print "Weyl group e6: matrix group over a 6-dimensional Z-module";
print "Order 51840 = 2^7 * 3^4 * 5";
print "Ring: Z; Group: G";

Z := Integers();
G := MatrixGroup<6, Z |
    \[ -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
     0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
    \[ 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
     0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
    \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0,
     0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
    \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, -1, 1,
     0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
    \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
     0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 1 ],
    \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
     0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1 ]
>;
