/* www-ATLAS of Group Representations. J3:2 represented as 85 x 85 matrices over GF(19). */ F:=GF(19); x:=CambridgeMatrix(3,F,85,\[ 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, 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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6,10,18,12,1,2,7,16,3,13,0,17,9,18,7,9,14,2,11,9,3,5,9,3,6,4,1,11,10,15,8,18,2,14,17,17,18,11,6,0,17,6,9,17,8,4,7,10,8,10,0,18,6,13,1,11,13,2,10,16,11,1,8,2,10,12,9,14,8,3,14,15,7,14,6,3,15,9,18,17,16,15,17,10,1, 14,9,1,3,10,10,0,0,10,0,12,6,3,3,1,11,12,5,0,3,8,5,4,4,16,7,18,10,10,4,0,16,4,14,8,15,10,9,16,18,17,8,1,4,15,17,12,11,13,3,2,18,15,8,16,5,4,5,8,5,5,15,15,6,12,5,4,10,7,7,3,0,9,16,18,2,18,18,5,12,7,11,5,13,0, 2,15,15,13,7,10,3,6,16,18,1,12,14,13,7,3,4,10,15,15,11,13,13,13,7,4,7,17,3,6,9,6,17,8,13,15,8,14,14,9,6,15,15,7,7,5,10,8,15,10,1,11,17,2,16,18,2,6,18,18,9,8,0,6,10,15,12,6,5,5,17,16,3,18,10,3,17,14,4,13,9,17,12,16,0, 8,7,10,15,14,6,14,12,11,8,17,4,15,4,3,14,0,10,14,16,10,6,3,3,5,2,14,10,10,13,9,1,14,17,15,8,1,10,2,18,0,13,11,1,10,8,10,1,17,14,11,12,7,4,10,4,18,15,0,11,13,9,10,9,16,4,16,11,6,9,15,2,3,4,10,9,11,9,16,5,16,3,15,10,18, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 5,17,11,11,9,12,5,13,0,10,9,2,10,6,7,4,2,18,0,1,16,1,13,16,16,18,6,8,9,3,13,15,1,12,12,8,0,17,16,1,3,18,13,10,0,10,6,18,8,14,7,16,9,17,10,1,0,16,8,17,13,3,7,4,12,6,16,12,9,6,0,12,10,16,9,5,7,13,17,9,5,12,0,10,15, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 7,14,8,10,3,10,9,16,0,16,15,16,16,10,1,17,6,2,6,1,6,1,10,5,5,17,15,13,7,13,9,7,10,12,10,9,17,17,13,6,3,17,9,5,2,8,1,18,2,6,12,8,1,13,18,16,1,14,11,15,8,2,13,15,12,12,12,10,17,15,15,17,15,13,3,5,4,2,6,12,18,17,0,13,0, 6,5,11,14,3,8,10,18,4,9,15,4,16,9,3,18,9,13,8,16,13,18,12,1,16,3,6,9,6,3,4,17,17,0,13,16,13,7,17,12,4,6,7,1,10,9,7,8,9,17,11,1,5,10,17,17,7,7,11,2,13,9,17,13,8,4,10,13,8,15,0,6,0,6,15,8,5,0,4,3,6,8,9,12,15, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 7,18,15,17,6,12,3,5,8,13,5,12,15,12,2,17,13,4,8,12,4,12,13,5,15,0,13,3,4,3,6,16,8,0,17,8,0,17,1,9,9,2,0,15,7,18,17,9,7,6,10,12,10,11,7,3,7,11,7,1,18,2,12,15,17,11,4,12,18,15,13,16,9,9,4,6,13,2,5,10,10,14,13,11,3, 3,11,16,18,14,15,2,1,7,15,16,7,11,10,10,7,0,15,13,1,6,14,5,0,6,16,10,2,12,17,17,11,11,4,16,12,13,12,7,13,5,0,16,12,7,0,16,1,8,18,12,5,1,1,10,3,6,15,5,10,12,13,15,15,3,14,17,6,7,14,17,2,3,9,12,13,11,9,6,8,0,1,5,0,1, 3,12,1,5,15,15,7,16,11,9,10,10,18,2,11,6,6,3,18,10,0,15,8,2,0,3,10,5,10,2,9,3,6,16,9,18,4,16,10,15,14,12,4,0,6,3,5,12,16,12,16,10,17,18,7,6,4,6,12,17,5,11,13,2,6,17,16,13,16,12,11,11,6,16,13,12,14,7,13,16,5,16,8,12,12, 12,10,14,3,5,1,2,4,15,4,3,15,13,17,14,13,9,3,5,15,4,16,17,18,11,2,15,2,16,0,14,14,17,15,16,16,12,2,9,6,4,13,12,17,16,14,10,1,13,13,5,5,6,18,14,14,6,16,9,16,9,18,6,9,11,7,17,13,8,0,3,17,16,17,5,5,7,15,17,12,0,6,9,15,17, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 13,13,5,7,3,18,9,1,9,13,5,14,10,1,5,15,0,11,14,13,1,6,4,3,15,8,13,17,6,13,3,4,7,8,10,10,16,4,14,18,0,0,8,3,17,14,8,15,1,6,6,8,1,11,13,4,4,11,16,3,8,0,4,4,6,10,10,7,13,4,6,5,14,15,8,14,3,3,2,6,2,1,12,1,5, 6,10,0,3,9,5,5,8,14,7,8,13,11,18,1,18,9,9,5,1,10,6,2,12,16,4,9,4,1,18,7,1,7,8,14,18,9,8,14,14,18,10,6,6,13,12,16,12,4,16,3,11,13,0,10,10,18,10,16,16,3,4,4,4,0,18,18,3,10,5,0,17,10,0,2,5,13,10,16,7,15,18,3,13,14, 7,2,2,0,0,0,6,2,10,13,12,4,17,5,13,10,14,3,17,4,14,18,10,18,1,17,9,7,6,7,18,2,8,17,14,2,7,3,5,18,18,16,1,2,15,10,6,1,17,0,5,17,11,8,13,8,9,16,13,8,15,11,0,8,0,6,9,8,4,3,13,0,6,5,11,13,15,5,2,6,16,2,9,7,7, 15,6,17,0,7,17,8,5,5,4,18,6,7,10,18,5,0,7,8,5,3,9,4,15,7,7,14,14,3,8,12,18,8,4,9,14,15,16,8,1,6,1,16,6,13,9,2,15,3,6,4,3,0,1,3,18,8,2,18,16,1,16,4,10,18,1,7,2,8,18,7,1,9,10,16,16,13,16,17,5,3,5,1,18,0, 4,4,8,12,10,12,7,17,16,0,4,14,17,8,13,3,0,12,12,14,5,6,16,16,2,9,6,18,7,3,6,17,7,2,4,15,9,11,0,1,7,0,15,5,5,8,9,0,11,4,4,12,12,1,14,4,18,14,11,13,2,12,6,8,3,15,10,14,0,15,14,10,15,4,16,7,18,4,13,4,4,18,2,3,8, 1,17,8,14,17,8,7,11,8,5,9,15,4,17,1,2,5,4,7,16,0,1,13,13,17,14,6,4,10,15,15,13,5,11,12,17,8,13,3,18,14,13,3,9,10,9,18,13,8,17,7,17,13,12,14,4,8,12,1,0,15,5,7,10,1,0,4,7,5,2,6,15,6,12,8,18,13,16,10,9,7,0,12,4,13]); G:=MatrixGroup<85,F|x,y>; print "Group G is J3:2 < GL(85,GF(19))";