There is a lot going on here, and for the first half of the book, it's fairly confusing. Let's see if I can break it down. I don't think I'm spoiling anything if I tell you this book is about a bunch of theoretical immortals. That's in the first chapter. There's a "scientific" reason for this, something to do with cleansing out all the bodily toxins when you are in pain and about to die and have accepted the inevitability of death. You also maybe have to be epileptic.
Those who have passed through that crucible are immune to aging, drowning, most diseases, although their condition carries its own looming death sentence if they're not careful. Each member of the Group names themselves after a major historical figure they identify with, except Jacy, who actually is a major historical figure.
One, who calls himself the Grand Guignol, is trying to make more of their kind - tracking down potential candidates, and trying to kill them in just the right way that they might achieve eternal life. He's not that successful, so far, and an interesting choice for a main character. But he has unexpected success with a Native American (this book was written in the 1970s, so yes, it's "Indian" all the way through) scientist, Sequoya. But for reasons that aren't entirely convincing, a seizure when an experiment goes weirdly awry, means that Extro, a huge computer network, infiltrates Sequoya's brain.
So we have a group of immortals, one of whom is possessed by a malevolent computer. And there may be other things behind the scenes. This is then a cat-and-mouse story, as the Group tries to track down the scientist and the computer, without tipping their hands to either. Along the way, Guignol gets married to the scientist's sister, and there are strangely problematic statements on squaws. But on the other hand, Native Americans are easily half the cast in this one, and range from scientists to politicians. It's a weird mix that perhaps only the 1970s could produce.
So it's a race around the planet, trying to stay off the grid in an increasingly computerized world (sound familiar?). The Computer Connection is such a weird mishmash of things that didn't quite achieve the status of a satisfying book, but parts of it are great, and other parts intriguing, and if I'm left with the feeling that the parts are greater than their sum, well, not every book is a classic. Bester will have to be satisfied with the two genuinely deserving classics he wrote.
I read this book as part of an attempt to read all the Hugo Nominees