gap-forum@samson.math.rwth-aachen.de
While we're on the subject of group characters; there seems to be
a mistake in the characters of 2.S4 . In case anyone is wondering
this all relates to John McKay's recent post on sci.math regarding
the link between the finite dicyclic groups <2,3,3>=SL(2,3),
<2,3,4>=2.S4, <2,3,5>=2.A5 and the exceptional Lie algebras E6,E7,E8.

gap> CharTable("2.S4");
  ....
 irreducibles :=
 [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, -1, -1, -1, 1, 1 ],
   [ 2, 2, 2, 0, 0, 0, -1, -1 ], [ 3, 3, -1, 1, -1, -1, 0, 0 ],
   [ 4, -4, 0, 0, 0, 0, 1, -1 ],
   [ 2, -2, 0, 0, E(8)+E(8)^3, -E(8)-E(8)^3, -1, 1 ],
   [ 2, -2, 0, 0, -E(8)-E(8)^3, E(8)+E(8)^3, -1, 1 ],
   [ 3, 3, -1, -1, 1, 1, 0, 0 ] ],
  ....

I could not duplicate John's constructions with the above characters
but using the table below everything seems to fit nicely:

[ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, -1, -1, -1, 1, 1 ],
  [ 2, 2, 2, 0, 0, 0, -1, -1 ], [ 3, 3, -1, 1, -1, -1, 0, 0 ],
  [ 4, -4, 0, 0, 0, 0, 1, -1 ],
  [ 2, -2, 0, 0, E(8)^3+E(8)^5, -E(8)^3-E(8)^5, -1, 1 ],
  [ 2, -2, 0, 0, -E(8)^3-E(8)^5, E(8)^3+E(8)^5, -1, 1 ],
  [ 3, 3, -1, -1, 1, 1, 0, 0 ] ],

both tables pass the TestCharacterTable tests!

Jacob Hirbawi
JcbHrb@CERF.net