It seems my user's group has no right to bind a port less than 1024.
Also I once that my user group can not operate the sound card, I add myselft to the sound group.
But I want the general answer, how can I check which group can do what? How to set authorize group? Is there any difference between different linux distribution?
Well only root can use ports less than 1024. You could always use iptables to forward a higher port to the lower port (See this stackoverflow post for an example). If I remember correctly, you would have to recompile the kernel to get access to those ports for other users, but I might be mistaken on that point. So this is kind of an exception to normal permissions.
Generally with UNIX things are about files. Devices, directories, connections are all files. So the sound card group, say 'audio' has access to the audio device files in dev. So you can just use find to search the file system for groups with access to read and/or write to certain files.