/*
www-ATLAS of Group Representations.
S4(5) represented as permutations on 300 points.
*/

G<x,y>:=PermutationGroup<300|\[
2,1,5,7,3,10,4,12,13,6,16,8,9,20,21,11,24,25,27,14,15,31,32,17,18,
35,19,37,38,40,22,23,43,34,26,46,28,29,41,30,39,50,33,53,54,36,57,58,60,42,
63,64,44,45,68,69,47,48,73,49,75,76,51,52,80,81,83,55,56,87,88,90,59,92,61,
62,96,97,99,65,66,103,67,105,106,108,70,71,112,72,113,74,115,116,118,77,78,122,79,124,
125,126,82,104,84,85,132,86,134,135,137,89,91,141,93,94,119,95,117,146,148,98,151,100,101,
102,156,157,158,159,161,107,133,109,110,167,111,169,170,172,114,174,175,177,179,120,181,121,183,184,
123,186,154,153,163,127,128,129,130,168,131,166,155,195,173,162,136,160,138,139,171,140,165,142,143,
203,144,205,145,206,147,209,149,150,188,152,214,185,215,193,216,218,190,220,164,213,197,221,222,223,
224,202,176,227,178,180,217,229,182,232,211,234,196,187,189,191,207,192,237,194,198,199,200,201,225,
240,204,243,208,245,246,210,236,212,250,233,219,252,254,226,257,258,228,255,230,231,264,265,267,235,
268,238,270,239,244,272,241,242,276,261,260,277,279,247,248,282,249,251,280,253,274,256,284,271,286,
259,262,289,263,269,291,266,293,273,294,275,296,288,278,290,281,292,283,285,295,287,299,300,297,298]
,\[
3,4,6,8,9,1,11,2,14,15,17,18,19,5,22,23,7,26,28,29,30,10,31,33,34,
12,36,13,39,41,16,42,44,37,45,47,25,48,20,49,21,51,52,24,55,56,27,59,61,62,
32,65,66,67,35,70,71,72,38,74,40,77,78,79,43,82,84,85,86,46,89,91,80,93,94,
95,50,98,100,101,102,53,104,54,107,109,110,111,57,103,58,114,60,117,119,120,121,63,123,64,
73,127,128,129,130,131,68,133,69,136,138,139,140,142,143,144,75,145,76,147,149,150,152,153,154,
155,81,90,83,160,162,163,164,165,166,87,168,88,171,173,118,92,176,178,141,180,96,182,97,179,
185,99,187,188,189,190,191,192,193,105,194,106,195,108,196,197,198,199,159,200,112,156,113,201,202,
115,204,116,122,207,208,210,175,211,212,213,124,125,126,172,217,219,169,206,132,134,135,220,137,218,
225,183,226,228,216,161,146,230,231,148,233,151,235,236,234,221,157,170,158,167,205,238,239,214,174,
241,242,177,244,181,247,248,184,249,186,224,251,253,255,256,203,259,260,261,262,263,209,266,215,246,
269,254,222,271,223,273,274,275,227,268,229,278,250,280,281,232,283,243,237,264,252,277,240,285,287,
282,288,245,290,270,284,292,294,265,257,295,258,272,296,297,298,276,286,267,293,299,279,300,289,291]
>;
print "Group G is S4(5) < Sym(300)";