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

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