PermutationGroup<112|
\[2,1,5,7,3,11,4,13,12,15,6,9,8,19,10,23,18,17,14,28,
29,26,16,24,25,22,34,20,21,30,39,41,33,27,44,46,47,49,31,
52,32,53,55,35,56,36,37,61,38,58,63,40,42,66,43,45,69,50,
68,72,48,62,51,77,78,54,79,59,57,70,71,60,85,86,87,89,64,
65,67,80,95,97,98,100,73,74,75,101,76,99,106,92,107,108,81,
102,82,83,90,84,88,96,103,104,105,91,93,94,109,110,111,112
],
\[3,4,1,8,9,2,12,6,14,5,16,7,18,10,21,24,11,25,26,13,
30,15,31,17,20,33,19,35,37,22,40,23,27,42,45,28,48,29,50,
32,44,54,34,41,36,57,59,38,53,62,39,64,49,43,67,65,70,46,
71,47,73,51,75,56,52,74,80,55,81,58,60,83,66,61,88,63,90,
92,93,68,96,69,99,72,101,103,97,76,100,105,77,78,106,79,
107,82,109,108,84,89,111,85,86,87,91,94,95,112,104,98,102,
110]
/*order=40320=2^7*3^2*5*7*/>
