PermutationGroup<364|
\[2,1,5,7,3,10,4,13,9,6,17,19,8,22,15,25,11,28,12,20,
31,14,34,35,16,38,40,18,43,45,21,48,47,23,24,53,54,26,57,
27,60,50,29,64,30,67,33,32,70,42,68,74,36,37,55,79,39,58,
82,41,61,86,88,44,91,66,46,51,94,49,97,72,98,52,87,93,102,
104,56,107,109,59,112,114,116,62,75,63,118,90,65,121,76,69,
95,125,71,73,129,131,133,77,103,78,138,139,80,142,81,126,
145,83,148,84,151,85,152,89,155,120,92,158,159,161,96,110,
157,165,99,162,100,169,101,170,171,173,137,105,106,140,163,
108,181,144,111,184,186,113,189,190,115,117,176,154,119,177,
127,122,123,160,124,130,141,196,128,166,201,203,132,134,135,
208,136,211,175,153,156,215,217,207,143,220,221,146,224,147,
227,229,149,150,232,231,234,236,238,164,241,243,244,245,167,
242,168,204,205,249,180,172,253,255,174,212,258,214,178,261,
179,218,256,182,183,266,268,185,270,226,187,228,188,275,192,
191,277,193,267,194,237,195,239,283,197,202,198,199,200,289,
291,293,206,250,259,297,209,254,210,219,296,213,251,300,216,
302,282,301,304,222,235,223,273,225,272,271,269,278,230,308,
233,274,314,315,295,263,240,319,285,321,318,288,246,290,247,
325,248,305,281,257,252,330,299,260,264,262,303,265,294,306,
327,276,320,310,312,311,335,279,280,331,340,287,284,309,286,
343,332,338,292,347,307,328,329,298,316,323,345,350,313,352,
342,324,339,317,344,337,322,341,333,353,326,357,349,334,358,
336,346,354,355,356,348,351,361,362,359,360,364,363],
\[3,4,6,8,9,11,12,14,15,16,18,20,21,23,24,26,27,1,29,30,
32,33,2,36,37,39,41,42,44,46,47,49,50,51,52,5,55,56,58,
59,61,62,63,65,66,7,68,69,71,72,73,75,76,77,78,80,81,10,
83,84,85,87,89,90,92,43,93,88,95,96,13,86,99,31,100,101,
103,105,106,108,110,111,113,115,17,22,117,74,45,119,120,19,
122,123,124,126,127,128,130,132,134,135,136,137,25,140,141,
143,142,144,146,147,149,150,152,153,28,154,97,156,157,118,
160,162,163,164,64,166,167,34,168,35,139,158,172,174,175,176,
177,178,179,180,38,182,183,185,187,188,40,131,191,192,193,67,
194,195,98,53,161,196,197,48,198,199,200,121,202,204,205,206,
207,209,210,54,212,213,214,216,218,169,219,57,222,223,225,
226,228,230,231,232,233,60,235,237,239,240,242,211,70,246,
247,220,248,114,109,250,251,252,254,221,256,257,259,260,217,
79,262,263,236,264,265,267,269,244,82,271,272,273,274,190,
276,148,270,278,279,280,281,282,91,94,284,285,286,287,288,
290,292,294,295,238,296,261,173,102,298,125,104,203,299,133,
301,303,107,129,253,275,305,306,307,308,309,229,112,310,311,
312,283,313,116,316,317,170,318,320,159,322,255,323,300,315,
324,304,326,327,328,329,243,224,138,249,331,332,333,334,145,
335,336,151,337,227,291,319,338,339,165,181,155,321,189,341,
342,344,345,266,346,314,258,289,171,348,208,349,215,201,351,
184,186,353,354,355,350,277,343,297,356,352,347,325,340,241,
359,330,234,293,302,245,358,360,268,363,357,362,361,364]
/*order=2^9*3^9*5*7*13*/>
