List of finite simple groups
Remarks: The triple cover has two 45-dimensional representations over the field with 7 elements, exchanged by an outer automorphism.
Remarks: Has a 111-dimensional representation over the field with 5 elements.
Remarks: The double cover is contained in the monster group. It has a representation of dimension 4371 over the complex numbers (with no nontrivial invariant product), and a representation of dimension 4370 over the field with 2 elements preserving a commutative but non-associative product.
Hall (1972) lists the 56 non-cyclic simple groups of order less than a million.