The integral Chern-class conjecture for \operatorname{SL}{\ell^2}/\mu\ell

Let $\ell$ be an odd prime, let $\mathrm{G}=\operatorname{SL}_{\ell^2}/\mu_\ell$ over $\mathds{C}$, and let $c_2$ generate $\operatorname{H}^4(\mathrm{BG},\mathds{Z})$. Integral Chern-class conjecture. The image of the cycle class map $\operatorname{cl}^2$ is

$$\mathds{Z}\cdot\ell c_2\subseteq\mathds{Z}\cdot c_2=\operatorname{H}^4(\mathrm{BG},\mathds{Z}).$$

The paper says that this expected generalization is established for the groups corresponding to $\ell=2,3$ and expects the analogous result for odd primes greater than $3$; its general status is therefore open.