Racing bikes are endurance bikes. They are designed to be ridden over long distances at high speeds, and unless you are planning rides of more than 5 hours per day, a racing bike is what you need to go fast in a group ride.
What is a "racing bike"? It is a lightweight road bike with a short wheelbase and steeper steering geometry. Racing bikes get your power to the tires most efficiently, and have much quicker handling than endurance bikes, which comes in handy when riding in a group. When you are heading toward and obstacle or fallen rider at 50 kph, being able to turn quickly is a great benefit.
Racing bikes can be steel frame bikes with aluminum components made when Nixon was president to the current carbon fiber rolling billboards which cost more than a decent car. A Nixon-era bike will have no problem keeping up in an average group ride if you update the gearing and brakes to something more modern. If your group rides on flat terrain in the midwest or South Florida, you can probably hang with the vintage 12 speed components.
The secret to riding faster is riding faster. On your solo rides you should add intervals. If you are familiar with your normal cruising speed on a long ride, pick up the pace by 3 mph for a set amount of time, 2 or 3 minutes should be okay. When the time is up, slow back down to your usual pace. Once you starting breathing normally, pick up the pace again for another 2 or 3 minutes. In time you can hold the faster pace for 3 or 4 minutes, or longer. Once you can do it for 5 minutes, pick up the speed a little more.
Look for a faster group ride. You may not be able to take long pulls in front of really fast guys, but riding with faster riders will make you a faster rider.
Add sprints to your rides. Choose a good place where you can ride straight and fast, and find a good target to sprint for, like a road sign, mile marker, or road marking. Go all out until you reach it. If your group doesn't do a sprint near the end of the ride, see if you can get together and find a good place to do such a sprint, you'll push much harder if you are sprinting against others.