---
tag: KHRDF4PGJ6
kind: concept
name: Binary octahedral group
sources:
  - wikipedia: en:10997598@r1376053394
    locator: Binary octahedral group
    note: adopted
    mention: wikipedia://en/10997598
    sections: [Summary]
same_as:
  wikidata: Q4913904
  wikipedia: Binary octahedral group
inventory: [6RH22NX9W1]
---

## Summary

In 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.