Malle's conjecture for for

We propose a framework to prove Malle's conjecture for the compositum of two number fields based on proven results and good uniformity estimates. Using this method we can $S_n\times A$ over any field $k$ $n=3$ with $A$ an abelian group order relatively prime 2, $n= 4$ 6 $n=5$ 30. As consequence, that is true $C_3\wr C_2$ in its $S_9$ representation, whereas $S_6$ representation first counter example given by Kl\"uners.