Geometry in Janko's first group (Q1110091)

The Janko group \(J_ 1\) is known to be the automorphism group of a certain graph or a set of curves in PG(6,11) [cf. \textit{P. Landrock} and \textit{G. O. Michler}, Math. Ann. 232, 205-238 (1978; Zbl 0355.20012), \textit{D. Livingstone}, J. Algebra 6, 43-55 (1967; Zbl 0225.20001, \textit{T. A. Whitelaw}, Proc. Camb. Philos. Soc. 63, 663-677 (1967; Zbl 0153.037)]. In this paper it is proved that \(J_ 1\) is also the full automorphism group of a certain finite plane (of 266 points and 266 lines). The author has given two permutations (derived from Livingstone) of orders 11 and 2 respectively which generate \(J_ 1\).