How do you specify the variable by which the By Group breakdown should occur when using the Break-Down by Groups workspace node that can be found in the Statistics tab?
Use the "Select Variables" node from the Data ribbon (from Variables drop down list) and place it between the data source and the Break-Down by Groups, then in the "Select Variables" node properties specify the categorical factor to be used for stratification by selecting the relevant variable on the "dependent categorical" list.
The "Group By" node which you have mentioned is one of those "old" ones, of the SVB kind (see the SVB label on the icon ?) and it requires specifying variables in the data flow before the node.
Note that the Break-Down by Groups performs only the break down operation (creates multiple data sources, one for each stratum). I don't know what you want to achieve, but to perform the actual break down analysis or visual data summary it might be easier to use the "Categorized" option of the "newer" nodes, then no additional step is necessary and no intermediate datasets are created.
This would also answer another of my posts in this forum, but does such a "Categorized" option exist for Boosted Trees regression? Or how could I combine the options you describe above to perform a By Group Boosted Trees regression?