/*
www-ATLAS of Group Representations.
U3(4):2 represented as permutations on 416 points.
*/

G<x,y>:=PermutationGroup<416|\[
1,4,5,2,3,10,11,12,13,6,7,8,9,22,23,24,17,25,26,27,28,14,15,16,18,
19,20,21,42,43,44,45,46,35,34,47,48,49,39,50,51,29,30,31,32,33,36,37,38,40,
41,65,66,67,68,69,70,71,72,61,60,73,74,75,52,53,54,55,56,57,58,59,62,63,64,
76,98,99,100,101,102,103,104,105,106,107,108,109,110,111,92,91,112,113,114,115,116,77,78,79,
80,81,82,83,84,85,86,87,88,89,90,93,94,95,96,97,140,141,120,119,142,143,144,145,146,
147,148,149,150,151,152,153,154,155,156,157,158,159,160,117,118,121,122,123,124,125,126,127,128,129,
130,131,132,133,134,135,136,137,138,139,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,
210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,161,162,163,164,165,166,
167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,
192,193,194,268,250,269,270,271,272,253,273,274,275,276,277,266,265,243,260,259,278,279,280,281,230,
282,283,235,284,285,286,287,288,245,244,261,263,262,264,242,241,289,229,231,232,233,234,236,237,238,
239,240,246,247,248,249,251,252,254,255,256,257,258,267,325,309,292,326,294,327,328,329,330,331,332,
333,334,335,336,337,338,322,339,291,340,341,342,343,344,345,346,347,348,349,350,351,307,352,353,290,
293,295,296,297,298,299,300,301,302,303,304,305,306,308,310,311,312,313,314,315,316,317,318,319,320,
321,323,324,391,392,357,356,387,365,379,393,394,377,395,359,396,373,372,371,370,369,368,367,374,381,
397,363,398,360,399,375,400,383,401,402,403,358,388,389,404,354,355,361,362,364,366,376,378,380,382,
384,385,386,390,412,413,414,410,415,408,411,405,406,407,409,416]
,\[
2,3,1,6,8,7,4,9,5,14,16,18,20,15,10,17,11,19,12,21,13,29,31,33,35,
37,39,41,30,22,32,23,34,24,36,25,38,26,40,27,42,28,52,54,45,44,55,57,59,61,
63,53,43,46,56,47,58,48,60,49,62,50,64,51,76,78,80,82,84,86,88,90,92,94,96,
77,65,79,66,81,67,83,68,85,69,87,70,89,71,91,72,93,73,95,74,97,75,116,98,117,
100,118,120,122,124,126,106,127,129,131,133,135,112,136,138,99,101,119,102,121,103,123,104,125,105,
107,128,108,130,109,132,110,134,111,113,137,114,139,115,161,163,165,142,166,168,170,172,174,176,178,
180,182,184,153,185,187,157,189,191,193,162,140,164,141,143,167,144,169,145,171,146,173,147,175,148,
177,149,179,150,181,151,183,152,154,186,155,188,156,190,158,192,159,194,160,228,230,232,234,210,237,
239,201,240,242,243,245,247,249,251,236,253,211,254,256,215,214,257,259,204,261,263,265,222,266,224,
267,226,229,195,231,196,233,197,235,198,199,238,200,202,241,203,219,244,205,246,206,248,207,250,208,
252,209,212,255,213,216,258,217,260,218,262,220,264,221,223,225,227,290,292,269,293,295,297,299,301,
303,305,307,278,308,280,309,311,313,315,317,319,321,323,291,268,270,294,271,296,272,298,273,300,274,
302,275,304,276,306,277,279,281,310,282,312,283,314,284,316,285,318,286,320,287,322,288,324,289,354,
339,357,359,342,362,330,363,365,366,368,370,372,352,356,375,377,361,379,381,344,382,346,383,385,333,
387,374,389,355,325,326,358,327,360,328,329,331,364,332,350,367,334,369,335,371,336,373,337,338,376,
340,378,341,380,343,345,347,384,348,386,349,388,351,390,353,404,403,398,406,408,391,409,405,395,392,
411,401,400,396,393,407,394,399,410,397,402,416,413,412,415,414]
>;
print "Group G is U3(4):2 < Sym(416)";