What is this 2-3cm insect found in Slovakia?
You have with you a Carpenter bee, which are species of the genus Xylocopa  of the subfamily Xylocopinae

Xylocopa violacea, the violet carpenter bee, is the common European species of carpenter bee, and one of the largest bees in Europe. It is also native to Asia.





Here is a link to a youtube video documentary about the bees.