Geodesic
Generic polynomials for transitive subgroups of the group~$S_4$ over fields of characteristic~2
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 247-258

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Generic polynomials for the symmetric group $S_4$, the Klein group $V_4$, the cyclic group of order 4, the dihedral group $D_4$ and the alternative group $A_4$ over fields of characteristic 2 are explicitly described. 
@article{ZNSL_2006_330_a13,
     author = {A. \`E. Sergeev and A. V. Yakovlev},
     title = {Generic polynomials for transitive subgroups of the group~$S_4$ over fields of characteristic~2},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {247--258},
     publisher = {mathdoc},
     volume = {330},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a13/}
}
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A. È. Sergeev; A. V. Yakovlev. Generic polynomials for transitive subgroups of the group~$S_4$ over fields of characteristic~2. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 247-258. http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a13/