Fatheaded deed by a minority group (7)
I believe the answer is:
faction
'a minority group' is the definition.
(thesaurus)
'fatheaded deed' is the wordplay.
'fatheaded' becomes 'f' (this could be a standard abbreviation I've not previously seen).
'deed' becomes 'action' (I've seen this before).
'f'+'action'='FACTION'
'by' acts as a link.
Can you help me to learn more?
(Other definitions for faction that I've seen before include "Wing" , "Dissenting group within a larger one" , "part of party" , "group of rebels" , "A dissenting clique" .)