/*
www-ATLAS of Group Representations.
A14 represented as permutations on 364 points.
*/

G<x,y>:=PermutationGroup<364|\[
1,4,7,6,11,2,8,3,14,18,13,23,5,16,27,9,31,20,36,10,12,35,21,42,25,
26,28,15,46,22,32,17,52,55,30,38,60,19,39,24,41,40,68,44,45,48,73,29,77,50,
51,53,33,84,57,89,34,37,88,58,95,62,63,64,100,43,67,66,105,70,71,72,74,47,109,
65,78,49,115,80,59,82,83,85,54,123,125,81,91,130,56,92,61,94,93,138,97,98,99,76,
101,102,69,104,103,106,107,108,111,151,75,155,113,114,116,79,162,118,119,120,121,122,124,86,127,
173,87,90,172,128,179,132,133,134,184,96,137,136,189,140,141,142,143,194,145,146,147,148,149,150,
152,110,199,144,156,112,205,158,135,160,161,163,117,164,165,129,167,168,169,170,218,166,175,223,126,
176,131,178,177,231,181,182,183,159,185,186,139,188,187,190,191,192,193,154,195,196,197,198,201,246,
153,250,203,204,206,157,257,208,209,210,211,212,213,214,215,216,217,220,269,171,174,268,221,275,225,
226,227,280,180,230,229,232,233,234,235,286,237,238,239,240,241,242,292,244,245,247,200,294,243,251,
202,300,253,236,255,256,258,207,259,228,261,262,263,222,265,266,295,264,271,314,219,272,224,274,273,
322,277,278,279,260,281,282,283,284,285,254,287,288,289,290,291,249,293,296,311,248,335,298,299,301,
252,302,303,304,305,306,307,308,309,334,267,270,333,312,350,316,317,318,352,276,321,320,323,324,357,
326,327,328,346,330,331,310,345,332,336,297,360,329,339,340,325,342,343,319,313,338,347,315,349,348,
351,344,353,354,355,356,341,358,359,361,337,362,363,364]
,\[
2,5,1,10,12,13,6,4,3,19,21,24,25,7,8,30,9,34,37,38,39,11,40,43,44,
14,22,35,15,20,16,51,17,56,18,58,61,62,63,64,23,66,69,70,26,27,28,76,29,31,
81,32,83,33,87,90,91,92,36,93,96,97,98,99,41,101,42,103,86,106,45,46,65,100,47,
59,48,114,49,50,57,52,120,53,122,54,126,55,128,131,132,133,134,60,136,139,140,141,142,88,
143,67,145,68,124,148,71,72,73,74,154,75,77,159,78,161,79,80,82,166,84,168,85,170,171,
174,175,176,89,177,180,181,182,183,94,185,95,187,117,190,191,192,193,102,195,104,105,107,108,109,
144,194,110,135,111,204,112,113,129,115,210,116,212,118,119,127,121,215,123,217,219,125,221,224,225,
226,227,130,229,207,232,233,234,172,235,137,237,138,163,164,149,240,241,184,242,146,147,150,151,152,
249,153,155,254,156,256,157,158,160,260,162,262,165,167,264,169,266,267,270,271,272,173,273,276,277,
278,279,178,281,179,258,213,208,284,285,186,287,188,189,198,290,291,196,197,199,243,292,200,236,201,
299,202,203,228,205,303,206,305,209,222,211,307,214,220,216,309,310,218,312,315,316,317,318,223,320,
252,263,259,323,268,324,230,231,253,327,280,328,238,239,245,331,286,244,246,247,334,248,250,338,251,
340,255,341,257,343,261,344,265,345,346,332,347,269,348,337,308,306,351,274,353,275,301,302,356,282,
283,298,359,288,289,294,293,295,329,296,349,297,325,300,362,319,304,363,313,311,357,330,358,314,361,
342,333,364,321,322,339,352,326,335,336,354,350,360,355]
>;
print "Group G is A14 < Sym(364)";