Untergruppenbach's name roughly means "below the 'Groppe' (a sort of small fish) stream", referring to a small stream that cuts across the valley in which Untergruppenbach and Obergruppenbach are located.
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Amongst the groups represented in the local politics one can find the CDU (Christian Democratic Union), the SPD (German Socialist Party), the Green Party, and the UWG (Independent Voter Community).