Geodesic
The characters of groups of type $X\wr\mathbb Z_p$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 1 (2004), pp. 110-116.

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The irreducible complex characters of the groups $G\wr\mathbb Z_p$ are calculated, where $p$ is a prime and $G$ is a finite group with known characters table. As a consequence, we get a simple inductive method to find the characters tables of the Sylow $p$-subgroups of the symmetric groups. In particular, it is proved that the values of irreducible complex characters of the Sylow $2$-subgroups in such groups are rational which solves the problem 15.25 from “Kourovka Notebook”. 
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D. O. Revin. The characters of groups of type $X\wr\mathbb Z_p$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 1 (2004), pp. 110-116. http://geodesic.mathdoc.fr/item/SEMR_2004_1_a9/

[1] B. Huppert, Character theory of finite groups, de Gruyter, Berlin, NY, 1988 | MR

[2] G. James, A. Kerber, The representation theory of the symmetric groups, Encyclopedia of Mathematics, 16, Addison-Wesley, 1981 | MR | Zbl

[3] M.I. Kargapolov, Yu.I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1977 | MR | Zbl

[4] I.M. Isaacs, Character theory of finite groups, Academic Press, NY, 1976 | MR | Zbl

[5] Kourovskaya tetrad. Nereshennye voprosy teorii grupp, izd. 15, Novosibirsk, 2002 | MR