# Difference between revisions of "D8 in S4"

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(Created page with "{{particular subgroup| group = symmetric group:S4| subgroup = dihedral group:D8}} This article is about the subgroup <math>H</math> in the group <math>G</math>, where <math>G</m...") |
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This article is about the subgroup <math>H</math> in the group <math>G</math>, where <math>G</math> is [[symmetric group:S4]], i.e., the symmetric group on the set <math>\{ 1,2,3,4 \}</math>, and <math>H</math> is the subgroup: | This article is about the subgroup <math>H</math> in the group <math>G</math>, where <math>G</math> is [[symmetric group:S4]], i.e., the symmetric group on the set <math>\{ 1,2,3,4 \}</math>, and <math>H</math> is the subgroup: | ||

− | <math>\! \{ (), (1,2,3,4), (1,3)(2,4), (1,4,3,2), (1,2)(3,4), (1,4)(2,3), (1,3), (2,4) \}</math> | + | <math>\! H = \{ (), (1,2,3,4), (1,3)(2,4), (1,4,3,2), (1,2)(3,4), (1,4)(2,3), (1,3), (2,4) \}</math> |

<math>H</math> is a 2-[[Sylow subgroup]] of <math>G</math>, and has two other [[conjugate subgroups]], which are given below: | <math>H</math> is a 2-[[Sylow subgroup]] of <math>G</math>, and has two other [[conjugate subgroups]], which are given below: |

## Revision as of 03:40, 17 December 2010

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).VIEW: Group-subgroup pairs with the same subgroup part | Group-subgroup pairs with the same group part | All pages on particular subgroups in groups

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: