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Is it true that if there is cn and sigma h operation sn observed?

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AussieKenDoll:
If there is a Cn(n fold rotation) and sigma h (Horizontal reflection) symmetry elements on a molecule, is an Sn (Improper rotation) observed?

Flatbutterfly:

“Improper axis One or more repetitions of the same sequence: rotation followed by reflection ┴ to the rotation axis.
…if an axis Cn and a perpendicular plane independently exists then Sn exists.  More important, however, is that an Sn may exist when neither the Cn nor the perpendicular σh exist separately.”
F.A. Cotton, Chemical Applications of Group Theory 2nd ed 1971 p15, 24

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