D8 in S4
From Groupprops
This article is about a particular subgroup in a group, up to equivalence of subgroups (i.e., an isomorphism of groups that induces the corresponding isomorphism of subgroups). The subgroup is (up to isomorphism) dihedral group:D8 and the group is (up to isomorphism) symmetric group:S4 (see subgroup structure of symmetric group:S4).
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This article is about the subgroup in the group
, where
is symmetric group:S4, i.e., the symmetric group on the set
, and
is the subgroup:
is a 2-Sylow subgroup of
, and has two other conjugate subgroups, which are given below:
and: