The most common and most likely answer to this crossword clue is the 6 letter word CHASTE
I've seen this crossword clue in The Times
C
H
A
S
T
E
More clues leading to the result CHASTE
- Hard to be expelled from immaculate social group
- Pure drug snorted by class
- Virgin pursued, by the sound of it
- Continent's cold precipitation
- Decent participants in match as televised
- Pure heroin smuggled by group from India
- Leader of expedition must be caught and restrained
- Pure speed, fastest possible speed to begin with
- “Like a Virgin” followed on the radio
- Pure charlie and speed
Buddy explains!

The straight part
We know that "social group" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case social group = chaste.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 CHASTE mean?
CHASTE adjective- Abstaining from immoral or unlawful sexual intercourse.
- Virginal, innocent, having had no sexual experience.
- Austere, simple, undecorative.
- Decent, modest, morally pure.