From:

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# The 2nd most commutative element of the cube group

# It is the position of 7 clockwise and 1 counter-clockwise twists

# This commutes with 1 out of every 8 elements of the cube

commuter := ( 1,35, 9)( 3,27,33)( 6,11,17)( 8,19,25)(24,43,30)(32,48,38) (14,40,46)(16,22,41);; # The least commutative element of the cube group ( I think! ) # This commutes with 1 out of every 450,541,700,775,936,000 # or approximately 1 out of every 4.5 * 10^17 patterns least := ( 1, 6,32,19, 3,41,24,46)( 2, 4,13,42,29, 7,31,15,39,37,26,21) ( 5,28,34,10,20,23,36,18,45,44,47,12)( 8,33,16,30,40, 9,17,38) (11,48,25,27,22,43,14,35);;

after thinking about it, i realized that

corners: (8) edges: (12)commutes with even fewer elements. again, elements with

this cycle structure split into two conjugacy classes.mike

With GAP we must deal with permutations of cube facelets, and that is

why the permutation 'least' has 3 sets of 8 numbers and 2 sets of

12 numbers. Moreover, as I'm sure Mike will appreciate, the least

commutative element I've found is has a 8-cycle of corners and a

12-cycle of edges.

Size (Centralizer (cube, least));

96

-> Mark <-