First Classification of Finite Subgroups of $SO(3)$

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One can find a classification of all isomorphism types of finite subgroups of $SO(3)$ on, say, GroupProps: https://groupprops.subwiki.org/wiki/Classification_of_finite_subgroups_of_SO(3,R). However, I would like to know who is generally agreed to have first found this classification. Does anyone know?

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According to nlab the earliest proof is due to Klein:

Felix Klein, chapter I of Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, 1884, translated as Lectures on the Icosahedron and the Resolution of Equations of Degree Five by George Morrice 1888, online version