The most common and most likely answer to this crossword clue is the 10 letter word FRATERNITY
I've seen this crossword clue in Financial Times
F
R
A
T
E
R
N
I
T
Y
More clues leading to the result FRATERNITY
- Men in a group try fine art for a change
- Trio’s appeal to enter Fight Club
- Angry quarrel about it after rent crippled social club
- Club‘s cook stuffing a bird with it
- Comradeship until the end of time, we hear!
- Female artist hereafter taking top off for male bonding?
- Brothers terrify ant in play
- The iron fist oddly seen in ‘Fight Club‘
- Weakness dropping pound, embracing bird in club …
- Fine merit seen by fool in railway company
Buddy explains!

The straight part
We know that "social club" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case social club = fraternity.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 FRATERNITY mean?
FRATERNITY noun- The quality of being brothers or brotherly; brotherhood.
- A group of people associated for a common purpose.
- A social organization of male students at a college or university; usually identified by Greek letters.