Yup to what others are saying... if you're not a people person, don't aim for management. You will be miserable, and the people that work for you will be miserable.

I say this as someone that is also not a people-person (and who has specifically chosen to avoid moving into management) and as someone who has had really terrible managers.

Remember, as a manager - you have to do more than delegate work. You have to inspire people to do their best work, coach them about their career, listen to them complain (endlessly, imho!) about issues with the coworkers or clients, resolve personal disputes between people on your team, assess their performance (my job requires our manager to do formal reviews twice a year!) and if you're telling them they need to improve - you have to do it in a way that helps them want to improve and teaches them how to do that, not in a way that destroys their confidence and makes them miserable/stop trying. Oh, and you have to deal with issues that come up when somebody gets a serious illness or a team member passes away (I've had this happen at my place of work too).

There's a ton of people stuff involved to be good at it. And, nobody deserves a bad manager - they can really make your life awful.

When you say this: " I want to focus on the big picture, on lots of technical data which keeps one place running." - I'm a little confused, because "the big picture" and "lots of technical data" seem to be at odds?

If you like analyzing data (as opposed to writing code/programming) - there's a lot of work (and job opportunities, I believe) for data analysts. It's late and I'm probably forgetting the correct term - but people who can organize tons of data into meaningful information. Have you looked at "big data"? Though... it will probably require programming skills and advanced math skills.

Good luck!