Feit numbers and $p^{\mathrm{\prime }}$-degree characters

Suppose that $\chi$ is an irreducible complex character of $G$ and let $f_{\chi }$ be the smallest integer $n$ such that the cyclotomic field $\mathbb Q_n$containsthevaluesof$\chi$\mathrm{.}Let$p$beaprime,andassumethat$\chi \in $\text{Irr}$(G)$hasdegreenotdivisibleby$p$\mathrm{.}If$G$issolvableand$\chi(1)$isodd,thenthereexists$g \in {\bf N}G(P) /P’$with$o(g)=f\chi$\mathrm{.}Inparticular$f_\chi$divides$|{\bf N}_G(P) /P’|$.