"exodon paradoxus" are characins, but are no more a "tetra" then a piranha or payara.
exodons are actually a monotypic characin, that doesn't really fit into any specific category.
dont let the common name fool you.
as previously stated, they are generally not a community fish, and with your current stock, will likely kill your fish. HOWEVER, contrary to what was posted earlier, they are not necessarily a species only fish. there are a couple of options for tank mates, but again, none of the ones you currently have are on that list.