The symmetric genus of sporadic groups

Given a finite group G G , the symmetric genus of G G is defined to be the smallest integer g g such that G G acts faithfully on a closed orientable surface of genus g g . Previous to this work, the task of determining the symmetric genus for the sporadic simple groups had been completed for all but nine groups: J 3 {{J}_3} , McL McL , Suz Suz , O’N {O’N} , Co 2 Co_2 , Fi 23 Fi₂₃ , Co 1 Co_1 , B {B} , and M {M} . In the present paper the authors resolve the problem for six of these groups, viz. J 3 {{J}_3} , McL McL , Suz <mml:annotati