PermutationGroup<400|
\[1,2,4,3,7,9,5,12,6,14,16,8,19,10,22,11,25,23,13,29,
31,15,18,34,17,37,38,40,20,43,21,41,47,24,49,51,26,27,55,
28,32,57,30,60,61,63,33,66,35,69,36,71,73,75,39,78,42,81,
83,44,45,87,46,89,65,48,92,94,50,97,52,99,53,102,54,105,
107,56,110,80,58,113,59,116,118,86,62,88,64,123,125,67,128,
68,130,132,70,134,72,137,138,74,141,133,76,145,77,148,150,
79,111,152,82,151,115,84,156,85,159,161,163,155,90,165,91,
167,169,93,172,95,158,96,104,98,135,180,100,101,184,186,103,
164,189,191,106,193,192,108,195,109,114,112,199,174,122,117,
204,131,119,187,120,206,121,142,124,179,126,168,127,213,215,
129,217,154,207,197,220,222,166,136,181,227,229,139,218,140,
160,234,143,230,144,147,146,238,149,208,176,242,153,225,210,
244,246,157,247,162,175,196,226,201,224,252,170,254,171,256,
173,185,260,177,239,178,236,211,200,209,182,266,183,190,270,
237,233,188,273,223,232,194,221,278,280,198,272,202,282,203,
205,281,263,285,287,212,275,214,265,216,292,293,294,219,295,
296,249,298,255,228,301,302,303,231,305,243,235,307,253,276,
286,240,311,241,248,245,289,315,250,277,251,317,283,319,308,
257,258,259,261,262,323,264,325,326,267,268,269,329,271,314,
274,291,332,333,279,335,337,306,284,322,288,318,290,340,339,
316,297,343,299,300,346,348,304,350,352,309,310,355,312,358,
313,342,321,320,363,338,324,366,368,327,369,328,349,330,373,
331,367,365,334,378,377,336,375,381,383,385,341,387,354,344,
353,345,347,386,379,374,351,372,359,388,357,356,371,389,360,
394,361,395,362,370,364,376,380,397,393,399,391,382,384,400,
390,398,392,396],
\[2,3,5,6,8,10,11,1,13,15,17,18,20,21,23,24,26,27,28,30,
32,33,4,35,36,34,39,41,42,44,45,46,48,7,50,52,53,54,40,
12,56,58,59,9,62,64,65,67,68,70,61,72,74,76,77,79,80,82,
84,85,86,69,88,14,90,91,93,95,96,16,98,100,101,103,104,106,
108,109,19,111,112,114,115,117,89,119,120,121,122,124,126,
127,22,129,131,31,133,135,136,25,139,140,142,143,144,146,147,
149,151,107,152,110,153,29,154,155,157,158,160,162,164,159,
118,145,166,168,170,171,173,174,175,176,177,178,179,181,182,
183,185,187,188,37,190,192,47,38,81,194,196,197,156,198,200,
201,202,203,43,205,60,51,97,207,208,209,210,113,211,193,212,
214,216,163,218,150,49,219,221,223,224,225,226,228,230,231,
191,232,233,235,236,237,73,167,66,239,240,55,241,57,217,125,
243,245,78,134,234,248,249,250,63,251,105,253,116,227,255,
257,258,259,261,128,161,262,263,71,264,265,92,267,268,269,
215,271,272,123,274,275,75,276,277,279,130,281,83,180,213,
283,184,284,87,286,288,165,289,290,247,291,220,256,94,132,
260,297,204,299,99,300,302,293,303,304,306,102,141,273,308,
246,309,310,312,206,305,313,314,294,316,172,315,252,318,320,
199,321,292,280,322,186,324,317,244,327,328,137,138,330,287,
296,331,329,148,334,335,336,311,238,242,338,339,169,333,341,
229,342,222,323,344,345,347,349,189,351,353,319,354,356,357,
195,359,360,361,362,364,365,326,367,363,355,370,352,371,372,
374,375,369,376,377,379,282,348,380,382,384,386,378,254,388,
346,385,389,390,266,383,391,392,270,381,332,393,343,278,387,
358,285,301,298,394,373,396,295,397,307,398,340,366,325,399,
337,395,400,368,350]
/*order=138297600=2^8*3^2*5^2*7^4*/>
