8 – How can I make a slider block with nodes grouped by letter?

I need to make a block that list all nodes of a content type grouped by the first letter of the title. This block should be a slider so the user can iterate by letter. Also, it should have an alphabet filter so the user can filter by letter.

Something like that:
This is an example of what I want1

I can make a block with nodes grouped by the first letter of the title.

But how can I convert this to a slider block? And also, how can I make an alphabet filter?