Dear Mrs. and Mr. Forum,
Jacob Hirbawi wrote
Is there a way to get the character tables of the exceptional Weyl
groups F4,E6,E7,E8 in GAP?
The table of the Weyl group of F4 is 'CharTable( "W(F4)" )' in GAP.
Unfortunately it is more complicated to get the others.
For E6 and E8 one can use 'CharTable( "U4(2).2" )' and
'CharTable( "2.O8+(2).2" )', respectively.
Since the Weyl group of E7 is a direct product of S_6(2) and a cyclic
group of order 2 one can construct (not simply fetch from the library)
its table by 'CharTable( "Cyclic", 2 ) * CharTable( "S6(2)" )'.
The names "W(E6)", "W(E7)", "W(E8)" will be admissible after the next patch of GAP-3.4.