| 21. | There are also isomorphic copies of the binary dihedral groups of orders 8 and 12 in 2 " O ".
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| 22. | You may also want to read the article Dihedral group . talk ) 07 : 27, 19 July 2013 ( UTC)
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| 23. | I also want to classify all finite subgroups of isometries in \ mathbb { R } ^ 2 into cyclic and dihedral groups.
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| 24. | The dihedral group of order 8 ( D 4 ) is the smallest example of a group that is not a T-group.
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| 25. | Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry.
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| 26. | There is a superficial resemblance between the dicyclic groups and dihedral groups; both are a sort of " mirroring " of an underlying cyclic group.
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| 27. | For " p " = 2, both the semi-direct products mentioned above are isomorphic to the dihedral group Dih 4 of order 8.
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| 28. | The Q 8 group has the same order as the dihedral group D 4, but a different structure, as shown by their Cayley and cycle graphs:
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| 29. | Both these two groups and the dihedral group are semidirect products of a cyclic group of order 2 n " 1 with a cyclic group of order 2.
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| 30. | For example, the dihedral group appears on page 419 . The coquaternion structure has also been mentioned briefly in the " Annals of Mathematics ".
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