The group 
is one of the three Abelian groups of order 8 (the other two groups are non-Abelian).
An example is the modulo multiplication
group 
(which is the only modulo multiplication group isomorphic to 
).
The cycle graph is shown above. The elements 
of this group satisfy 
, where 1 is the identity
element.
Its multiplication table is illustrated above.
Each element is in its own conjugacy class. The subgroups are given by 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, and 
. Since the group is Abelian, all of these
are normal subgroups.
