If Giant Garlic is the same thing as Elephant Garlic, the bulbs stay about four inches below ground and will mature about Mid July. They'll throw up a flower stem, some gardeners say cutting the flower off improves bulb size but after reading it makes no difference conducted my own experiments and now let the flowers grow for the bees and for dried flower arrangements.
When you harvest the bulbs there will be small bulblets attached near the base. These can be popped straight back into the ground, some will grow and after a few years make full sized plants.
Full sized cloves can be planted back in autumn for another crop too. I have a patch of plants (from a mixture of bulblets and leftover cloves) that are left as perennials. These are used as a cut and come again crop. The tender, finger thick stems are cut at ground level and the tops used like garlic scapes in risotto, stir-fries etc. The tops soon grow back after cutting and each plant will yield three or four harvests per season. TBH I prefer the tops to the taste of the bulbs and they're ready in the hungry gap.