Interference effects strongly affect the transport characteristics of a benzene single-electron transistor, and for this reason we call it interference single-electron transistor (I-SET). We focus on the effects of degeneracies between many-body states of the isolated benzene. We show that the particular current blocking and selective conductance suppression occurring in the benzene I-SET are due to interference effects between the orbitally degenerate states. Further we study the impact of reduced symmetry due to anchor groups or potential drop over the molecule. We identify in the quasidegeneracy of the involved molecular states the necessary condition for the robustness of the results.