A 195, 747, 435 vertex graph related to the Fischer group \(Fi_{23}\). II. (Q2883288)

Let \(\Gamma\) be a geometry of rank 4 associated with the second large Fisher group \(Fi_{23}\). A desription of each type of objects (base, heptad, tri-transposition, transposition) in \(\Gamma\) is given in the Atlas of finite groups. Maximal subgroups and ordinary characters for simple groups [Oxford: Clarendon Press (1985; Zbl 0568.20001), p. 177]. Let \(\mathfrak G\) be the point-line collinearity graph of \(\Gamma\), i.e., the graph where vertices are bases with two vertices joined whenever they intersect in a heptad. The group \(Fi_{23}\) acts flag transitively on \(\Gamma\) and so is a subgroup of \(\Aut\,\mathfrak G\) acting transitively on 195,747,435 vertices of \(\mathfrak G\). -- This is the second in a three part series of papers devoted to the analysis of this graph. Part I is published by the authors [in JP J. Algebra Number Theory Appl. 23, No. 1, 87-120 (2011; Zbl 1241.20022)].