The most common and most likely answer to this crossword clue is the 6 plus 7 letter word ROGUES GALLERY
I've seen this crossword clue in Independent
R
O
G
U
E
S
G
A
L
L
E
R
Y
Buddy explains!
The straight part
We know that "Group of undesirables" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case group of undesirables = rogues gallery.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.