# What is the factor group $C_{12}/C_{6}$?

I know this factor group is isomorphic to $$C_2$$, but I have tried calculating it and I only get one coset.

• We have the coset $e C_6=C_6$ and another one. – Dietrich Burde Apr 3 at 9:31

$$C_6$$, as a subgroup of $$C_{12}$$, contains $$6$$ of the $$12$$ elements. The remaining $$6$$ must make up the second coset.
Specifically, if $$C_{12} = \{0,1,2,3,4,5,6,7,8,9,10,11\}$$ with addition modulo $$12$$ as the group operation, then the two cosets of $$C_6$$ are $$C_6 = \{0,2,4,6,8,10\}\\ 1 + C_6 = \{1,3,5,7,9,11\}$$
$$C_{12}/C_6\cong C_2$$, as the order is $$2$$ and there is only one $$2$$-element group.