  Symmetry group methods are applied to obtain all explicit group-invariant
radial solutions to a class of semilinear Schrodinger equations in dimensions
$n\neq 1$. Both focusing and defocusing cases of a power nonlinearity are
considered, including the special case of the conformal power $p=4/n$ relevant
for critical dynamics.The methods involve, firstly, reduction of the semilinear
Schrodinger equations to group-invariant complex 2nd order ODEs with respect to
an optimal set of one-dimensional point symmetry groups, and secondly, use of
inherited symmetries, hidden symmetries, and conditional symmetries to solve
each ODE by quadratures. Through Noether's theorem, all conservation laws
arising from these point symmetry groups are listed.
