/*
www-ATLAS of Group Representations.
U4(3):D8 represented as permutations on 280 points.
*/

G<x,y>:=PermutationGroup<280|\[
1,4,6,2,10,3,14,15,17,5,11,21,23,7,8,28,9,32,33,35,12,39,13,42,43,
45,47,16,50,51,53,18,19,59,20,37,36,64,22,68,69,24,25,74,26,77,27,81,82,29,
30,88,31,92,93,56,96,98,34,102,103,104,106,38,72,110,112,40,41,117,118,65,121,44,123,
124,46,128,129,131,48,49,83,134,127,136,87,52,89,140,142,54,55,147,149,57,151,58,154,100,
156,60,61,62,161,63,107,108,163,66,165,67,168,162,122,170,70,71,119,174,73,115,75,76,177,
126,85,78,79,130,80,137,138,84,186,86,132,133,172,90,190,91,193,195,155,198,94,202,95,204,
97,152,153,99,145,101,208,209,210,181,105,114,109,164,111,213,214,113,180,116,171,139,189,120,218,
220,125,223,187,169,160,225,226,228,185,135,179,230,173,141,232,215,143,237,144,229,197,146,242,200,
201,148,203,150,246,248,224,157,158,159,239,254,166,167,192,245,247,175,257,176,259,222,178,207,182,
183,227,184,196,188,231,191,262,264,235,266,194,269,211,258,241,199,243,244,216,205,217,206,271,250,
251,252,256,212,267,253,219,240,221,260,261,233,273,234,265,236,255,270,238,268,249,274,263,272,275,
276,277,278,279,280]
,\[
2,5,1,8,11,12,3,16,4,19,7,22,6,23,26,29,30,9,34,10,37,40,41,13,14,
46,15,43,18,52,17,55,57,60,61,20,63,21,66,24,70,71,73,25,75,78,79,27,28,84,
86,89,90,31,94,32,97,33,100,36,81,35,107,108,38,111,39,88,115,44,119,42,122,123,125,
45,82,48,130,47,133,127,49,135,50,137,51,139,54,141,53,143,145,148,56,91,152,153,58,155,
59,114,159,110,62,161,65,160,64,164,166,104,67,68,169,69,85,172,173,72,132,83,175,74,178,
76,77,179,180,121,182,80,105,184,154,98,187,87,158,188,150,191,194,92,197,93,200,95,156,96,
205,99,128,117,202,207,101,102,109,103,162,106,136,211,212,113,112,201,216,118,116,217,120,181,219,
124,221,126,163,224,129,165,131,189,134,170,138,185,140,222,233,142,235,238,239,144,241,174,146,243,
147,157,149,245,247,151,249,250,252,225,167,227,255,231,168,171,229,232,176,226,214,177,246,198,260,
210,183,240,186,204,190,261,263,192,265,193,206,196,266,195,199,270,215,203,253,254,268,267,244,218,
208,230,209,256,223,213,228,220,259,258,251,272,234,242,248,257,236,237,271,276,262,277,278,264,269,
280,275,279,273,274]
>;
print "Group G is U4(3):D8 < Sym(280)";