is one of the three Abelian
groups of group order 8 (the other two being non-Abelian).
Examples include the modulo multiplication
groups 
,
, 
, and 
(and no others).
The elements 
of this group satisfy 
,
where 1 is the identity element, and four of
the elements satisfy 
.
The cycle graph is shown above.
Its multiplication table is illustrated above.
Since the group is Abelian, each element is in its own conjugacy class.
The subgroups are 
,
,
,
,
,
,
,
and 
,
A, B, C, D, E, F, 
.
Since the group is Abelian, all of these are normal.
