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  "body": "\n## Summary\n\nIn mathematics, the **binary octahedral group**, name as 2O or $\\langle 2,3,4\\rangle$ is a certain nonabelian group of [[order|0B85S2V2DR]] 48. It is an extension of the chiral octahedral group *O* or (2,3,4) of order 24 by a [[cyclic group|0B85Q41RP6]] of order 2, and is the preimage of the octahedral group under the 2:1 covering homomorphism $\\operatorname{Spin}(3) \\to \\operatorname{SO}(3)$ of the special orthogonal group by the spin group. It follows that the binary octahedral group is a discrete subgroup of Spin(3) of order 48.\n",
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