/* www-ATLAS of Group Representations. J3 represented as 110 x 110 matrices over GF(19). */ F:=GF(19); x:=CambridgeMatrix(3,F,110,\[ 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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18,16,4,7,4,15,12,5,16,15,9,13,1,13,5,11,13,2,0,1,12,4,12,2,17,18,9,1,16,15,17,9,5,5,10,18,14,13,13,18,10,12,1,18,13,15,0,18,17,2,10,0,9,10,7,6,6,2,5,15,0,12,14,0,2,11,18,13,5,14,12,17,6,12,10,9,16,15,9,18,7,10,14,5,9,1,11,4,7,7,8,11,0,17,12,14,0,1,2,8,0,13,4,5,14,10,3,17,11,10, 3,5,14,0,6,4,7,6,10,17,6,5,13,5,1,17,1,6,3,18,10,14,18,5,6,4,6,18,1,10,4,12,5,10,11,8,2,2,10,3,6,2,1,0,18,0,18,5,14,17,15,12,14,0,1,13,9,5,11,7,6,5,9,7,5,1,2,5,4,16,16,18,13,10,3,9,15,6,9,17,16,13,7,12,2,8,3,14,7,2,1,2,0,15,7,18,14,9,14,18,14,16,18,0,9,10,4,13,6,18, 1,11,7,12,0,10,14,7,9,9,18,5,2,11,10,10,4,13,10,5,10,17,17,5,2,5,1,13,13,14,14,17,9,13,0,7,2,1,10,6,16,0,2,8,10,12,16,4,7,5,9,9,3,3,8,10,18,11,11,18,5,3,12,10,11,2,5,2,0,13,4,10,17,13,6,7,6,5,1,7,7,11,0,14,13,0,8,9,12,17,9,7,14,1,1,0,8,14,4,14,4,7,12,7,12,13,16,10,0,10, 10,17,10,2,16,9,17,10,9,18,12,2,3,1,6,7,18,6,10,0,16,10,5,10,13,4,9,3,15,9,18,15,13,3,7,5,4,18,1,0,18,0,17,8,9,11,5,9,17,3,13,16,18,8,17,1,14,5,9,3,8,7,2,14,4,17,0,4,6,0,15,10,7,8,7,1,7,5,8,6,7,0,2,6,15,18,1,3,1,6,1,0,13,13,5,8,10,7,12,16,9,8,3,15,13,18,9,10,8,14, 6,13,1,15,17,13,7,15,13,15,6,5,16,16,4,17,12,7,4,4,6,12,5,3,15,1,11,17,1,8,18,12,16,10,2,3,13,6,7,11,1,0,13,18,18,1,17,1,3,7,1,3,1,15,2,16,2,7,4,14,3,7,13,8,8,7,0,7,4,8,11,8,10,17,15,0,17,16,14,0,8,9,6,8,0,3,10,11,3,14,12,7,8,9,4,8,18,7,13,11,16,11,10,6,7,18,8,12,6,12, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 8,6,15,13,17,13,12,2,11,0,18,17,11,3,16,10,3,7,4,4,13,14,13,11,12,1,17,1,9,10,12,12,4,0,0,18,4,8,3,4,12,9,9,8,13,9,9,1,12,5,7,1,5,0,11,8,12,1,14,11,6,1,0,10,6,3,11,8,2,4,10,17,11,12,17,13,3,10,14,11,13,18,0,11,7,11,8,8,8,14,11,18,6,10,0,5,3,3,2,1,5,10,5,4,18,14,2,5,13,17, 12,14,14,15,7,13,5,0,18,3,16,1,0,11,1,14,6,8,15,5,18,10,9,7,7,10,17,16,12,0,7,18,5,4,2,11,11,17,3,17,2,13,7,18,10,18,16,13,10,5,14,18,15,7,5,9,10,6,5,18,17,1,7,13,16,4,6,12,6,14,10,0,3,14,12,2,8,11,2,2,8,14,12,10,8,2,9,11,5,17,15,4,12,10,7,7,5,11,7,17,4,11,12,2,4,3,13,3,16,1, 16,17,12,13,7,12,1,3,14,8,8,6,0,9,9,3,1,12,6,11,17,7,17,5,0,15,10,9,2,12,3,12,16,9,9,8,9,8,5,16,3,7,8,4,1,10,12,11,9,14,18,11,15,17,8,9,12,16,16,7,9,18,11,5,7,18,13,5,3,5,8,4,7,13,17,16,6,16,15,11,1,7,9,0,7,13,10,13,14,14,13,2,5,1,3,6,9,14,17,8,9,3,6,15,6,12,7,6,15,6, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 