Abstract: M_24 is one of the 26 sporadic simple groups, first to be discovered by Mathieu in the 1860s. As well as being associated with the Golay code and the Leech lattice, it is the automorphism group of the Steiner System S(5,8,24). The blocks of this system are referred to as octads. In this talk we introduce Steiner Systems, Curtis’s MOG and octad triples. We then discuss a theorem, motivated by a question in coding theory, which gives a combinatorial description of the orbits of octad triples under M_24.