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    Dihedral Group

    Finite groups with available data

    dihedral group of order 2 | dihedral group of order 4 | point group D_2 | dihedral group of order 6 | point group D_3 | dihedral group of order 8 | point group D_4 | point group D_2d | point group D_2h | dihedral group of order 10 | point group D_5 | dihedral group of order 12 | point group D_6 | point group D_3d | point group D_3h | dihedral group of order 14 | point group D_7 | dihedral group of order 16 | point group D_8 | point group D_4d | ... (total: 42)

    Group elements

     | element names
dihedral group of order 2 | 1 | s
dihedral group of order 4 | 1 | r | s | r ∘ s
point group D_2 | E | C_2(z) | C_2(y) | C_2(x)
dihedral group of order 6 | 1 | r | r^2 | s | r ∘ s | r^2 ∘ s
point group D_3 | E | C_3 | C_3^2 | C_2(1) | C_2(2) | C_2(3)
 | named generators | order
dihedral group of order 2 | s | 2
dihedral group of order 4 | r | s | 4
point group D_2 | C_2(z) | C_2(y) | 4
dihedral group of order 6 | r | s | 6
point group D_3 | | 6

    Related groups

     | isomorphic groups
dihedral group of order 2 | inversion group | reflection group | 1st finite group of order 2 | C_i | C2 | ...
dihedral group of order 4 | vierergruppe | 2nd finite group of order 4 | abelian group Z_2 × Z_2 | C(2h) | D2 | ...
point group D_2 | vierergruppe | 2nd finite group of order 4 | abelian group Z_2 × Z_2 | C(2h) | C(2v) | ...
dihedral group of order 6 | 2nd finite group of order 6 | Chevalley group of type B1 over a field with 2 elements | D3 | C(3v) | point group C_3v | ...
point group D_3 | 2nd finite group of order 6 | Chevalley group of type B1 over a field with 2 elements | D3 | C(3v) | dihedral group of order 6 | ...
 | Abelian decomposition
dihedral group of order 4 | abelian group Z_2 × Z_2
point group D_2 | abelian group Z_2 × Z_2

    Common group theory properties

    nonalternating | noncyclic | nonperfect | nonsimple | nonsporadic | solvable

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