The Ree groups 2F4(22n+1) were constructed by Ree (1961), who showed that they are simple if n ≥ 1. The first member of this series 2F4(2) is not simple. It was studied by Jacques Tits (1964) who showed that its derived subgroup 2F4(2)′ of index 2 was a new simple group. The group 2F4(2) is a group of Lie type and has a BN pair, but the Tits group itself does not have a BN pair. Because the Tits group is not strictly a group of Lie type, it is sometimes regarded as a sporadic group.
The Tits group is one of the simple N-groups, and was overlooked in John G. Thompson's first announcement of the classification of simple N-groups, as it had not been discovered at the time. It is also one of the thin finite groups.
L3(3):2 Two classes, fused by an outer automorphism. These subgroup fix points of rank 4 permutation representations.
2..5.4 Centralizer of an involution.
A6.22 (Two classes, fused by an outer automorphism)
The Tits group can be defined in terms of generators and relations by
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