PermutationGroup<344|
\[1,4,5,2,3,10,11,12,13,6,7,8,9,22,23,24,25,26,27,28,
29,14,15,16,17,18,19,20,21,33,46,47,30,48,35,49,50,51,52,
40,53,54,55,56,57,31,32,34,36,37,38,39,41,42,43,44,45,76,
77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,58,59,
60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,121,122,
123,124,125,126,127,128,129,130,131,132,133,110,134,135,107,
119,136,137,138,139,140,141,142,111,143,94,95,96,97,98,99,
100,101,102,103,104,105,106,108,109,112,113,114,115,116,117,
118,120,184,185,186,187,188,189,150,190,191,192,169,193,194,
195,196,197,198,199,200,201,202,203,204,205,206,154,207,208,
209,210,211,175,212,213,214,215,216,217,218,219,144,145,146,
147,148,149,151,152,153,155,156,157,158,159,160,161,162,163,
164,165,166,167,168,170,171,172,173,174,176,177,178,179,180,
181,182,183,262,263,264,265,266,267,268,269,270,249,271,272,
273,274,275,276,277,278,279,280,259,281,282,256,283,284,251,
285,286,229,287,246,288,253,289,290,243,291,292,240,293,294,
220,221,222,223,224,225,226,227,228,230,231,232,233,234,235,
236,237,238,239,241,242,244,245,247,248,250,252,254,255,257,
258,260,261,318,319,303,310,309,306,316,320,297,321,317,300,
322,323,299,298,324,325,326,314,327,301,305,295,296,302,304,
307,308,311,312,313,315,335,329,339,340,341,334,333,328,337,
336,342,330,331,332,338,344,343],
\[2,3,1,6,8,7,4,9,5,14,16,18,20,15,10,17,11,19,12,21,
13,30,32,34,36,38,40,42,44,31,22,33,23,35,24,37,25,39,26,
41,27,43,28,45,29,58,60,61,63,65,67,69,71,73,47,74,54,59,
46,55,62,48,64,49,66,50,68,51,70,52,72,53,57,75,56,94,78,
95,96,98,100,76,102,104,106,108,110,111,113,115,117,119,87,
82,77,97,79,99,80,101,81,103,83,105,84,107,85,109,86,93,
112,88,114,89,116,90,118,91,120,92,144,146,148,150,152,153,
155,157,159,125,161,163,165,167,168,170,172,134,174,176,178,
180,182,145,121,147,122,149,123,151,124,130,154,126,156,127,
158,128,160,129,162,131,164,132,166,133,138,169,135,171,136,
173,137,175,139,177,140,179,141,181,142,183,143,220,215,222,
216,223,225,194,228,230,232,227,234,235,211,238,209,195,241,
243,245,217,248,187,250,252,240,254,237,256,258,186,218,206,
247,185,260,221,184,214,224,188,226,189,190,229,191,231,192,
233,193,200,236,196,197,239,198,199,242,201,244,202,246,203,
204,249,205,251,207,253,208,255,210,257,212,259,213,261,219,
291,269,296,265,273,298,277,295,300,302,267,276,274,286,266,
299,305,306,292,308,279,310,312,284,304,313,278,262,315,289,
307,316,290,263,297,264,272,268,301,270,303,271,275,288,282,
280,309,281,311,283,285,314,287,294,317,293,328,330,331,333,
321,334,335,319,337,323,329,318,325,332,320,322,327,336,324,
338,326,343,339,342,344,340,341]
/*order=5663616=2^7*3*7^3*43*/>
