/*
www-ATLAS of Group Representations.
S4(7):2 represented as permutations on 400 points.
*/

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