Representations
The smallest faithful complex representation has dimension 51; there are two such representations that are duals of each other.
It centralizes an element of order 7 in the Monster group. As a result the prime 7 plays a special role in the theory of the group; for example, the smallest representation of the Held group over any field is the 50 dimensional representation over the field with 7 elements, and it acts naturally on a vertex operator algebra over the field with 7 elements.
The smallest permutation representation is a rank 5 action on 2058 points with point stabilizer SP4(4).2.
The automorphism group He.2 of the Held group He is a subgroup of the Fischer group Fi24
Read more about this topic: Held Group