PRESENTATIONS OF SOME 3-TRANSPOSITION GROUPS

We classify all 3-transposition groups which are generated by at most five of their 3-transpositions. Module a center these are 27 specific groups plus various quotients of a particular group of order 2(3(49)). For each of the 27 groups at least one presentation is given. We also give presentations for many groups of importance in the recent classi fication of 3-transposition groups with trivial center. Our presentati ons include ones for the three sporadic 3-transposition groups of Fisc her, each on a a-transposition generating set of minimal size.