Is the size of the normalizer of a Sylow p-subgroup determined by the ordinary character table of the group?
And if so, how does one calculate it?
In a solvable group, apparently one can compute the prime divisors of the Sylow normalizers from the character table (Isaacs–Navarro, 2002), but I don't see any discussion of the entire order. I suppose it must be harder to compute the order, and I somewhat hope it is too hard, that is, the character table does not determine the Sylow normalizer's order. If it helps to prove you can find the order, then I am happy to assume one also knows the power maps (and so element orders).