"Natural" example of cosets Do you know natural/concrete/appealing examples of right/left cosets in group theory ?
This notion is a powerful tool but also a very abstract one for beginners so this is why I'm looking for friendly examples. 

In the dihedral group $G =  D_{n}$ the group of symmetries of the regular $n$-gon, which is a group with $2n$ elements, the rotations form a subgroup $H$ of order $n$, and there are two right (or left in this special case as $H \lhd G$) cosets of $H$ in $G$. One of these cosets is $H$ itself, and the other coset consists of the $n$ reflections of $G$.
