Yazd University Algebraic Structures and Their Applications 2382-9761 12 3 2025 08 01 The ranks of the classes of the Chevalley group $G_{2}(4)$ 243 261 3702 10.22034/as.2025.21872.1730 EN Ayoub Basheer Mohammed Basheer School of Mathematical and Computer Sciences, University of Limpopo (Turfloop) P Bag X1106, Sovenga 0727, South Africa. Malebogo John Motalane School of Mathematical and Computer Sciences, University of Limpopo (Turfloop) P Bag X1106, Sovenga 0727, South Africa. 0000-0003-4484-4355 Mahlare G Sehoana School of Mathematical and Computer Sciences, University of Limpopo (Turfloop) P Bag X1106, Sovenga 0727, South Africa. Thekiso Trevor Seretlo School of Mathematical and Statistical Sciences, PAA Focus Area, North-West University (Mahikeng) P. Bag X2046, Mmabatho 2735, South Africa. Journal Article 2024 07 12 Let $G $ be a finite simple group and $X$ be a non-trivial conjugacy class of $G.$ The {rank} of $X$ in $G$, denoted by $rank(G{:}X),$ is defined to be the minimal number of elements of $X$ generating $G$. In this paper we establish the ranks of all the conjugacy classes of elements for Chevalley group $G_{2}(4)$ using the structure constants method. The Groups, Algorithms and Programming, GAP [14] is used frequently in our computations. https://as.yazd.ac.ir/article_3702_9e44d9d4ecad261998cf7c2fae6fa837.pdf