Re: Irrep Weirdness

In article <d9bo28$iqd$1@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
Hauke Reddmann <fc3a501@xxxxxxxxxxxxxx> wrote:

> It must have been pure boredom when I tried to compute
> the character table of S8.
> Suddenly I got a zero-dimensional irrep!
> (At least it's orthogonal to all other irreps, has
> integer characters and fulfils sum(char^2*class)=40320).
> Can someone check this with GAP? In the multiplication
> table now half-integers crop up, this is impossible?!
>
> 1 2 3 4 5 6 7 8 22 23 24 25 26 33 34
> 35 44 222 223 224 233 2222
> Permutation classes
> 1 28 112 420 1344 3360 5760 5040 210 1120 2520 4032 3360 1120 3360
> 2688 1260 420 1680 1260 1120 105
> Class member number
> ( 0, 14, 0, -4, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, -1,
> 0, 0, 2, 0, 0, 2, 0),
> Weirdo Irrep

Did you get
1,1,7,7,14,14,20,20,21,21,28,28,35,35,42,56,56,64,64,70,70,90
for the degrees of the (non-weird) irreducible representations?
That's what's in Sloane.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.