What kind of bug is it?
It is a Coleopteran insect (Beetle order) in the Ground beetle (Carabidae) family. Based on the elytra (protective wings) and the dark first antennal segment, it looks like Carabus granulatus. C. cancellatus is very similar, but has reddish first antennal segments. I don't think there are any other similar species in the Czech republic, but don't know the fauna there well. Overall, Carabus has many species and several are native to Eurasia and can be a size of 2 inches.

https://en.wikipedia.org/wiki/Beetle#Wings

https://en.wikipedia.org/wiki/Carabus

https://en.wikipedia.org/wiki/Carabus_granulatus

https://www.insecte.org/forum/viewtopic.php?t=160369