In this paper, we classify groups which faithfully act on smooth cubic threefolds. It turns out that there are exactly 6 maximal ones and we describe them with explicit examples of target cubic threefolds.
The second author is partially supported by the National Natural Science Foundation of China (Grant No. 11701413).
"Automorphism groups of smooth cubic threefolds." J. Math. Soc. Japan 72 (4) 1327 - 1343, October, 2020. https://doi.org/10.2969/jmsj/83088308