print "The Hall-Janko-Wales group extended by an automorphism and given by a";
print "  6-dimensional representation over GF(5).";
print "Field: K; Group: G.";
print "Order 2 * 604800 = 2^8 * 3^3 * 5^2 * 7";

K := GF(5);
G := MatrixGroup<6, K |
    \[ 1, 1, 1, 3, 1, 1, 3, 4, 3, 1, 2, 3, 0, 0, 3, 1, 0, 2, 3, 0, 3, 2, 3,
     3, 1, 4, 3, 2, 4, 4, 2, 1, 1, 0, 3, 0 ],
    \[ 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, 1, 0,
     0, 0, 4, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0 ],
    \[ 0, 0, 0, 1, 0, 0, 0, 3, 3, 0, 1, 3, 0, 0, 2, 0, 3, 4, 4, 0, 0, 0, 0,
     0, 0, 4, 2, 0, 2, 0, 0, 2, 1, 0, 2, 3 ]
>;
