Final answer:
The closest living relatives to primates in the taxonomic order are tree shrews from the group Scandentia. They are more closely related to primates than rodents, carnivores, or colugos.
Step-by-step explanation:
In the taxonomic order, the group considered to be the closest living relatives to primates is Scandentia, which includes tree shrews. This group belongs to the superorder Euarchontoglires, which also includes the Primates. Scandentia and Primates share a more recent common ancestor when compared to the other eutherian mammals, making them more closely related to each other than to rodents (Rodentia), carnivores (Carnivora), or colugos (Dermoptera).
Order Primates consists of two groups: prosimians such as lemurs, and anthropoids, which includes monkeys and apes. Prosimians are generally more primitive and tend to be nocturnal, while anthropoids tend to have larger brains and are more varied in their ecological niches, including being diurnal. Humans, being part of the Primates order, share common traits with these groups, such as adaptations for climbing trees, large brains relative to body size, and stereoscopic vision.
The closest living relatives to primates within the taxonomic order are not the Rodentia (despite their high number of species), the Carnivora (which includes familiar animals such as cats and dogs), or the Dermoptera (also known as colugos or flying lemurs), but the Scandentia, with which they form a monophyletic group under the Euarchontoglires clade.