The cyclic group 
is one of the two Abelian groups of the five groups total of group
order 12 (the other order-12 Abelian group being finite
group C2×C6). Examples include the modulo
multiplication groups of orders 
and 26 (which are the only modulo multiplication groups
isomorphic to 
).
The cycle graph of 
is shown above. The cycle
index is
 |
Its multiplication table is illustrated above.
The numbers of elements satisfying 
for 
, 2, ..., 12 are 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12.
Because the group is Abelian, each element is in its own conjugacy class. There are six subgroups: 
,
, 
, and 
. 
, and 
which, because the group is Abelian,
are all normal. Since 
has normal subgroups other than the trivial subgroup and the entire group, it is
not a simple group.
