Dyckia fosteriana no matter cultivar or collected species they hardly produce basal sprouts.
We have to rely on old head divisions to  produce new plants.
I let the plant stay without water for a time, remove it from the pot, clean it and then if I want I separate the heads. A nice measure is to seal the scar to avoid any  lose by fungi attacks. There are good  commercial disinfectant and sealers to do this properly. I usually let the scar dry without planting the head and during this time I use a mist maker to keep the plant from dehydrating too much.
Thisz plant here I did not separate any head as I wand an old many heads plant.