Mammillaria perbella K.Schum.

Solitary, body elongate, to 8 cm wide and 10 cm high. Tubercles obscure. Central spines 2, 3-5 mm long, black, later grey, tips black. Radial spines 20-30, 3 mm long, white. Flowers pink with darker central stripe, 15 mm long and wide. Fruit red.

Probably of garden origin

Source: Thompson, A, ; Forbes, S.; Spencer, R. (1997). Cactaceae. In: Spencer, R.. Horticultural Flora of South-eastern Australia. Volume 2. Flowering plants. Dicotyledons. Part 1. The identification of garden and cultivated plants. University of New South Wales Press. (as Mammillaria pseudoperbella)

kingdom Plantae
phylum   Tracheophyta
class    Magnoliopsida
superorder     Caryophyllanae
order      Caryophyllales
family       Cactaceae
genus        Mammillaria Haw.