What do the various people/groups in the book symbolize?
That's a very vague question, and the groups can symbolize a variety of things. The groups that the reader belongs to will likely influence your perspective on this question.
For example, look at the Brotherood. I have seen it quoted that this group is communist. Fine. However, there is a Communist review of the book that refutes this idea, as well as other "Anti-communist" suggestions.
As there are similarities to communism for some people, the Brotherhood could also be seen as a Union, not unlike what the narrator faces at the paint factory.
That's another good example; the paint factory group looks quite a bit like a union, more than the Brotherhood looks like a communist group. At least to me.
In Ralph Ellison’s novel “Invisible Man,” a cast of characters symbolize societal outcasts who are disillusioned and truth telling. Ironically, the people with a clear view of the world are those who are looked down upon by society as outcasts. Trueblood, the vet and blueprint man illustrate this point, the price one pays for knowing and telling the truth is removal from society.
The protagonist completes the circle. The prologue begins with the end. The reader learns the protagonist lives in a hole. Battle Royal and other situations demonstrates his position in society, subservient and enraged. The circle is completed in the epilogue, when he decides to live in a hole.
The prologue begins with “I am an invisible man” (3). He is invisible “because people refuse to see [him] (3). He finds “a home or hole” to live. Although Trueblood and the blueprint man were ridiculed during their brief appearances, they shows us verity. The epilogue provides the protagonist with understanding as to why he is “in a hole.” His experiences “showed [him] the hole [he] was in” (572). In the hole, he meditates, and is in a state of contemplation. Throughout the novel, Ellison stresses that while legitimacy is valuable in society, it seems unattainable unless one sacrifices their responsibility to humanity. The protagonist desires to become one of the symbolic disillusioned and truth telling outcasts, similar to Trueblood, the vet and blueprint man.