gens:=[ 
    Matrix(GF(3),9,9,[0, 0, 2, 1, 1, 1, 0, 1, 1, 0, 1, 2, 1, 2, 2, 2, 2, 0, 0, 0, 2, 0, 
    0, 1, 2, 2, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
    2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 2, 0, 
    1, 0, 1, 2, 2, 2, 0, 2, 0 ]),

    Matrix(GF(3),9,9,[1, 1, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 2, 1, 2, 0, 0, 0, 1, 0, 
    2, 2, 2, 0, 0, 0, 2, 0, 0, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 1, 
    0, 0, 0, 1, 2, 2, 0, 2, 2, 0, 0, 2, 2, 1, 1, 0, 1, 2, 0, 1, 0, 0, 1, 0, 2, 
    2, 0, 0, 1, 1, 1, 1, 1, 0 ]),

    Matrix(GF(3),9,9,[0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 2, 2, 2, 1, 2, 
    0, 0, 2, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 2, 1, 0, 
    0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
    1, 1, 0, 1, 0, 0, 1, 0, 1 ]),

    Matrix(GF(3),9,9,[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 1, 0, 0, 0, 1, 2, 
    1, 0, 2, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 
    0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 0, 2, 1, 2, 1, 0, 0, 
    0, 0, 0, 2, 0, 1, 0, 2, 1 ]),

    Matrix(GF(3),9,9,[2, 0, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 0, 1, 0, 0, 0, 2, 2, 2, 
    0, 1, 1, 2, 0, 2, 1, 1, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2, 0, 1, 2, 1, 2, 1, 0, 
    1, 1, 1, 0, 1, 2, 1, 2, 2, 0, 0, 2, 2, 1, 1, 0, 2, 0, 2, 0, 2, 1, 2, 1, 1, 
    0, 1, 2, 1, 0, 2, 2, 1, 1 ]),

    Matrix(GF(3),9,9,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 1 ])
];




NC32:=PermutationGroup<24|(2, 5)(3, 7)(4, 19)(10, 22)(11, 14)(12, 13)(16, 24)(17, 20), (1, 10)(3, 17)(4, 6)(5, 8)(7, 16)(11, 14)(12, 18)(20, 24),(1, 4)(3, 19)(6, 7)(8, 9)(10, 16)(11, 23)(13, 18)(20, 24),(3, 7)(4, 12)(6, 18)(9, 15)(11, 14)(13, 19)(16, 17)(20, 24),(3, 7)(4, 19)(10, 17)(11, 12)(13, 14)(15, 21)(18, 23)(20, 22), (1, 7, 3)(4, 19, 6)(10, 17, 16)(11, 14, 23)(12, 18, 13)(20, 22, 24)>;



V252:=GModule(NC32,gens);


print("the Green correspondent V252 of the simple M24-module D252 over
GF(3) in NC32 (normalizer of vertex C32 in M24), and a permutation
representation of NC32 on 24 points");