The simple group of order 6048

Abstract

The group of the title is one of the classical groups and can be represented—will indeed be represented here—as the group of those projectivities in a certain finite plane that leave invariant the set of zeros of a Hermitian ternary form. Its properties in the large, so to speak, are common knowledge, being particular instances of those of unitary finite groups; the conjugate sets, and sufficient information to determine, or perhaps nearly to determine, the group characters are given in (7). The methods to be used here are elementary; they take advantage of the base field, and consequently the numbers of points in the geometry, being relatively small. Much detailed information emerges that seems worth putting on record; it does not occupy a disproportionate amount of room and might elude the coarser net of an investigation based on generalities.