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

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