13,8,14,3,4,16,4,8,15,17,9,1,13,9,9,2,5,15,12,2,3,13,11,9,18,18,6,7,8,14,7,2,11,11,18,9,11,13,7,18,0,15,0,11,0,8,13,10,4,15,13,3,5,7,9,14,12,1,16,15,10,5,2,17,6,8,9,3,16,0,1,1,11,1,1,6,4,4,5,2,3,10,9,13,11,15,15,10,11,6,9,2,4,10,6,16,3,11,2,4,1,17,11,12,1,0,13,0,11,13, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9,12,3,17,11,2,9,4,13,9,9,2,7,2,18,0,2,3,11,7,12,7,15,17,5,3,7,1,15,1,15,18,3,6,3,9,2,16,14,1,7,4,8,9,16,4,11,3,9,16,8,3,10,3,4,5,11,10,8,4,16,7,15,14,11,3,4,8,17,16,7,1,7,18,18,17,5,8,15,6,7,8,8,5,6,0,6,11,11,18,13,8,0,14,13,18,11,11,10,17,4,10,9,9,11,14,0,10,14,16, 1,10,17,18,10,7,11,17,4,13,6,10,2,7,6,12,0,10,10,6,16,1,1,3,7,8,17,18,9,18,3,0,0,12,1,11,14,18,12,11,8,4,7,3,12,14,6,3,7,13,7,1,10,1,0,5,17,16,2,7,2,4,1,16,9,15,8,4,10,12,12,11,1,5,6,2,6,4,9,3,18,14,0,13,18,2,7,3,13,6,4,9,16,2,8,8,11,15,7,2,8,4,12,3,9,17,1,1,9,4, 1,17,8,6,12,14,0,2,7,7,8,13,2,12,1,14,0,10,10,5,7,5,6,11,6,12,2,16,3,17,13,9,7,14,9,8,7,4,4,0,13,1,15,15,10,10,7,3,8,6,1,4,15,14,17,14,3,17,16,17,2,3,13,9,18,13,0,1,9,3,13,1,0,7,7,14,14,14,2,18,8,11,1,17,8,9,7,16,3,17,5,0,2,0,7,15,2,12,18,8,2,12,7,7,18,3,18,13,10,17, 13,8,5,2,7,17,14,5,5,11,14,8,11,15,10,10,12,12,13,6,8,2,13,6,6,2,12,2,0,11,2,0,14,12,2,13,9,11,14,7,12,18,10,1,18,8,3,7,9,10,11,1,4,11,9,3,0,3,13,12,3,11,0,8,9,16,8,18,2,5,15,3,8,6,0,18,4,12,2,18,7,17,4,3,7,14,10,10,12,2,4,16,16,8,0,3,9,0,17,18,6,6,18,4,15,2,9,14,14,9, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 16,7,6,12,12,4,12,2,3,3,1,5,7,0,9,4,15,0,6,18,12,2,13,10,9,16,1,2,18,2,10,15,11,12,14,3,16,3,14,14,2,12,4,13,15,7,5,6,7,13,14,0,18,16,3,8,18,0,12,18,5,3,16,18,6,5,14,5,4,17,18,4,4,9,14,13,4,7,15,14,2,3,10,18,7,5,15,4,7,12,16,15,7,10,0,8,0,17,6,1,2,3,11,13,6,3,11,18,18,10, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 12,9,3,14,8,9,16,15,17,16,17,1,14,3,13,10,0,9,4,17,3,3,14,9,5,7,1,1,7,0,6,6,13,11,9,8,0,5,16,17,13,16,16,7,8,15,15,10,0,6,3,3,18,18,16,18,14,8,1,3,12,0,8,2,18,14,13,12,11,5,0,2,16,11,16,9,9,5,5,13,0,12,7,8,3,9,4,13,1,14,17,5,2,16,5,10,10,4,3,16,8,9,13,9,3,0,4,15,13,10, 3,17,13,13,3,11,13,7,0,0,18,4,3,5,1,1,11,5,8,15,12,5,11,17,13,9,0,9,1,2,6,12,14,5,13,6,0,11,3,14,2,9,5,14,3,13,17,14,18,18,9,16,17,17,9,2,14,8,2,6,18,4,8,4,5,1,15,4,16,3,4,7,3,1,2,7,18,9,11,14,7,6,13,15,9,15,6,16,15,16,18,16,1,14,4,18,17,5,4,14,0,12,16,17,2,9,12,16,0,5]); G:=MatrixGroup<110,F|x,y>; print "Group G is J3 < GL(110,GF(19))";