PermutationGroup<120|
\[2,1,3,6,8,4,11,5,14,16,7,18,20,9,23,10,24,12,27,13,
21,30,15,17,34,36,19,39,40,22,43,45,46,25,49,26,52,54,28,
29,58,59,31,44,32,33,62,64,35,51,50,37,68,38,71,73,75,41,
42,67,79,47,66,48,82,63,60,53,70,69,55,78,56,89,57,91,92,
72,61,95,97,65,100,102,87,104,85,107,74,93,76,77,90,111,80,
96,81,99,98,83,105,84,108,86,101,106,88,103,116,110,94,112,
114,113,118,109,119,115,117,120],
\[3,4,5,7,9,10,12,13,15,16,17,19,21,22,1,23,25,26,2,28,
29,31,32,33,35,37,38,40,41,42,44,6,47,48,50,51,53,55,56,
57,8,60,30,46,61,14,63,65,27,11,66,67,69,70,72,74,76,77,
78,62,80,43,75,81,83,84,85,45,18,86,87,49,88,90,24,20,93,
71,94,96,98,99,101,102,103,105,106,108,109,92,110,39,91,112,
113,68,114,115,107,116,34,36,111,117,118,59,104,100,119,58,
52,97,89,79,120,73,82,54,95,64]
/*order=174182400=2^12*3^5*5^2*7*/>
