  $^{17}$C has three states below the $^{16}$C + $n$ threshold with quantum
numbers $J^P=3/2^+,1/2^+,5/2^+$. These states have relatively small neutron
separation energies compared to the neutron separation and excitation energies
of $^{16}$C. This separation of scales motivates our investigation of $^{17}$C
in a Halo effective field theory (Halo EFT) with a $^{16}$C core and a valence
neutron as degrees of freedom. We discuss various properties of the three
states such as electric radii, magnetic moments, electromagnetic transition
rates and capture cross sections. In particular, we give predictions for the
charge radius and the magnetic moment of the $1/2^+$ state and for neutron
capture on $^{16}$C into this state. Furthermore, we discuss the predictive
power of the Halo EFT approach for the $3/2^+$ and $5/2^+$ states which are
described by a neutron in a $D$-wave relative to the core.
