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

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