  In \cite{Ku0}, the ambiguity index $a_{(G,O)}$ was introduced for each
equipped finite group $(G,O)$. It is equal to the number of connected
components of a Hurwitz space parametrizing coverings of a projective line with
Galois group $G$ assuming that all local monodromies belong to conjugacy
classes $O$ in $G$ and the number of branch points is greater than some
constant. We prove in this article that the ambiguity index can be identified
with the size of a generalization of so called Bogomolov multiplier
(\cite{Kun1}, see also \cite{BO87}) and hence can be easily computed for many
pairs $(G,O)$.
