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I'm trying to understand what it means for a molecule to have orthorhombic symmetry. According to Di Lauro's "Rotational Structure in Molecular Infrared Spectra," a molecule is orthorhombic if the three components of translation span three different symmetry species. From reading the spectroscopy literature, it also seems like people use 'orthorhombic symmetry' to signify molecules with symmetry higher than $C_{2v}$. What confuses me, though, is that the $C_{3v}$ point group should have such higher symmetry, but in this group the $x$ and $y$ translation operators both have species $E$, which would seem to violate Di Lauro's definition. So how should I think about orthorhombic symmetry?

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