Solution
= Solution
Sylow gives $n_7\mid24$ and $n_7\equiv1\pmod7$. Simplicity excludes $n_7=1$, so $n_7=8$. Distinct order-seven <subgroups> intersect trivially, hence there are
$$
8(7-1)=48
$$
elements of order seven.
= Solution
Sylow gives $n_7\mid24$ and $n_7\equiv1\pmod7$. Simplicity excludes $n_7=1$, so $n_7=8$. Distinct order-seven <subgroups> intersect trivially, hence there are
$$
8(7-1)=48
$$
elements of order seven.