The phylum Cnidaria is not a class or genus. The reason is that Cnidaria is a phylum rather than a class or genus.

Phylum: Cnidaria

There are four major groups of cnidarians:

Anthozoa, which includes true corals, anemones, and sea pens;

Cubozoa, the amazing box jellies with complex eyes and potent toxins;

Hydrozoa, the most diverse group with siphonophores, hydroids, fire corals, and many medusae; and

Scyphozoa, the true jellyfish.