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In this article, we prove that two versal Galois covers for S4 and A5 introduced in [17], [18] and [19] are birationally distinct to each other. As a corollary, we obtain two non-conjugate embeddings of S4 and A5 into Cr2(C).

A Note on Embeddings of $S_4$ and $A_5$ into the Two-dimensional Cremona Group and Versal Galois Covers