en تخصصي Special پژوهشي Research paper <pre class="tw-data-text tw-text-large tw-ta" data-placeholder="Translation" data-ved="2ahUKEwjXvdmggNOBAxVySfEDHVcxAgkQ3ewLegQIBhAP" dir="rtl" id="tw-target-text" style="text-align: right;"> </pre> For a finite group G, the Hurwitz space Hⁱⁿ_r,g(G) is the space of genus g covers of the Riemann sphere P1 with r branch points and the monodromy group G. In this paper, we study the connectedness of the Hurwitz space Hⁱⁿ_r,g(G) where G is almost simple groups of Lie rank two, with at least four branch points and genus two. Our approach uses computational tools, relying on the computer algebra system GAP and the MAPCLASS package, to find the connected components of Hⁱⁿ_r,g(G). This work gives us the complete classification of G. Genus two groups, Almost simple groups, Braid orbits, Connected components. 173 180 http://ijmsi.ir/browse.php?a_code=A-10-7175-1&slc_lang=en&sid=1 Haval M. Mohammed Salih havalmahmood07@gmail.com 100319475328460012043 100319475328460012043 Yes Department of Mathematics, Faculty of Science, Soran University, Kawa St.-Soran, Erbil, Iraq