PermutationGroup<240|
\[2,1,5,7,3,10,4,13,15,6,18,20,8,23,9,25,27,11,29,12,
31,33,14,36,16,37,17,40,19,39,21,44,22,46,47,24,26,51,30,
28,54,56,58,32,60,34,35,63,64,66,38,68,70,41,73,42,75,43,
77,45,80,82,48,49,84,50,86,52,89,53,92,94,55,96,57,98,59,
101,103,61,106,62,109,65,105,67,113,115,69,112,117,71,120,
72,110,74,125,76,99,108,78,129,79,130,85,81,134,100,83,95,
139,90,87,142,88,136,91,147,148,93,151,152,140,131,97,157,
159,160,102,104,124,164,165,107,168,116,170,161,111,123,172,
114,173,156,174,175,118,119,176,178,121,122,180,182,183,144,
126,185,127,128,138,188,189,132,133,190,191,135,194,137,171,
141,143,145,146,149,197,150,200,153,202,154,155,206,158,208,
210,162,163,166,167,215,217,169,198,219,177,195,214,179,222,
181,203,207,223,184,204,186,209,187,211,212,213,199,192,228,
193,227,196,221,220,201,205,232,233,234,218,216,237,236,238,
224,225,226,235,230,229,231,240,239],
\[3,4,6,8,9,11,12,14,16,17,19,21,22,24,15,26,28,18,1,30,
32,34,35,2,25,38,39,41,20,42,43,45,33,37,48,49,50,5,52,
53,55,57,59,44,7,61,62,56,65,13,67,69,71,72,10,74,29,76,
78,79,81,70,83,66,75,85,87,88,90,91,93,95,73,23,97,99,100,
102,104,105,107,108,110,63,111,112,114,116,89,27,118,119,121,
122,123,124,36,126,115,127,128,31,103,131,132,133,135,136,
137,138,140,141,113,143,144,145,146,47,149,150,40,153,154,
155,156,158,117,161,129,162,163,130,166,167,46,169,96,84,171,
64,120,142,51,58,157,77,176,152,177,86,179,160,181,54,109,
184,68,186,159,185,187,80,60,148,165,139,192,193,195,170,106,
172,196,197,134,178,198,199,201,183,203,204,205,207,164,209,
211,212,168,213,214,216,218,188,82,220,219,92,221,180,191,
182,94,190,224,194,225,226,98,227,101,223,202,151,215,175,
173,229,230,231,147,222,206,200,125,235,236,210,189,234,217,
232,228,174,237,233,239,238,208,240]
/*order=348364800=2^13*3^5*5^2*7*/>
