# Counting Principal G-Bundles

How many principal G-bundles, $P\stackrel{\pi}{\to} X$, are there if $X$ is a point and $G$ is $\mathbb{Z}_2$, $\mathbb{Z}_4$, or the symmetries of a triangle?

• There is only one: $P = G$. – Michael Albanese Sep 14 '17 at 22:40
• You can only have nontrivial G-bundles when the base has interesting topology, and a discrete set does not. – user98602 Sep 15 '17 at 13:57
• Yes, correct. I was confused. – Bob Sep 17 '17 at 1:21