Cardinal invariants related to permutation groups

We consider the possible cardinalities of the following three cardinal invariants which are related to the permutation group on the set of natural numbers:ag≔ the least cardinal number of maximal cofinitary permutation groups;ap≔ the least cardinal number of maximal almost disjoint permutation families; the cofinality of the permutation group on the set of natural numbers.We show that it is consistent with that ; in fact we show that in the Miller model .