/*
www-ATLAS of Group Representations.
S6(3) represented as permutations on 364 points.
*/

G<x,y>:=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]
>;
print "Group G is S6(3) < Sym(364)";