Is SO(3)/O isomorphic to SO(3)? By O, I mean the octahedral rotation symmetry group. My intuition says that they are not. But I don't know how to disprove it
2026-03-30 16:44:44.1774889084
Is SO(3)/O isomorphic to SO(3)?
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I don't think any such subgroup is normal, so the quotient isn't a group. Hence it's not a group isomorphic to $SO(3)$.