Dear Forum,

Maybe there is someone who is able to
answer some of the following questions :

1. Does the character table of a group with n
conjugacy classes only contain
character values which are algebraic of degree
strictly smaller than n ?
(Clearly, this is not a consequence of the fact that
character values of a group G are sums of
Exponent(G)'th roots of unity)

2. Let d be the 'determinant' of the character table
of a group G of order n
(in GAP : d := DeterminantMat(List(Irr(G),ValuesOfClassFunction))).

- Is d always different from zero ?

- Is d^2 always an integer which is divisible by n ?

(Obviously, d is determined up to the sign by the group G,
hence d^2 is uniquely determined by G)

Thanks in advance,

Stefan

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