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 S_4 and A_5 into Cr2(C).
[17] H. Tokunaga, 2-dimensional versal S4-covers and rational elliptic surfaces, Seminaire et Congres 10, Societe Mathematique de France (2005), 307–322
[18] H.Tokunaga, Two-dimensional versal G-covers and Cremona embeddings of finite groups, Kyushu J. Math. 60 (2006), no. 2, 439–456.
[19] H. Tsuchihashi, Galois coverings of projective varieties for dihedral and symmetric groups, Kyushu J. Math. 57 (2003), no. 2, 411–427.
