Final answer:
The property that increases with an increasing atomic number in a group on the periodic table is metallic character.
Step-by-step explanation:
The property that increases as the atomic number in the group increases in the periodic table is D. Metallic character. As one moves down a group on the periodic table, the atomic radius increases, and thus, the valence electrons are farther from the nucleus. This increase in distance between the valence electrons and the nucleus makes it easier to remove these electrons, enhancing the metal's reactivity and metallic properties such as conductivity and malleability. Therefore, as the atomic number increases down a group, the elements become more metallic in character.