All Questions

I am interested in series of finite subgroups of the classical compact simple Lie groups which have big orbits on compact symmetric spaces and where the double coset space has some nice explicit ...

I believe it is the case that any finite subgroup of SO$(3)$ (the $3 \times 3$ orthogonal matrices of determinant $1$) is either a cyclic group $C_n$, or a dihedral group $D_n$, or one of the groups ...