Held group - Definition and Overview

In mathematics, the Held group, He, is the unique finite simple sporadic group of order <math>2^{10} 3^3 5^2 7^3\,17<math>. It can be defined in terms of the generators a and b and relations

<math>a^2 = b^7 = (ab)^{17} = [a,\, b]^6 = [a,\, b^3]^5 = [a,\,babab^{-1}abab] =<math>

<math>(ab)^4ab^2ab^{-3}ababab^{-1}ab^3ab^{-2}ab^2 = 1.<math>

It is named for Dieter Held.