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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 Lee Dec 12 '14 at 11:00

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  • $\begingroup$ There seem to be two completely unrelated questions here. And what have you tried? Have you found other conjugacy classes? $\endgroup$ – Tobias Kildetoft Dec 12 '14 at 10:35
  • $\begingroup$ I found {r^4},{r,r^7},{r^3,r^5},{r^2,r^6}..then centre is { e,r^4} class equation is 16 .third part stuck $\endgroup$ – M Alrantisi Dec 12 '14 at 10:38
  • $\begingroup$ Can't get that please $\endgroup$ – M Alrantisi Dec 12 '14 at 10:40
  • $\begingroup$ You should at least name your questions informatively. Also, you can format mathematical symbols and text here with $\LaTeX$ commands. $\endgroup$ – Leppala Dec 12 '14 at 10:51
  • $\begingroup$ Will try it next time thanks ..does any one have a clue about this question please $\endgroup$ – M Alrantisi Dec 12 '14 at 10:56