In my exercise I have to find all one dimensional representations of $D_8/C_2$ and their characters and they give us the hint 'which group is this isomorphic to?'. I have tried to maybe find a groupshomomorphism with $C_2$ as its kernel to apply the isomorphism theorems, but I haven't quite been able to. How would I have to tackle this problem? I also know that the order of the group would have to be $8/2 = 4$.
2026-03-27 01:45:13.1774575913
Isomorphic group of $D_8/C_2$
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$D_{8}/C_{2}$ has elements $C_{2}, a + C_{2}, a^{2} + C_{2}, a^{3} + C_{2}$, where $a \in D_{8}$ is the element of order $4$. Theres only two groups of order 4 up to isomorphism. Can you see which one $D_{8}/C_{2}$ is isomorphic to now?