Much of the group, which refers to itself as Trump’s Online War Machine, operates anonymously, adopting the cartoonish aesthetic and unrelenting cruelty of internet trolls.

Cheered on by Mr. Trump, the group traffics freely in misinformation, artificial intelligence and digital forgeries known as deepfakes. Its memes are riddled with racist stereotypes, demeaning tropes about L.G.B.T.Q. people and broad scatological humor.