Groups of prime-ninth order

This article is about groups of prime-ninth order, i.e., groups of order $p^{9}$ where $p$ is a prime number.

Groups of order $p^{9}$ have not been completely classified for odd primes $p$. The classification is complete for the case $p=2$ (see groups of order 512) and the number of groups is known for the case $p=3$ (see groups of order 19683). Further, Higman's PORC conjecture has not been verified for groups of order $p^{9}$.