Xjyuk

Not much information about this story, read in the 60s or 70s in an English-language anthology. Humanoid aliens having superior technology take over the Earth, and people mostly buckle under peacefully. No one knows where the aliens came from. At the end, humans stage a successful coup, capture the space fleet, and threaten retribution on the aliens' home world. When the alien chief smugly tells his captors that they'll never learn where it is, the coup leader says it's Sigma Draconis [strike that; it was Octantis]. The alien is shocked to hear this and demands to know how they found out. It turns out that over the past twenty or so years, humans pointed out one star after another to members of the invasion force, who were always happy to say, "No, that's not our star," and Sigma Draconis [Octantis] was determined by a process of elimination.

Sigma Draconis is a 4.7-magnitude star, only 19 light-years distant from Earth, so it makes a plausible home for alien civilizations. But it's arguable that aliens are unlikely even to learn the terrestrial names for stars. [I misremembered the name of the star, which was Sigma Octantis, not Sigma Draconis. Sigma Octantis is Polaris Australis, the star closest to the Southern Celestial Pole. It is a giant star, not a likely abode for life, about 281 light-years from Earth, and with a magnitude of only 5.47, only a little brighter than Uranus. Not the most likely topic of conversation while stargazing.]

Basic Right by Eric Frank Russell. Previously identified as the answer to Short story about alien invasion with a twist.

However you have misremembered the star. It is Sigma Octantis not Sigma Draconis. The bit of the story where the alien home system is identified is:

Zalumar still had an ace up his sleeve; without giving them time to speak, he played it.
"The ships won't do you any good. We shall never tell you where Raidan is."

"There's no need to," said Fox, evenly. "We know."

"You're a liar. None of my men would give you that information, not even a self-seeking swine like Heisham."

"Nobody did tell us. We found out from what they did not tell."

"Don't give me that! I—"

"It was a long and tedious task but finally we made it," Fox chipped in. All your wandering, sight-seeing tourists were willing to talk, being lonesome and far from home. We chatted with them at every opportunity. Not one would say just where he came from but every one of them readily admitted he did not come from some other place. We have analyzed records of eighty thousand conversations spread across six years. By simple process of elimination we've narrowed it down to the system of Sigma Octantis."