Hyraxes belong to Hyracoidea, one of the orders in Afrotheria, and their closest relatives are the elephants and the sirenians. The anatomical hints are real if easy to miss: hyraxes have continuously growing upper incisors that erupt as small tusks, flat nails rather than claws on most digits, and a foot structure with rubbery, moist soles that grip rock.
Temperature control is a second oddity. Hyraxes hold body temperature less steadily than most mammals of their size and rely heavily on behaviour, huddling in groups overnight and basking in long sessions in the morning. That basking, easily read as laziness, is a physiological necessity.
The familiar line that the hyrax is the elephant's closest relative needs qualification, since sirenians are equally close and the relevant common ancestors are ancient. Hyraxes also communicate with structured calls that vary between individuals and regions, and whether those song-like sequences carry the information some researchers propose is still an open question.