# Binary octahedral group

The group $\langle 4,3,2 \rangle$ abstractly presented as: $$\langle A,B \ |\ A^4=B^3=(AB)^2 \rangle \ .$$ It is finite of order 48. It has the binary tetrahedral group $G_4 = \langle 3,3,2 \rangle$ as a subgroup of index 2. It occurs as a subgroup of the unit quaternions.