Frankly I wouldn't have purchased Calibre Companion! It's abandoned by the developer.
I don't believe that CC allows you to assign groups on the device otself. Rather I think it's Grouping Drawer feature depends on data downloaded from calibre; ie Series / Publisher / Tags. For instance, i just download 7 random books to CC and where I select the Groupin Drawer and Group by Tags I get a list A / C / E / F / H / M / S / T corresponding to the first letter of various Tags from my library; expanding F I see Fantasy (3 books), Fiction (2 Books), Fiction & Literature (1 book).
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