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We prove more precisely the following main result of \cite{Isk1}. There is two non-conjugate embeddings of $S_3\times \ZZ_2$ into the Cremona group that is given by the linear action of this group on the plane and the action on the two-dimensional torus.

Two non-conjugate embeddings of $S_3 \times \mathbb{Z}_2$ into the Cremona group II