The $(p,q,r)$-generations of the symplectic group $Sp(6,2)$

Abstract

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 29, 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 $Sp(6,2).$ GAP 20 and the Atlas of finite group representations 33 are used in our computations.