You may be looking for Science Fiction Book Club.
A book club was a social activity centered on the reading and discussing of books.
One such club was the Interstellar Adventure Book Club, devoted to science fiction titles. (DS9: "Far Beyond the Stars")
In 2153, upon seeing the movie Frankenstein, T'Pol suggested that it might be more illuminating to do a dramatic reading of the book instead. Charles Tucker III answered that she was welcome to start a book club if she wanted. (ENT: "Horizon")
A line from the script of Star Trek that did not make it into the movie had Kirk sarcastically suggesting that he might start a book club upon being challenged to make something of his life by Captain Pike. This detail was retained in the novelization of Star Trek.