View source for Binary octahedral group

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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 quaternion]]s.

The group has an action on the three-sphere with [[octahedral space]] as quotient.

====References====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top"> H.S.M. Coxeter, "Regular complex polytopes", Cambridge Univ. Press (1991) pp. 77 {{ISBN|0-521-20125-X}}  {{ZBL|0732.51002}}</TD></TR>
</table>