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It's been a while since I've dealt with these, but do character tables include all possible symmetry operations?

I am looking at the $D_{\infty h}$ point group table and it lists $C_\infty$, $\sigma_v$, $S_\infty$, $i$, and $C_2$. But doesn't it also have a $\sigma_h$? Why is this not included?

Am I missing something here?

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