The finite group 
is the finite group of order 12 that is the group
direct product of the cyclic group C2 and cyclic group C6. It is one of the two Abelian groups
of order 12, the other being the cyclic group C12.
Examples include the modulo multiplication groups 
, 
, 
, and 
(and no other modulo multiplication groups).
The multiplication table is illustrated above. The numbers of elements for which 
for 
, 2, ..., 12 are 1, 4, 3, 4, 1, 12, 1, 4, 3, 4, 1, 12.
Each element of 
is in its own conjugacy class. There are 10 subgroups: the trivial subgroup, 3 of
length 2, 1 of length 3, 1 of length 4, 3 of length 6, and the improper subgroup
consisting of the entire group. Since 
is Abelian, all its subgroups are normal. Since
it has normal subgroups other than the trivial subgroup and the improper subgroup,
is not a simple group.
