The most common and most likely answer to this crossword clue is the 6 letter word FURIES
I've seen this crossword clue in The Guardian
F
U
R
I
E
S
Buddy explains!

The straight part
We know that "Vengeful group" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vengeful group = furies.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 FURIES mean?
FURIES noun- Extreme anger.
- Strength or violence in action.
- An angry or malignant person.
- A thief.