We study the compaction of genomic DNA by a series of alkyltrimethylammonium bromide surfactants having different hydrocarbon chain lengths n: dodecyl-(DTAB, n=12), tetradecyl-(TTAB, n=14) and hexadecyl-(CTAB, n=16), in the absence and in the presence of negatively charged silica nanoparticles (NPs) with a diameter in the range 15-100 nm. We show that NPs greatly enhance the ability of all cationic surfactants to induce DNA compaction and that this enhancement increases with an increase in NP diameter. In the absence of NP, the ability of cationic surfactants to induce DNA compaction increases with an increase in n. Conversely, in the presence of NPs, the enhancement of DNA compaction increases with a decrease in n. Therefore, although CTAB is the most efficient surfactant to compact DNA, maximal enhancement by NPs is obtained for the largest NP diameter (here, 100 nm) and the smallest surfactant chain length (here, DTAB). We suggest a mechanism where the preaggregation of surfactants on NP surface mediated by electrostatic interactions promotes cooperative binding to DNA and thus enhances the ability of surfactants to compact DNA. We show that the amplitude of enhancement is correlated with the difference between the surfactant concentration corresponding to aggregation on DNA alone and that corresponding to the onset of adsorption on nanoparticles.