https://youtube.com/shorts/VyRSOwPSmnc?feature=share
In a previous lesson, we looked at the symmetries of a triangle. This constituted the dihedral group of degree 3, which we denote $D_6$. We also generalized this, to think of the symmetries of any regular n-gon. This group is denoted $D_{2n}$.
You can think of $D_{2n}$ as permuting the vertices of the figure. A rotation permutes them by shifting them around in a counter-clockwise motion. A reflection exchanges some of the vertices across an axis.
In fact, we will eventually see that every group can be understood in terms of permutations!
Hopefully that's some pretty good motivation for you to care about the example of permutation groups!