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Why is CO2 not in the C∞v point group?

It will be easier to understand by giving an example of molecules: $D_{\infty h} \to \ce{CO_2}$, $C_{\infty v} \to \ce{HCN}$. Both are linear molecules, however $\ce{CO_2}$ has an inversion, $\ce{HCN}$...
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