PermutationGroup<325|
\[3,4,1,2,5,161,163,164,162,135,137,134,136,85,82,83,84,
104,105,102,103,122,123,124,125,239,237,238,236,187,188,190,
189,95,97,96,94,205,155,206,204,267,266,264,265,148,149,147,
146,79,78,81,80,175,173,172,174,284,285,283,282,118,120,121,
119,106,108,109,107,201,234,272,273,279,278,276,277,51,50,53,
52,15,16,17,14,218,221,219,220,167,165,158,166,37,34,36,35,
297,294,295,296,20,21,18,19,66,69,67,68,274,275,203,235,288,
287,289,286,62,65,63,64,22,23,24,25,241,242,240,243,208,209,
207,210,12,10,13,11,280,157,200,281,194,192,191,193,49,48,
46,47,263,261,262,260,312,39,255,139,92,170,223,6,9,7,8,91,
93,90,177,176,159,178,56,55,57,54,169,168,171,181,182,179,
180,186,185,184,183,30,31,33,32,144,143,145,142,197,198,195,
196,217,140,70,253,112,41,38,40,132,130,131,133,290,292,293,
291,216,215,199,86,88,89,87,224,160,222,226,225,228,227,230,
229,232,231,321,71,113,29,27,28,26,128,126,127,129,245,244,
247,246,268,269,271,270,306,202,307,156,258,259,256,257,153,
151,152,150,44,45,43,42,248,249,251,250,72,73,110,111,76,77,
75,74,138,141,61,60,58,59,117,115,114,116,211,214,212,213,
99,100,101,98,299,298,301,300,303,302,305,304,252,254,309,
308,311,310,154,314,313,315,316,317,318,324,322,233,320,325,
319,323],
\[236,117,247,212,13,29,98,316,297,187,254,90,198,239,237,3,
238,17,129,235,308,325,221,49,41,199,18,151,290,310,106,63,
202,5,245,246,244,96,281,304,283,25,233,306,144,70,170,88,
259,97,111,224,249,192,231,60,31,242,180,268,9,133,154,276,
43,54,280,209,299,64,74,140,183,125,178,301,94,47,84,278,
253,150,105,52,101,168,120,229,6,302,205,66,177,288,226,263,
50,2,116,115,114,56,248,176,282,156,76,14,147,4,213,214,211,
193,257,174,7,264,32,87,8,95,207,206,167,137,225,99,19,165,
55,305,113,108,275,139,22,179,30,72,172,148,127,23,184,110,
200,123,68,69,166,251,298,119,313,57,285,191,24,100,261,295,
20,78,118,241,71,323,277,164,93,145,65,128,201,309,273,75,
11,10,1,12,311,141,143,149,59,256,266,240,314,92,85,219,220,
279,197,34,312,210,175,155,51,48,189,35,142,16,186,109,62,
146,203,322,255,39,163,83,40,196,45,287,216,79,185,307,274,
272,204,112,300,284,173,270,217,293,289,27,134,153,28,228,81,
250,124,303,208,103,315,286,21,15,320,138,234,157,160,158,
159,271,232,73,267,130,36,91,38,102,26,215,260,58,171,294,
135,46,132,162,195,67,223,218,42,161,188,37,44,324,252,89,
121,61,181,317,80,53,292,190,82,131,319,182,265,194,169,222,
122,152,318,136,262,269,33,258,296,291,227,104,107,243,86,
230,321,77,126]
/*order=1018368000=2^12*3^2*5^3*13*17*/>
