О группах, изоспектральных группе изоморфизмов второй спорадической группы Янко

We prove that every finite group having the same set of element orders as $Aut(J_2)$ is isomorphic either to $Aut(J_2)$ or to an extension of a non-trivial $2$-group by $A_8$, or to some soluble group.