How to construct direct product of cyclic groups

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If I use

D = direct_product_permgroups([G1,G2])

where

G1 = CyclicPermutationGroup(3)
G2 = CyclicPermutationGroup(4)

then I get D presented as a subgroup of SymmetricGroup(7). Is there a way to obtain the product of G1 and G2 as a subgroup of SymmetricGroup(12)?

More generally, is there a way to obtain direct product of CyclicPermutationGroup(n1) and CyclicPermutationGroup(n2) as a subgroup of SymmetricGroup(n1 n2) rather than SymmetricGroup(n1+n2)?