The class three groups of order p⁹ with exponent p

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We give a complete list of the class two groups with exponent p and order dividing p⁸. For each group in the list we compute the number of immediate descendants of order p⁹ with exponent p. In each case the number of descendants is PORC, and so the total number of class three groups of order p⁹ with exponent p is PORC. Nevertheless, there are groups of order p⁸ with exponent p which have a non-PORC number of class three descendants of order p⁹ with exponent p.