/* www-ATLAS of Group Representations. J1 represented as 55 x 55 matrices over GF(19). */ F:=GF(19); x:=CambridgeMatrix(3,F,55,\[ 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, 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 16,4,4,15,2,4,2,4,3,1,17,3,11,0,5,1,3,8,17,10,17,9,7,4,12,16,11,5,7,13,4,16,6,9,9,6,1,3,18,18,11,0,1,5,15,13,3,13,18,18,5,6,8,9,2, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 18,15,9,11,2,4,15,5,12,6,1,7,11,9,11,18,1,13,16,13,9,0,13,3,9,8,0,10,2,14,9,2,13,2,18,10,9,8,9,13,16,2,14,5,6,9,1,4,13,16,18,7,14,5,16, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 3,17,2,15,1,0,3,6,15,5,1,4,12,4,17,1,8,14,15,8,8,16,16,3,2,8,15,15,18,18,10,16,1,9,1,8,0,10,6,1,10,14,6,12,12,4,14,1,15,10,11,17,17,8,0, 10,15,4,14,6,10,16,18,13,4,6,2,10,15,10,15,1,14,5,17,12,17,9,10,15,11,14,14,2,10,11,14,14,16,5,16,10,3,14,3,17,9,12,3,3,7,14,0,16,13,5,17,6,18,15, 15,9,12,2,16,12,5,2,14,3,15,17,18,5,4,8,6,6,8,7,9,10,5,8,3,3,6,7,6,17,11,2,18,9,9,15,16,4,2,13,16,12,3,8,12,3,1,16,11,13,18,16,13,16,3, 11,8,15,15,7,16,0,10,16,18,0,17,13,3,11,4,4,7,18,10,6,17,0,1,9,15,13,17,2,11,8,1,14,17,6,8,8,18,9,5,14,18,15,12,2,16,13,15,11,6,1,8,10,16,9, 13,8,16,15,16,13,15,9,6,17,8,10,1,16,17,8,11,10,10,10,12,5,1,12,16,6,8,3,3,16,4,14,7,14,13,10,7,11,4,4,0,6,14,18,3,11,9,3,16,8,11,6,10,2,4]); G:=MatrixGroup<55,F|x,y>; print "Group G is J1 < GL(55,GF(19))";