In R. Brown, D. K. Harrison *Abelian Frobenius kernels and modules over number rings.* J. Pure Appl. Algebra 126 (1998), no. 1-3, 51–86, Remark 11.13 (A), the authors show that the number of isomorphism classes of metabelian Frobenius groups of order $\leq 10^3$ is 569 and of order $\leq 10^6$ is 568220. I am interested in similar statistics if we change some of the restrictions on the Frobenius kernel and keep the restriction on the Frobenius complement.

More specifically, for $n=10^3$ or $10^6$ how many isomorphism classes of Frobenius groups of order at most $n$ are there subject to the following restrictions: (a) the Frobenius complement is abelian, (b) the Frobenius complement is abelian and the Frobenius kernel is of $p$-power order for any prime $p$?

I suspect one should be able to find the answers to (a) and (b) when $n=10^3$ by using GAP or Magma and the small groups database, but I've been unable to do this because I don't see an easy way to identify Frobenius groups (and their corresponding Frobenius kernels and complements). When $n=10^6$ I would guess this isn't going to work, but maybe there is some other approach (an approximate number would also be interesting if it's not possible to find the exact answer).