/* www-ATLAS of Group Representations. U3(4) represented as 78 x 78 matrices over GF(13). */ F:=GF(13); x:=CambridgeMatrix(3,F,78,\[ 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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12,1,6,4,4,4,11,2,10,8,6,5,10,5,9,11,7,4,6,8,4,3,9,4,4,0,0,5,4,9,7,5,2,11,3,8,7,2,5,6,4,5,5,4,4,2,8,6,9,7,1,4,6,1,1,0,10,4,8,8,3,11,10,7,10,9,1,11,9,2,11,1,2,9,10,7,5,12, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 4,11,2,11,2,11,10,8,10,2,4,10,3,12,4,6,10,8,11,1,10,0,3,11,3,2,7,8,12,6,5,2,2,7,12,9,5,5,5,7,9,7,7,10,0,1,1,11,2,6,0,10,9,12,0,4,3,5,10,5,3,9,11,8,8,4,4,12,6,5,10,7,0,0,10,0,1,9, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,2,8,11,7,7,3,0,5,10,3,2,9,1,5,7,10,7,0,5,4,9,12,9,9,6,1,5,4,4,5,10,10,11,8,8,2,10,5,2,4,9,3,6,0,9,1,11,10,8,4,7,9,11,7,11,0,11,12,3,9,9,5,0,0,5,11,10,11,7,6,0,10,9,0,0,4,2, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 5,7,5,2,6,12,5,8,0,3,2,8,8,7,3,12,6,9,10,8,1,7,4,4,1,5,12,5,12,7,11,6,10,2,8,11,10,12,11,8,0,6,7,5,9,4,7,6,10,6,2,11,12,8,6,1,2,5,7,11,5,4,10,3,2,6,11,1,2,2,5,11,7,5,5,2,0,2, 8,3,7,11,6,10,7,1,2,0,0,1,8,12,4,7,12,1,11,6,8,1,3,7,2,7,5,0,7,5,2,9,8,8,10,2,7,4,2,12,3,6,6,9,9,0,3,1,0,0,6,9,4,11,0,10,12,5,3,2,6,5,9,8,10,0,1,6,11,7,3,7,8,4,6,3,9,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]); G:=MatrixGroup<78,F|x,y>; print "Group G is U3(4) < GL(78,GF(13))";