Neither would a tiger or lion. A cross of those would be less so.
Doh! My bad, tigers are : Animalia, Chordata, Mammalia, Carnivora, Felidae, Panthera, Tigris
lions are : Animalia, Chordata, Mammalia, Carnivora, Felidae, Panthera, Leo
Panthera -> Includes cougar (P. concolor), jaguar (P. onca), jaguarundi (P. jaguarundi), leopard (P. pardus), lion (P. leo), margay (P. tigrina), ocelot (P. pardalis), tiger (P. tigris), Siberian tiger (P. tigris altaica), snow leopard (P. uncia).
Thus both Lions and Tigers are all part of the same genus.
A house cat on the other hand is Animalia, Chordata, Mammalia, Carnivora, Felidae, Felis, Domesticus
They are of the same Family, but not the same Genus.