The free lattice-ordered group F. (of rank n) has been studied in two ways: via the Conrad representation on the various right orderings of the free group G71 (sharpened by Kopytov's observation that some one right ordering must by itself give a faithful representation), and via the Glass-McCleary representation as a pathologically o-2-transitive I-permutation group. Each kind of representation yields some results which cannot be obtained from the other. Here we construct a representation giving the best of both worlds-a right ordering (GC,, <) on which the action of F. is both faithful and pathologically o-2-transitive. This (GC, <) has no proper convex subgroups. The construction is explicit enough that variations of it can be utilized to get a great deal of information about the root system 9,, of prime subgroups of F.. All RX's with 1 < n < o are o-isomorphic. This common root system gf has only four kinds of branches (singleton, three-element, 9f, and 9'.,O), each of which occurs 2wo times. Each finite or countable chain having a largest element occurs as the chain of covering pairs of some root of Sf. 1. The Conrad representation has been used most extensively by Arora and McCleary [1], who studied centralizers of certain elements of F. The GlassMcCleary representation was exploited (and partially developed) by McCleary in [7], to which the present paper is a sequel. Familiarity with [7] (but not [1]) is assumed. The Conrad representation [2] proceeds as follows: Given any right ordering (GV, <) of the free group G,, the right regular representation T of G, preserves the order (but is not in general an i-permutation group). By the freeness of F on the free generating set x (which generates G, as a group), T can be extended to a unique i-homomorphism into A((G',, <)) (i.e., to a unique action on the chain (G,, ), namely WT =(V Awi)c = V AwjT. We shall refer to this as the natural action of F on (Gn, s). When this action is a representation (i.e., faithful), we shall call (G',, < ) a representing right ordering. Another kind of action of F is usual transitive action on the chain F/P of right cosets of a prime subgroup P (namely (Pf )w = P(fw)). When this action is a representation, P is called a representing subgroup of F,. Received by the editors February 21, 1984. 1980 Mathematics Subject Classification. Primary 06F15.