The rank of a finite $p$-group $G$, where $p$ is a prime number, is the minimum number of generators of $G$.

The PGroupRank( G ) command returns the rank of the finite $p$-group G, which must be an instance of a permutation group.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{DihedralGroup}\left(8\right)$

$G≔{\mathbf{D}}_8$

$\mathrm{PGroupRank}\left(G\right)$

$2$

$\mathrm{PGroupRank}\left(\mathrm{QuaternionGroup}\left(4\right)\right)$

$2$

$\mathrm{PGroupRank}\left(\mathrm{WreathProduct}\left(\mathrm{QuaternionGroup}\left(\right)\,\mathrm{CyclicGroup}\left(4\right)\right)\right)$

$3$

$\mathrm{PGroupRank}\left(\mathrm{ElementaryGroup}\left(5\,5\right)\right)$

$5$