Questions about the dihedral group $D_8$ [duplicate]

Consider the dihedral group $D_8$ of order $16$.

Consider $D_8$ with the presentation $D_8=\{r^i s^j : i=0,...,7; j=0,1; r^8=s^2=e; sr=r^7s=r^{-1}s\}$, where $\{e\}, \{rs, r^3s, r^5 s, r^7s\}$ and $\{s, r^2s , r^4s, r^6s\}$ are three of its conjugacy classes (here $r$ is a rotation and $s$ is a reflection).

1) Find the remaining conjugacy classes.

2) Find the centre and class equation for $D_8$.

3) Find the subgroups of order $4$ and explain which is normal and why.

marked as duplicate by Dietrich Burde, Claude Leibovici, Aditya Hase, Davide Giraudo, Gyu Eun LeeDec 12 '14 at 11:00

• You should at least name your questions informatively. Also, you can format mathematical symbols and text here with $\LaTeX$ commands. – Leppala Dec 12 '14 at 10:51