Can you group Calculated Fields

I have a few Calculated Fields which already are segregated by a column i.e. PRIORITY, and I wanted to add another grouping for the Calculated Fields. which just shows the Calculated Fields with a specific Category

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No you cant make a new field that groups other field together. If you use the Free-form layout mode (from Settings) you could add an Insight visual and just put some text in it and then float it next to or above the headers to indicate they are grouped together (will need to play around with moving them up/down pixel by pixel, but its possible!). You can also add conditional formatting to the fields to visually separate them with color. See screenshot (ignore that little line on the bottom, was just my cursor when I took the screenshot):
image

And can reverse engineer it in DemoCentral (move your mouse all the way to the right edge and you will see a new menu and button to open the Analysis):
https://democentral.learnquicksight.online/#Dashboard-TipsAndTricks-Grouped-Table-Pivot-Table-Headers

Yes this is exactly how I want the Pivot table to look thanks a lot for this. However I’m new to insights and following the steps on the democentral site, while adding insights it creates a new visuals whereas I want to make changes to the pivot table itself.
Could you suggest ways in which to add the Insight visuals to the Pivot Table or are we supposed to overlap the Insight Visual onto the Pivot table

This is the only way to do it (by floating Insights, which we are basically just using as text boxes) on top of the pivot. You cannot group a set of fields in a pivot (you can only group a set of values within a given field).