The (p,q,r)-generations of the symplectic group Sp(۶,۲)

A finite group G is called \textit{(l,m, n)-generated}, if it is a quotient group of the triangle group T(l,m, n) = \left. In ۲۹, Moori posed the question of finding all the (p,q,r) triples, where p,\ q and r are prime numbers, such that a non-abelian finite simple group G is a (p,q,r)-generated. In this paper we establish all the (p,q,r)-generations of the symplectic group Sp(۶,۲). GAP ۲۰ and the Atlas of finite group representations ۳۳ are used in our computations.

Keywords:

Conjugacy classes , generation , simple groups , structure constants , symplectic groups