWORD
nonn,fini,full
AUTHOR
Ben Whitmore, Nov 13 2020
STATUS
approved