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/γ 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.