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

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