/* www-ATLAS of Group Representations. U3(4) represented as 52 x 52 matrices over GF(13). */ F:=GF(13); x:=CambridgeMatrix(3,F,52,\[ 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, 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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0,12,1,8,10,10,8,0,10,0,3,0,8,11,2,3,1,5,7,8,7,6,2,8,5,3,1,2,6,8,11,3,12,5,1,2,12,3,7,3,5,5,0,9,10,12,1,0,8,10,9,4, 11,8,7,10,10,9,6,12,2,5,5,8,12,7,10,3,3,9,0,0,10,0,8,6,4,3,10,1,10,3,9,6,8,6,8,4,10,2,11,10,3,4,0,3,4,9,4,0,6,3,1,10, 2,0,11,12,1,1,0,0,0,0,12,12,12,11,0,1,0,1,0,2,1,1,12,2,2,11,12,0,12,12,2,11,0,0,11,0,12,2,11,0,0,0,0,12,2,0,1,1,0,0,0,1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 11,2,0,6,9,1,11,6,9,12,6,6,7,5,3,11,7,7,11,5,7,7,4,10,6,5,5,4,12,6,1,1,2,1,0,10,1,3,8,12,6,1,0,12,9,3,12,0,4,2,10,1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 2,9,2,2,8,10,3,12,8,0,4,0,1,6,6,5,0,12,4,2,0,0,4,3,10,5,3,4,0,2,9,2,10,10,1,4,11,7,12,4,1,11,0,4,8,9,2,0,5,9,5,10]); G:=MatrixGroup<52,F|x,y>; print "Group G is U3(4) < GL(52,GF(13))";