Geodesic
Parabolic permutation representations of the group $F_4(q)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 39-59
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The degrees, ranks, subdegrees, and double stabilizers of permutation representations of the group of Lie type $F_4(q)$ on the conjugate classes of its parabolic maximal subgroups of nonminimal index are determined. 
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     author = {V. V. Korableva},
     title = {Parabolic permutation representations of the group $F_4(q)$},
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     pages = {39--59},
     year = {1998},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_1998_5_a2/}
}
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V. V. Korableva. Parabolic permutation representations of the group $F_4(q)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 39-59. http://geodesic.mathdoc.fr/item/TIMM_1998_5_a2/