/*
www-ATLAS of Group Representations.
U4(3):D8 represented as permutations on 324 points.
*/

G<x,y>:=PermutationGroup<324|\[
2,1,7,8,9,11,3,4,5,19,6,23,24,26,28,30,32,34,10,38,39,41,12,13,46,
14,50,15,53,16,56,17,58,18,62,63,64,20,21,70,22,73,74,76,77,25,48,47,82,27,
85,54,29,52,89,31,84,33,95,79,97,35,36,37,105,106,107,108,92,40,113,88,42,43,117,
44,45,101,60,123,103,49,111,57,51,100,116,72,55,119,131,69,134,135,59,139,61,142,143,86,
78,146,81,149,65,66,67,68,155,157,83,159,71,162,163,87,75,167,90,170,172,174,80,178,179,
180,182,184,185,187,91,190,192,93,94,196,197,198,96,201,202,98,99,206,207,102,208,209,104,210,
212,214,215,216,109,204,110,220,112,221,222,114,115,224,193,211,118,226,227,120,229,121,233,122,236,
237,239,124,125,126,203,127,217,128,129,243,130,245,246,132,248,133,165,250,251,136,137,138,254,235,
140,141,181,156,238,144,145,147,148,150,166,151,232,152,153,154,183,249,263,158,160,161,267,164,242,
168,169,268,171,269,270,213,173,273,200,175,176,205,177,277,278,225,186,279,188,189,281,191,218,194,
195,284,285,199,287,283,288,280,289,290,276,291,219,292,293,286,223,228,230,231,295,275,234,297,272,
261,240,241,244,258,247,303,256,252,253,266,255,257,259,260,262,264,265,308,271,312,274,313,314,306,
315,317,282,318,319,300,320,294,321,322,323,296,298,299,301,324,302,304,305,307,309,310,311,316]
,\[
3,5,4,1,10,2,13,15,17,20,21,6,25,7,29,8,33,9,36,12,40,11,43,45,47,
48,14,51,54,24,16,41,59,60,18,53,19,66,68,71,72,22,75,23,78,79,27,81,26,44,
86,28,88,31,30,91,32,82,35,96,34,99,101,103,37,67,38,109,39,111,42,114,115,104,84,
118,120,90,122,46,125,126,49,50,73,128,52,65,129,55,132,56,57,58,137,140,141,61,106,62,
145,63,148,64,150,152,112,154,156,69,158,70,160,93,164,74,165,168,76,171,77,175,176,80,83,
181,85,87,186,89,177,191,92,193,195,94,161,95,199,98,97,203,204,100,184,142,102,116,210,190,
105,144,107,108,167,110,218,153,205,138,113,194,135,183,225,117,221,179,119,228,230,231,121,234,124,
238,123,166,169,241,136,170,127,147,242,244,180,130,131,247,133,249,239,134,229,252,253,146,255,139,
159,257,227,256,143,226,217,220,259,243,149,162,151,198,207,261,155,237,157,265,215,196,163,197,240,
266,214,187,245,173,185,172,211,192,174,274,276,189,212,178,182,271,272,188,223,200,213,275,270,250,
283,206,208,286,280,201,258,202,260,209,262,216,268,219,224,222,251,254,294,235,232,233,296,298,236,
264,281,300,269,246,302,248,267,293,263,304,292,305,284,287,306,289,290,309,310,273,299,282,277,278,
279,303,297,285,318,288,291,311,316,315,295,308,313,321,312,301,324,307,320,319,314,322,323,317]
>;
print "Group G is U4(3):D8 < Sym(324)";