PermutationGroup<240|
\[2,3,1,6,8,10,12,14,16,4,19,21,23,5,26,28,30,32,34,36,
7,39,40,41,43,45,46,9,49,51,53,55,57,11,50,61,42,64,66,
13,69,71,72,74,15,77,68,80,81,83,17,85,87,78,18,90,92,94,
96,98,20,101,103,105,106,22,109,111,24,114,37,25,118,120,
121,123,27,125,126,128,29,131,35,88,133,134,31,95,137,138,
110,33,79,141,84,143,145,147,148,150,151,135,154,156,38,159,
142,160,161,157,47,165,167,168,169,171,173,175,176,44,179,
180,158,172,54,93,185,48,119,187,178,190,52,192,136,102,194,
56,197,198,58,163,59,200,162,199,60,201,203,205,62,124,170,
63,207,208,91,76,65,177,67,97,107,140,189,214,216,70,218,
186,211,152,191,166,73,129,108,82,75,184,220,222,224,122,223,
153,195,210,112,215,117,86,204,89,130,219,233,164,230,209,99,
226,206,225,100,149,234,104,144,213,116,183,188,174,132,113,
182,115,232,229,231,217,127,212,193,239,237,235,181,146,240,
196,139,155,238,227,236,228,202,221],
\[1,4,5,7,9,11,13,15,17,18,20,22,24,25,27,29,31,33,35,
37,38,30,21,42,44,2,47,48,50,52,54,56,58,59,60,62,63,65,
67,68,70,26,73,75,76,78,79,71,82,84,66,86,32,88,89,91,93,
95,97,99,100,102,104,8,107,108,110,112,113,115,116,117,119,
36,122,118,124,87,127,129,130,94,39,132,28,135,136,3,61,139,
123,137,140,133,142,144,146,43,149,109,152,153,155,157,158,
106,148,143,162,163,164,166,125,74,170,172,174,101,177,178,
85,181,182,183,184,92,64,186,128,188,189,191,154,111,151,193,
195,196,80,96,40,199,197,120,16,190,171,202,204,206,12,187,
175,169,83,209,6,208,46,179,210,211,103,212,213,215,41,217,
205,207,69,121,219,77,114,220,221,57,105,81,214,223,225,226,
98,227,228,229,200,218,145,19,230,231,232,173,161,131,10,156,
160,23,150,192,49,168,224,235,236,51,55,176,203,14,237,34,
165,216,222,238,185,194,53,167,72,147,90,45,233,159,138,234,
239,240,201,198,141,134,180,126]
/*order=40320=2^7*3^2*5*7*/>
