The dihedral group is one of the two nonAbelian groups of the five groups total of group order 8. It is sometimes called the octic group. An example of is the symmetry group of the square.
The cycle graph of is shown above. has cycle index given by
(1)

Its multiplication table is illustrated above.
has representation
(2)
 
(3)
 
(4)
 
(5)
 
(6)
 
(7)
 
(8)
 
(9)

Conjugacy classes include , , , , and . There are 10 subgroups of : , , , , , , , , and , . Of these, , , , , , and are normal