/*
www-ATLAS of Group Representations.
G2(4) represented as permutations on 416 points.
*/

G<x,y>:=PermutationGroup<416|\[
2,1,5,7,3,10,4,13,12,6,11,9,8,20,22,24,26,27,29,14,32,15,23,16,36,
17,18,40,19,43,31,21,47,49,50,25,53,55,57,28,60,42,30,62,64,66,33,69,34,35,
72,74,37,77,38,79,39,82,84,41,87,44,90,45,92,46,95,97,48,100,101,51,104,52,107,
76,54,111,56,109,114,58,117,59,120,122,61,125,89,63,128,65,131,132,67,135,68,138,99,70,
71,140,142,73,143,144,75,147,80,150,78,153,155,81,156,158,83,133,161,85,164,86,166,167,88,
170,171,91,174,176,93,94,118,181,96,184,137,98,186,102,188,103,105,106,145,192,108,195,196,110,
179,200,112,203,113,115,157,116,208,209,119,212,211,121,165,123,124,217,219,126,127,223,225,129,228,
130,230,232,151,235,134,238,183,136,241,139,244,141,193,248,250,146,189,252,148,149,254,255,257,152,
220,259,154,262,214,240,264,159,160,267,163,162,221,205,263,274,168,276,169,201,213,224,172,222,173,
280,282,175,247,177,266,178,287,289,180,277,291,182,294,206,185,284,278,187,301,302,229,190,304,191,
307,194,308,197,198,311,199,313,202,275,261,204,215,207,319,231,210,322,324,326,327,328,330,216,260,
218,236,243,333,226,281,227,336,242,339,340,233,299,234,343,237,345,347,239,349,296,351,352,288,354,
245,246,356,249,359,306,251,253,362,310,256,365,258,314,315,316,368,370,265,373,350,268,375,269,325,
270,271,272,377,273,338,376,279,379,363,283,348,331,285,286,384,383,290,353,292,387,293,337,295,321,
297,298,344,300,392,303,357,395,305,396,389,309,335,398,312,381,397,317,369,318,399,380,320,401,323,
332,329,403,334,372,366,382,342,341,405,393,346,388,361,390,394,355,386,391,358,360,367,364,371,400,
374,407,378,411,385,408,402,406,409,410,404,412,414,413,415,416]
,\[
3,4,6,8,9,11,12,14,15,16,17,18,19,21,23,25,1,28,30,31,2,33,34,35,37,
38,39,41,42,44,45,46,48,5,51,52,54,56,58,59,7,61,22,63,65,67,68,70,71,50,
73,75,76,10,78,80,81,83,85,86,88,89,13,91,93,94,96,98,99,43,102,103,105,106,108,
109,110,60,112,113,115,116,118,119,121,123,124,126,82,127,129,130,20,133,134,136,137,139,140,64,
47,141,107,104,24,145,146,148,149,151,152,154,26,74,157,159,160,27,162,163,165,90,55,168,169,
29,172,173,175,177,178,179,180,182,183,32,185,132,101,187,143,189,49,190,191,193,194,36,197,198,
199,201,202,204,77,205,206,207,62,210,211,213,214,79,40,215,216,218,220,221,222,224,226,227,100,
229,231,233,234,236,237,239,166,240,242,243,245,246,247,249,114,251,72,238,230,253,53,256,155,195,
258,260,261,164,263,57,265,266,181,268,269,270,271,272,273,228,275,267,219,241,277,278,279,122,262,
281,283,250,284,235,285,286,288,290,287,66,292,293,295,296,297,298,299,300,69,252,223,303,305,306,
188,192,309,208,310,212,312,314,315,316,276,317,244,318,320,321,87,323,325,150,84,329,135,259,313,
331,328,332,142,304,334,335,337,338,92,341,200,342,282,138,344,346,322,348,95,350,125,97,353,156,
355,170,357,358,360,167,361,161,363,280,364,366,294,111,347,367,369,371,372,365,374,147,117,339,308,
171,376,302,120,352,378,326,377,128,380,381,382,362,383,340,327,131,379,385,386,209,388,217,319,389,
390,373,391,264,393,225,394,255,307,144,397,176,392,291,158,351,153,289,356,248,400,398,387,254,349,
232,402,203,345,368,333,174,404,384,311,403,406,274,184,257,186,196,407,370,408,396,409,375,405,354,
410,336,343,412,413,330,411,401,359,414,301,324,415,395,416,399]
>;
print "Group G is G2(4) < Sym(416)";