On a finite group of order 576

Abstract

Bagnera(1) shows that when a certain primitive finite group of order 576, G576, is represented as a group of collineations in three-dimensional space, it contains twenty-four harmonic inversions with respect to points and planes, and he shows how to calculate the coordinates of the points and planes of the inversions. The purpose of this note is to discuss the configuration of these points, which we shall call vertices, to show that the whole group is generated by the twenty-four harmonic inversions, termed projections after Prof. Baker (2) and Dr J. A. Todd (4), and to enumerate the conjugate sets of the group.