In Telegram, find a button New Group:

Select at least one group member from your contact list (you can add @InviteMemberBot). 

Now you can change group photo (if you don't have a logo, you can get a free photo/icon from websites like unsplash.io and iconfinder.com).

There is one more step you need to do. The group must be converted to a supergroup. Otherwise, InviteMember won't be able to add/remove users:

Confirm conversion:

Done!

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