Maybe it's a little odd question, but I encountered a classification of homogeneous spaces, and I'm stuck with the following description (c.f. Onishchick, "Topology of transitive transformation groups", p. 264):
[...]; $(SO_6,A_1^{10})$, where $A_1^{10}$ is the subgroup of type $A_1$ given by the representation $\rho(4\pi_1)$; [...].
Obviously, $SO_6/\rho(4\pi_1)(A_1)$ does not work for dimensional reasons and $\rho(G)/\rho(H)$ is the same as $G/H$ for faithful representations. Sadly, I can't find any further explanations on this. Does anybody knows how to interpretate this or can provide a reference?