/*
www-ATLAS of Group Representations.
S4(7) represented as permutations on 400 points.
*/

G<x,y>:=PermutationGroup<400|\[
1,2,4,3,7,9,5,12,6,14,16,8,19,10,22,11,25,23,13,29,31,15,18,34,17,
37,38,40,20,43,21,41,47,24,49,51,26,27,55,28,32,57,30,60,61,63,33,66,35,69,
36,71,73,75,39,78,42,81,83,44,45,87,46,89,65,48,92,94,50,97,52,99,53,102,54,
105,107,56,110,80,58,113,59,116,118,86,62,88,64,123,125,67,128,68,130,132,70,134,72,137,
138,74,141,133,76,145,77,148,150,79,111,152,82,151,115,84,156,85,159,161,163,155,90,165,91,
167,169,93,172,95,158,96,104,98,135,180,100,101,184,186,103,164,189,191,106,193,192,108,195,109,
114,112,199,174,122,117,204,131,119,187,120,206,121,142,124,179,126,168,127,213,215,129,217,154,207,
197,220,222,166,136,181,227,229,139,218,140,160,234,143,230,144,147,146,238,149,208,176,242,153,225,
210,244,246,157,247,162,175,196,226,201,224,252,170,254,171,256,173,185,260,177,239,178,236,211,200,
209,182,266,183,190,270,237,233,188,273,223,232,194,221,278,280,198,272,202,282,203,205,281,263,285,
287,212,275,214,265,216,292,293,294,219,295,296,249,298,255,228,301,302,303,231,305,243,235,307,253,
276,286,240,311,241,248,245,289,315,250,277,251,317,283,319,308,257,258,259,261,262,323,264,325,326,
267,268,269,329,271,314,274,291,332,333,279,335,337,306,284,322,288,318,290,340,339,316,297,343,299,
300,346,348,304,350,352,309,310,355,312,358,313,342,321,320,363,338,324,366,368,327,369,328,349,330,
373,331,367,365,334,378,377,336,375,381,383,385,341,387,354,344,353,345,347,386,379,374,351,372,359,
388,357,356,371,389,360,394,361,395,362,370,364,376,380,397,393,399,391,382,384,400,390,398,392,396]
,\[
2,3,5,6,8,10,11,1,13,15,17,18,20,21,23,24,26,27,28,30,32,33,4,35,36,
34,39,41,42,44,45,46,48,7,50,52,53,54,40,12,56,58,59,9,62,64,65,67,68,70,
61,72,74,76,77,79,80,82,84,85,86,69,88,14,90,91,93,95,96,16,98,100,101,103,104,
106,108,109,19,111,112,114,115,117,89,119,120,121,122,124,126,127,22,129,131,31,133,135,136,25,
139,140,142,143,144,146,147,149,151,107,152,110,153,29,154,155,157,158,160,162,164,159,118,145,166,
168,170,171,173,174,175,176,177,178,179,181,182,183,185,187,188,37,190,192,47,38,81,194,196,197,
156,198,200,201,202,203,43,205,60,51,97,207,208,209,210,113,211,193,212,214,216,163,218,150,49,
219,221,223,224,225,226,228,230,231,191,232,233,235,236,237,73,167,66,239,240,55,241,57,217,125,
243,245,78,134,234,248,249,250,63,251,105,253,116,227,255,257,258,259,261,128,161,262,263,71,264,
265,92,267,268,269,215,271,272,123,274,275,75,276,277,279,130,281,83,180,213,283,184,284,87,286,
288,165,289,290,247,291,220,256,94,132,260,297,204,299,99,300,302,293,303,304,306,102,141,273,308,
246,309,310,312,206,305,313,314,294,316,172,315,252,318,320,199,321,292,280,322,186,324,317,244,327,
328,137,138,330,287,296,331,329,148,334,335,336,311,238,242,338,339,169,333,341,229,342,222,323,344,
345,347,349,189,351,353,319,354,356,357,195,359,360,361,362,364,365,326,367,363,355,370,352,371,372,
374,375,369,376,377,379,282,348,380,382,384,386,378,254,388,346,385,389,390,266,383,391,392,270,381,
332,393,343,278,387,358,285,301,298,394,373,396,295,397,307,398,340,366,325,399,337,395,400,368,350]
>;
print "Group G is S4(7) < Sym(400)";