Monster group ($\mathbb{M}$)

The Monster group $\mathbb{M}$ is the largest of the twenty-six sporadic simple groups. Its order isIt is a finite nonabelian simple group: it has no nontrivial proper normal subgroups. Size alone does not specify its multiplication; its structure is studied through representations and subgroups.^[ref]

The ATLAS specifies generators $a,b$ in conjugacy classes $2A,3B$, with $ab$ of order $29$. The letters distinguish different conjugacy classes having the same element order; the relations $a^2=b^3=(ab{)}^{29}=1$ alone are not a presentation of the Monster group. This illustrates how computational data about enormous groups can still start from two carefully chosen elements.