On the second homotopy group of $SC(Z)$

In our earlier paper (K. Eda, U. Karimov, and D. Repovv{s}, emph{A construction of simply connected noncontractible cell-like two-dimensional Peano continua}, Fund. Math. textbf{195} (2007), 193--203) we introduced a cone-like space $SC(Z)$. In the present note we establish some new algebraic properties of $SC(Z)$.