over the field with 32n+1 elements preserving a bilinear form, a trilinear form, and a bilinear product. The Ree group has order where q = 32n+1 The Schur multiplier is trivial for n ≥ 1 and for 2G2(3)′. The outer automorphism group is cyclic of order 2n + 1. The Ree group is also occasionally denoted by Ree(q), R(q), or E2*(q) The Ree group 2G2(q) has a doubly transitive permutation representation on points, and more precisely acts as automorphisms of an S(2, q+1, q3+1) Steiner system. It also acts on a 7-dimensional vector space over the field with q elements as it is a subgroup of G2(q). The 2-sylow subgroups of the Ree groups are elementary abelian of order 8. Walter's theorem shows that the only other non-abelian finite simple groups with abelian Sylow 2-subgroups are the projective special linear groups in dimension 2 and the Janko group J1. These groups also played a role in the discovery of the first modern sporadic group. They have involution centralizers of the form , and by investigating groups with an involution centralizer of the similar form Janko found the sporadic group J1. determined their maximal subgroups. The Ree groups of type 2G2 are exceptionally hard to characterize. studied this problem, and was able to show that the structure of such a group is determined by a certain automorphism of a finite field of characteristic 3, and that if the square of this automorphism is the Frobenius automorphism then the group is the Ree group. He also gave some complicated conditions satisfied by the automorphism . Finally used elimination theory to show that Thompson's conditions implied that in all but 178 small cases, that were eliminated using a computer by Odlyzko and Hunt. Bombieri found out about this problem after reading an article about the classification by , who suggested that someone from outside group theory might be able to help solving it. gave a unified account of the solution of this problem by Thompson and Bombieri. Ree groups of type 2F4 The Ree groups of type were introduced by . They are simple except for the first one , which showed has a simple subgroup of index 2, now known as the Tits group. gave a simplified construction of the Ree groups as the symmetries of a 26-dimensional space over the field of order 22n+1 preserving a quadratic form, a cubic form,