Point group of cis- and trans-decalin
cis-Decalin

Here is a view of cis-decalin with the bridging C-C bond in the plane of the paper:



(It was made using the Jmol software, e.g. at https://chemapps.stolaf.edu/jmol/jsmol/simple.htm using the "Load by name" button and entering "cis-decalin".) At https://www.chemtube3d.com/stdecalinflips/, you can see that this can flip into the mirror image (much like a cylcohexane chair flip).


  What is the point group of of cis-decalin?


I see a two-fold axis (perpendicular to the paper). I don't see a center of inversion or any mirror planes; the molecule looks chiral (the flip mentioned above changes it to its mirror image). So maybe C2?

trans-Decalin

Here is a view of trans-decalin with 5 carbons closer to us and 5 further away from us:



I see a center of inversion, a mirror plane (left:right swap), and a two-fold horizontally in the plane of view. I guess that's C2h.