Which group of elements has the highest ionization energies?
The noble gases
Ionization energy is the amount of energy required to remove one electron from an atom. So the groups further to the right of the periodic table would have greater ionization energies because they are more stable, so they don't want to lose electrons, and there is a greater number of protons attracting the negative charges (the electrons).
So technically, the noble gases have the largest ionization energies, but since they're special and it's not often that electrons would even be removed from the atom (it rarely occurs), we would usually say that the halogens is the group with the largest ionization energies.