gens:=[ 
    Matrix(GF(3),19,19,[1, 0, 0, 2, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 
    1, 1, 0, 0, 0, 0, 0, 2, 1, 2, 1, 1, 2, 2, 1, 0, 0, 0, 1, 2, 1, 2, 2, 1, 0, 
    2, 0, 0, 2, 2, 2, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 2, 0, 0, 2, 
    0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 
    0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 
    1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 
    0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
    0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 
    0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 2, 2, 0, 1, 0, 
    0, 0, 1, 0, 1, 2, 2, 0, 0, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 2, 2, 0, 1, 
    1, 0, 0, 1, 2, 2, 1, 1, 0, 2, 2, 0, 1, 2, 2, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]),

    Matrix(GF(3),19,19,[1, 1, 1, 0, 2, 0, 1, 2, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 1, 1, 1, 0, 
    2, 0, 0, 1, 1, 1, 0, 0, 2, 2, 1, 1, 0, 1, 1, 2, 0, 0, 0, 0, 0, 1, 0, 2, 2, 
    2, 2, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 1, 
    0, 0, 2, 0, 0, 2, 1, 0, 1, 2, 2, 0, 0, 1, 2, 1, 0, 0, 1, 1, 1, 2, 1, 0, 0, 
    2, 1, 0, 1, 0, 0, 0, 1, 0, 2, 1, 2, 0, 0, 1, 2, 1, 0, 0, 1, 2, 0, 1, 2, 0, 
    0, 2, 0, 1, 2, 1, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 0, 
    1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 
    0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 
    0, 1, 0, 1, 1, 2, 1, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 1, 2, 2, 1, 0, 0, 0, 1, 
    2, 1, 1, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 2, 2, 
    0, 0, 1, 2, 1, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 1, 1, 0, 1, 0, 2, 1, 0, 
    1, 2, 2, 0, 2, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2, 2, 
    0, 1, 0, 2, 1, 0, 1, 0, 1, 2, 1, 1, 0, 0, 0, 1, 2, 0, 0, 2, 2, 0, 2, 2, 1, 
    2, 0, 2, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 1, 2, 0, 2, 0, 0, 0, 0, 0, 
    2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]),

    Matrix(GF(3),19,19,[2, 2, 0, 1, 2, 1, 1, 2, 1, 2, 0, 0, 2, 2, 1, 1, 1, 2, 2, 0, 1, 0, 
    0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 
    2, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 
    0, 2, 1, 2, 2, 1, 1, 2, 2, 0, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 0, 0, 1, 0, 0, 
    2, 1, 0, 2, 1, 1, 0, 1, 0, 2, 1, 0, 0, 0, 1, 2, 2, 0, 0, 1, 2, 0, 2, 0, 2, 
    0, 2, 0, 1, 2, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 
    0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 2, 1, 0, 1, 1, 2, 0, 0, 
    0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 1, 1, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 0, 0, 1, 
    1, 2, 2, 1, 2, 0, 1, 2, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 0, 
    0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 
    0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 2, 2, 1, 2, 1, 
    1, 0, 0, 1, 2, 2, 0, 2, 2, 0, 2, 1, 1, 1, 1, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 
    1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 0, 1, 2, 2, 1, 1, 0, 2, 0, 2, 
    0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 2, 1, 1, 2, 2, 0, 2, 0, 2, 1, 0, 0, 0, 0, 0, 
    1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]),

    Matrix(GF(3),19,19,[1, 0, 0, 1, 1, 0, 2, 2, 0, 1, 2, 0, 0, 2, 1, 2, 0, 0, 1, 0, 1, 1, 
    2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0, 2, 
    1, 1, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 1, 2, 2, 0, 
    2, 1, 2, 1, 1, 0, 0, 1, 1, 2, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 1, 1, 0, 0, 
    0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 
    2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 
    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 1, 2, 2, 1, 0, 1, 1, 2, 1, 0, 
    0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 1, 1, 2, 0, 2, 2, 1, 2, 1, 0, 1, 1, 1, 2, 0, 
    1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 2, 1, 1, 2, 2, 2, 
    2, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 
    0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 2, 0, 2, 1, 0, 0, 2, 0, 1, 1, 1, 0, 
    0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 2, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 
    1, 2, 0, 0, 0, 1, 2, 1, 0, 0, 0, 2, 0, 0, 2, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 
    2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]),

    Matrix(GF(3),19,19,[1, 2, 1, 2, 2, 2, 0, 1, 1, 1, 2, 1, 0, 0, 2, 0, 2, 1, 2, 1, 2, 2, 
    2, 2, 0, 2, 1, 0, 2, 1, 1, 0, 0, 2, 2, 0, 2, 2, 0, 1, 1, 0, 1, 0, 2, 1, 0, 
    1, 1, 0, 2, 0, 2, 1, 2, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 0, 
    0, 0, 2, 1, 2, 0, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 1, 0, 0, 2, 1, 0, 1, 0, 0, 
    1, 1, 2, 2, 0, 0, 0, 2, 1, 1, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2, 1, 1, 0, 2, 2, 
    2, 2, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 2, 1, 2, 2, 1, 1, 1, 0, 
    1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 1, 1, 2, 0, 2, 2, 1, 2, 0, 
    0, 0, 2, 0, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 2, 2, 1, 1, 2, 0, 0, 1, 1, 0, 0, 
    0, 1, 2, 0, 0, 0, 1, 1, 2, 0, 2, 1, 0, 2, 1, 2, 2, 0, 0, 1, 0, 1, 2, 2, 1, 
    2, 0, 0, 1, 2, 0, 2, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 
    1, 0, 1, 1, 2, 0, 1, 2, 2, 1, 2, 0, 0, 1, 1, 2, 2, 2, 2, 0, 1, 0, 0, 1, 1, 
    1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 1, 1, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 
    0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 
    1, 1, 2, 0, 2, 1, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 1, 0, 0, 0, 1, 0, 
    2, 2, 1, 2, 0, 1, 2, 2, 1, 0, 1, 1, 2, 1 ]),

    Matrix(GF(3),19,19,[1, 0, 2, 1, 2, 1, 0, 2, 0, 0, 2, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 
    1, 0, 2, 2, 1, 1, 1, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 2, 2, 
    1, 2, 1, 1, 2, 0, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 1, 2, 1, 2, 1, 1, 0, 0, 1, 0, 1, 0, 0, 
    0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 
    1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 2, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 
    2, 2, 1, 0, 1, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 
    1, 1, 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, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 
    0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2, 1, 
    0, 1, 2, 2, 0, 2, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ])
];


NGP:=PermutationGroup<24|(1, 3, 7)(4, 6, 19)(10, 16, 17)(11, 23, 14)(12, 13, 18)(20, 24, 22),(2, 15, 21)(3, 17, 19)(4, 10, 7)(5, 23, 18)(8, 14, 13)(9, 11, 12),(4, 10)(5, 9)(6, 16)(11, 18)(12, 23)(13, 14)(15, 21)(17, 19),(1, 3)(4, 10)(5, 9)(6, 17)(11, 14)(13, 18)(16, 19)(22, 24),(1, 23, 3, 12)(2, 20)(4, 9)(5, 10)(6, 14, 19, 18)(7, 8)(11, 17, 13, 16)(15,22, 21, 24), (1, 6, 16)(3, 19, 17)(4, 10, 7)(5, 8, 9)(11, 23, 14)(12, 18, 13)>;



V1243:=GModule(NGP,gens);

print("the Green correspondent V1243 of the simple M24-module D1243 over GF(3)
in NGP (normalizer of vertex P in M24), and a permutation representation
of NGP on 24 points");