PermutationGroup<144|
\[2,4,6,8,10,9,13,1,15,14,18,19,16,22,3,25,26,23,24,11,
29,5,20,32,7,31,35,36,33,39,40,12,43,45,41,42,38,49,44,
17,53,54,21,56,52,58,59,61,55,63,64,66,27,28,37,30,72,67,
68,50,69,77,70,71,79,34,81,82,83,60,85,80,88,89,91,87,84,
95,86,97,46,47,48,102,51,104,101,98,99,94,100,108,73,109,
103,78,57,93,112,113,111,62,96,65,106,116,117,114,115,120,
76,74,75,123,90,121,122,126,125,124,105,128,92,131,130,129,
133,107,135,134,110,137,136,119,118,141,140,142,132,139,127,
144,138,143],
\[3,5,7,9,11,12,1,14,16,17,2,20,21,23,24,4,27,15,28,6,
30,31,8,18,33,34,10,37,38,13,41,42,44,46,47,48,19,50,51,
52,22,49,55,25,57,26,60,62,32,29,65,67,68,69,70,71,73,74,
75,35,76,36,53,78,39,80,40,63,84,43,86,87,45,90,92,93,94,
96,89,98,99,100,101,54,103,56,105,83,106,58,107,59,61,110,
85,64,111,66,109,114,88,115,95,112,72,79,118,119,81,77,116,
121,122,82,124,97,125,91,127,117,104,129,130,102,120,132,108,
134,113,136,128,138,139,131,140,123,142,126,143,144,137,141,
133,135]
/*order=357840=2^4*3^2*5*7*71*/>
