Solution
= Solution
All 63 <involutions> lie in <Sylow subgroups> for $2$. Each such <subgroup> has exactly seven nonidentity elements and distinct ones have no nonidentity overlap. Hence
$$
\boxed{n_2=63/7=9.}
$$
= Solution
All 63 <involutions> lie in <Sylow subgroups> for $2$. Each such <subgroup> has exactly seven nonidentity elements and distinct ones have no nonidentity overlap. Hence
$$
\boxed{n_2=63/7=9.}
$$