I am reading [this paper](https://www.worldscientific.com/doi/abs/10.1142/S0219498816501759) where the object $C\_4\times C\_2 : C\_2$ is used as a group structure. I know that $C\_n$ is a cyclic group but don't know what kind of operation between groups is identified by the symbol "$:$". Does anyone know about that? Thanks to everyone for the help.



$C_4\times C_2 : C_2$: what does this mean?
The colon means "semidirect product", but it does not specify which semidirect product. This notation is a concise shorthand that gives important structural information without necessarily uniquely specifying the group. You can read more about similar notation conventions in the introduction to the ATLAS of finite groups.


