Skype group chats will not work on the current version of Skype (It is a known bug reported on their forums for Linux users & other places). You can voice talk, but typing something or having actual access to the chat will not work.
With that said, the Skype for Linux (Alpha Version) will work (Confirmed by me). You can send text, images and other normal stuff done on the chat (Be it 1 to 1 or group chat). The options you get are "Send Photos and Files" and "Send Contacts". I have uploaded an image where you can also see a group of 8 I was chatting on while also having the option to upload (Using Ubuntu 16.04)
Note that, although it says "Alpha" it works much better and has more features than the "Current" version found on Ubuntu 16.04 and previous versions. Each incremental update to Skype in the past was simply making things worse. The Alpha version is here to solve all issues (I hope).
Using Skype Alpha with Current Skype 4.X on Linux will not work as pointed by Pilot6. If the Alpha user calls, the Current Skype Linux User will never get the call. If the Current Skype Linux user call the Alpha, the Alpha user will get the following message:
This person tried to contact you but there was a problem connecting the call, try calling them back.
This is because Skype Linux 4.3 clients always use p2p and the Alpha version does not support this. Because of this you cannot establish a call between Skype 4.3 clients and Skype for Linux Alpha.