The cyclic group 
is unique group of group order 11. An example is the
integers modulo 11 under addition (
). No modulo
multiplication group is isomorphic to 
. Like all cyclic groups, 
is Abelian.
The cycle graph of 
is shown above. The cycle
index is
 |
Its multiplication table is illustrated above.
Because the group is Abelian, each element is in its own conjugacy class. Because it is of prime order, the only subgroups are the trivial group and entire group.
is therefore a simple
group, as are all cyclic graphs of prime order.
