Geodesic
Properties of permutation representations of nonabelian $2$-groups with a cyclic subgroup of index~$2$
Matematičeskie voprosy kriptografii, Tome 12 (2021), pp. 65-85

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For all nonabelian $2$-groups with cyclic subgroup of index $2$ (the dihedral group $D_{2^m}$, the generalized quaternion group $Q_{2^m}$, the modular maximal-cyclic group $M_{2^m}$, the quasidigedral group $SD_{2^m}$) we describe properties of regular permutation representations. For each group we characterize all nontrivial imprimitivity systems and corresponding homomorphisms. 
@article{MVK_2021_12_a4,
     author = {B. A. Pogorelov and M. A. Pudovkina},
     title = {Properties of permutation representations of nonabelian $2$-groups with a cyclic subgroup of index~$2$},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {65--85},
     publisher = {mathdoc},
     volume = {12},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2021_12_a4/}
}
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B. A. Pogorelov; M. A. Pudovkina. Properties of permutation representations of nonabelian $2$-groups with a cyclic subgroup of index~$2$. Matematičeskie voprosy kriptografii, Tome 12 (2021), pp. 65-85. http://geodesic.mathdoc.fr/item/MVK_2021_12_a4/