| 11. | One of the simplest examples of a nonabelian group is the dihedral group of order 6.
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| 12. | It is the dihedral group of order 2, also known as the Klein four-group.
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| 13. | For an example, the lattice of subgroups of the dihedral group of order 8 is not modular.
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| 14. | The dihedral groups are both very similar to and very dissimilar from the quaternion groups and the semidihedral groups.
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| 15. | The dihedral group Z 2 & times; Z 2, generated by pairs of order-two elements.
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| 16. | For this reason the dicyclic group is also known as the "'binary dihedral group " '.
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| 17. | If the flower also has 3 lines of mirror symmetry the group it belongs to is the dihedral group D3.
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| 18. | Hence the dihedral group " D " 5 acts faithfully on this subset of Young's lattice.
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| 19. | The dihedral group of order 8 is isomorphic to the permutation group generated by ( 1234 ) and ( 13 ).
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| 20. | This group is in fact the smallest non-abelian group, the dihedral group " D " 3:
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