  We study the Hilbert space of the Class 5 model described in
arXiv:1904.12005. Despite being integrable, neither its transfer matrix nor its
Hamiltonian are diagonalisable, meaning that the usual Algebraic Bethe Ansatz
does not provide the full Hilbert space. Instead, we make use of the symmetries
of the model to construct the Jordan blocks of the transfer matrix. We also
show that the Hamiltonian and the transfer matrix, despite commuting, do not
have the same Jordan block structure.
