Are you sure Gamma is Ionizing? I mean, it's pure Energy and not consisting of Electrons or Protons.
I'm kinda sure it is. Gamma rays are high energy waves capable of "exciting" electrons and causing other unexpected behavior.
However it is the least ionizing, as it is just energy, with the greatest "range" of all radiations.
Alpha and beta are very ionizing, but their "range" is low and can't go through many stuff, unlike gamma rays.