/* www-ATLAS of Group Representations. TF4(2)' 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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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 11,9,12,0,8,11,0,10,11,0,2,12,8,11,1,4,0,0,6,10,3,3,0,7,0,3,11,5,6,7,0,11,0,3,2,8,7,8,6,0,12,2,6,10,9,9,7,7,4,7,12,1,11,7,9,3,4,4,0,0,12,9,6,0,1,0,0,2,0,0,4,10,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 4,5,0,5,8,0,4,2,8,4,7,1,7,12,1,2,0,1,10,8,8,2,6,6,5,0,10,12,6,0,5,7,6,9,10,8,7,6,1,2,7,1,4,10,9,3,4,6,10,8,2,4,9,11,8,11,10,9,5,4,0,12,0,2,11,8,2,5,12,2,3,12,3,7,4,0,0,11, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 8,7,8,6,2,5,11,10,5,11,7,10,10,1,5,9,0,2,0,7,4,8,5,3,7,7,7,7,3,11,10,4,0,6,2,1,0,4,9,6,11,3,5,4,10,9,6,11,4,2,4,11,1,9,1,10,7,5,12,4,8,3,6,6,6,6,12,3,3,11,0,6,4,4,5,4,10,3, 0,9,8,7,4,3,11,4,6,7,10,9,8,10,4,7,1,11,10,1,10,12,12,4,8,1,6,6,1,6,9,4,4,6,0,6,11,1,2,7,6,1,4,5,5,7,10,2,3,4,5,2,1,0,5,8,10,0,2,12,5,7,3,9,7,2,0,9,0,1,6,9,4,6,9,5,7,3, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 2,8,1,12,10,3,7,5,4,2,9,6,11,3,12,4,3,12,7,4,7,10,8,5,9,10,7,10,8,2,0,0,8,1,6,12,5,9,9,8,3,6,11,8,0,9,1,7,9,6,2,12,9,8,9,2,4,8,9,7,2,3,6,12,10,1,6,12,6,3,11,5,7,7,2,8,1,1, 1,4,11,7,0,1,5,8,11,1,12,8,8,10,6,11,2,1,6,12,9,9,3,11,1,12,5,11,8,6,6,2,5,12,9,2,9,8,12,5,9,7,1,0,12,2,6,1,7,2,4,1,10,3,9,12,1,0,6,1,2,1,8,10,1,9,0,1,0,12,12,6,6,3,6,4,5,10, 9,3,9,6,1,3,10,9,1,3,3,12,1,11,5,11,10,3,0,11,2,12,5,1,6,11,5,2,6,0,7,10,10,11,10,5,6,11,9,12,1,6,1,11,6,11,7,9,0,10,5,4,9,12,7,11,7,3,1,0,4,10,4,5,1,7,1,9,12,11,8,5,4,3,8,4,10,8, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 2,11,7,5,12,10,10,11,10,0,10,10,11,1,10,8,8,7,9,3,1,11,1,6,7,6,11,7,6,6,12,7,6,4,7,5,7,3,0,2,11,2,2,0,4,9,7,6,12,4,8,9,3,10,7,1,7,5,10,1,10,8,1,10,11,4,6,11,8,4,3,12,12,9,7,3,1,4, 9,3,11,10,0,8,6,12,8,3,1,4,4,2,11,2,2,6,4,4,8,0,12,4,6,4,1,10,1,12,5,1,3,9,10,4,5,5,2,0,12,2,5,3,11,4,2,10,3,1,12,0,8,12,8,6,3,10,5,8,5,10,5,7,7,7,6,12,12,3,3,4,1,5,12,0,6,5, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 2,11,10,2,12,9,11,11,3,10,4,3,11,11,3,0,8,9,1,5,4,12,7,11,8,3,1,4,7,9,8,12,5,4,8,3,1,10,5,10,1,8,2,0,4,8,11,6,6,7,0,4,11,2,11,6,12,8,6,9,9,8,2,4,7,2,6,8,8,1,12,7,11,4,1,0,2,3, 6,9,3,9,12,0,1,7,4,10,6,7,1,5,10,2,6,2,5,6,9,6,7,9,6,6,5,10,4,7,0,5,0,12,7,12,3,6,9,8,0,10,4,5,4,3,3,12,6,0,0,2,8,4,11,7,1,10,12,0,2,3,1,0,9,2,8,12,12,1,3,7,4,9,5,0,10,0]); G:=MatrixGroup<78,F|x,y>; print "Group G is TF4(2)' < GL(78,GF(13))";