The most common and most likely answer to this crossword clue is the 9 letter word OLIGARCHY
I've seen this crossword clue in The Guardian
O
L
I
G
A
R
C
H
Y
More clues leading to the result OLIGARCHY
- As a rule, check oily rag’s been flicked round
- Go with a richly varied social system
- Gay choir formed around end of April, a powerful group
- System of rule in chaos — go charily
- Perhaps go charily with this form of rule
- Rule exercised by limited company?
- Not many people can control this, as a rule
- Rule established by limited company?
- Holy crag I scrambled up for ruling junta
- Peak I see scaled by extremely healthy powerful few
Buddy explains!

The straight part
We know that "a powerful group" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a powerful group = oligarchy.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does OLIGARCHY mean?
OLIGARCHY noun- A government run by only a few, often the wealthy.
- Those who make up an oligarchic government.
- A state ruled by such a government.