  Let $K$ be a field and $n\geq 3$. Let $E_n(K)\leq H\leq GL_n(K)$ be an
intermediate group and $C$ a noncentral $H$-class. Define $m(C)$ as the minimal
positive integer $m$ such that $\exists i_1,\dots,i_m\in\{\pm 1\}$ such that
the product $C^{i_1}\dots C^{i_m}$ contains all nontrivial elementary
transvections. In this article we obtain a sharp upper bound for $m(C)$.
Moreover, we determine $m(C)$ for any noncentral $H$-class $C$ under the
assumption that $K$ is algebraically closed or $n=3$ or $n=\infty$.
