Binary octahedral group

Summary

In mathematics, the binary octahedral group, name as 2O or $\langle 2,3,4\rangle$ is a certain nonabelian group of order 48. It is an extension of the chiral octahedral group O or (2,3,4) of order 24 by a cyclic group 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.