groups of order $p^8$ and exponent $p$

we prove that for $p>7$ there are‎ ‎[‎ ‎p^{4}+2p^{3}+20p^{2}+147p+(3p+29)gcd (p-1,3)+5gcd (p-1,4)+1246‎ ‎] ‎groups of order $p^{8}$ with exponent $p$‎. ‎if $p$ is a group of order $p^{8}$‎ ‎and exponent $p$‎, ‎and if $p$ has class $c>1$ then $p$ is a descendant of $‎p/gamma _{c}(p)$‎. ‎for each group of exponent $p$ with order less than $‎p^{8} $ we calculate the number of descendants of order $p^{8}$ with‎ ‎exponent $p$‎. ‎in all but one case we are able to obtain a complete and‎ ‎irredundant list of the descendants‎. ‎but in the case of the three generator‎ ‎class two group of order $p^{6}$ and exponent $p$ ($p>3$)‎, ‎while we are able‎ ‎to calculate the number of descendants of order $p^{8}$‎, ‎we have not been‎ ‎able to obtain a list of the descendants‎.