/* www-ATLAS of Group Representations. J1 represented as 77 x 77 matrices over GF(11). */ F:=GF(11); x:=CambridgeMatrix(3,F,77,\[ 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, 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, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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4,0,7,0,8,5,0,0,7,0,0,0,0,4,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 8,5,6,3,8,0,8,0,0,0,10,0,0,0,9,10,8,0,0,0,0,0,0,7,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,0,8,0,0,1,0,0,0,0,0,0,0,0,0,0, 5,5,4,0,6,6,0,0,4,0,0,0,0,8,0,0,0,0,0,0,3,9,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,3,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,9,5,0,0,4,8,9,3,9,4,9,7,10,7,3,8,1,6,5,0,1,6,8,7,0,1,3,8,10,7,4,4,7,5,10,1,5,0,5,3,10,6,2,10,0,0,2,7,10,3,3,6,0,7,1,4,4,4,3,6,6,1,8,3,8,8,2,1,4,6,5,3,2,4,9,7, 9,9,6,3,2,4,1,8,5,1,6,3,7,3,4,2,4,10,9,3,3,2,8,0,10,1,9,5,10,9,6,10,1,10,0,8,4,3,10,2,3,10,1,8,5,10,9,7,4,7,10,0,4,4,8,10,6,1,6,4,0,9,0,0,6,1,3,8,7,9,4,5,6,2,5,4,1, 1,8,3,2,4,1,1,7,1,7,5,6,1,3,7,3,5,3,1,5,9,9,3,4,8,6,7,5,7,7,9,2,4,3,9,3,6,7,1,9,10,8,0,8,8,9,7,1,0,3,10,1,4,9,10,0,5,3,9,0,2,8,2,2,0,0,4,10,6,0,2,10,10,3,3,0,10, 7,0,9,7,6,7,4,9,8,0,6,9,6,8,4,1,10,4,8,5,9,9,0,0,3,6,5,8,0,7,0,5,8,2,2,6,9,10,0,8,10,2,4,10,1,4,8,6,6,10,6,2,9,5,7,3,9,10,10,8,7,9,1,10,5,4,8,3,4,9,2,1,3,6,0,7,10, 6,3,3,4,0,6,2,0,1,1,6,2,4,8,3,10,2,4,3,6,4,4,3,5,4,5,4,7,6,6,3,10,4,4,0,5,0,7,9,1,0,5,7,7,4,10,4,9,5,4,1,7,10,3,5,9,9,3,4,3,5,6,6,9,7,0,1,3,7,0,5,8,8,2,6,1,10, 7,9,5,1,5,5,4,10,5,2,3,3,7,3,4,8,8,0,8,0,0,5,0,8,9,10,0,10,0,6,4,6,10,7,1,2,6,2,5,0,1,6,3,5,1,8,6,10,7,8,9,6,0,8,5,4,6,2,3,8,0,3,8,9,2,3,1,1,1,10,0,7,2,3,9,2,2, 10,0,0,3,8,4,5,2,1,0,6,2,5,1,6,10,10,3,9,9,6,8,6,3,9,3,1,0,4,6,8,9,3,3,3,0,3,3,5,10,4,0,5,1,2,3,5,10,9,1,3,0,6,10,3,6,2,3,1,10,0,1,1,4,9,7,10,5,1,6,7,6,6,0,6,3,4, 8,3,10,4,2,8,1,9,1,6,4,3,8,6,3,9,2,5,0,8,4,9,5,8,8,10,9,0,10,6,6,2,4,3,9,6,2,2,5,1,0,6,8,8,0,6,5,5,9,0,2,1,6,3,9,9,6,5,8,7,0,9,6,5,1,10,2,4,3,2,3,10,9,8,1,0,4, 2,1,8,3,3,3,4,8,1,10,2,5,0,10,3,1,7,3,4,6,7,0,5,0,0,5,1,2,3,6,3,10,4,0,10,2,1,4,5,1,7,8,5,10,2,10,9,0,3,0,0,8,10,2,5,2,7,9,7,9,6,4,9,8,10,6,3,10,2,2,2,1,5,8,3,6,5]); G:=MatrixGroup<77,F|x,y>; print "Group G is J1 < GL(77,GF(11))";