Which Jewish group around the first century CE did not believe in resurrection or the afterlife?

Answer 1

The Sadducees. These were men of politics and secular life, similar to the Hellenising Jews. They had abandoned various parts of Judaism; and they claimed no earlier source or tradition for their attitudes. They harassed the Torah-sages; and, like the tiny breakaway group called the Essenes, dwindled away after the time of the Second Destruction, like the earlier Jewish idolaters after the First Destruction.
Note that there is a common misconception that the Sadducees, like the much later (and now largely defunct) Karaites, made a deliberate decision to reject the Oral Law and reinterpret the Scriptures.
However, a careful perusal of the Talmud reveals that the Sadducees were actually opportunists who had nothing much at all to do with religion in any fashion. They were lax in Judaism and had little interest in Torah-matters.
At that time the Jewish courts still had the ability to enforce the Torah laws, and almost all Jews were Torah-observant; so, in order to avoid total rejection by the surrounding community, the Sadducees outwardly maintained a facade of keeping the major Torah precepts (such as the Sabbath), while simply ignoring the Oral Torah and customs.
They went lost not long after.
The group that did (on rare occasions) debate against the Torah-Sages concerning subjects of religious observance, were a tiny sect called the Baitusim (Boethusians), who quickly died out.

Josephus talks of three groups among the Jews in late Second-Temple times: Pharisees, Sadducees, and Essenes. This may convey the mistaken impression that the Pharisees were just one "sect" among others, when in fact Josephus himself admits that the Pharisees (Torah-sages) with their disciples and followers constituted the large majority of the Jewish people. As he himself writes (Antiquities book 18), "the cities give great attestations to them."
Although the Christian Testament portrays them poorly, in fact the Pharisees were very egalitarian. They taught that all men were created in God's image and that all had the same rights, and the same right to an education, etc. They were devoted to the practicing of kindness, charity, the fulfillment of mitzvot, the study and teaching of Torah and the education of all people, regardless of status in society. They detested hypocrisy and actively sought it out and criticized it whenever they encountered it.
The Pharisees were the only movement to survive the destruction of the Second Temple and were the ancestors of modern Judaism.
Our traditional Jewish beliefs today, including the afterlife and the resurrection, are traditions continuing from the Prophets and the Sages of the Talmud ("Pharisees").

Answer 2

The 2 prominent religious groups in ancient Jerusalem were the Pharisees and the Sadducees. Acts 23:8 says that the Sadducees were the group that did not believe in angels or the resurrection, while Pharisees were the one who believe in it.

Answer 3

The Sadducees.

See also:

The groups in ancient Israel