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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     author = {D. O. Revin},
     title = {The characters of groups of type $X\wr\mathbb Z_p$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {110--116},
     publisher = {mathdoc},
     volume = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2004_1_a9/}
}
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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/