Is the Weylgroup W(E,7) available in GAP?
In GAP (currently only Version 3) there is the CHEVIE package which
contains constructers for Weyl groups and programs to deal with them.
(I see that this can be difficult to find out, since the group is
constructed with `CoxeterGroup' - probably we should add a help
section whose header contains the keyword `Weyl'. For now ask
You may try the following example commands (and have a look at the
corresponding help pages):
e7 := CoxeterGroup("E", 7); # a permutation group on the roots
x := Random(e7);
u := ReflectionSubgroup(e7, [1,2,3,5,6,7]);
Please, ask if there are more questions.
With best regards, Frank