Core of global faction starting off crooked (7)
I believe the answer is:
oblique
'crooked' is the definition.
(thesaurus)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for oblique that I've seen before include "Slanted" , "This angle is obtuse or acute" , "Indirect - devious" , "Aslant" , "Backhanded" .)