Say I am part of various groups $ groupsusers git engineering ....And I can execute sudo in that machine, How can I tell which group is responsible for my sudo execution ability ? 
How to tell which group is responsible for your sudo permissions?
sudo;group;ldap
Execute:  sudo less /etc/sudoers  or even just  sudo cat /etc/sudoersand look for something like the following:  %wheel ALL=(ALL) ALLwhere the key to your question is the group name following the %.See man sudo.conf for an excellent explanation of who gets what privileges based on the line % line above and other parameters available in /etc/sudoers and /etc/sudoers.d.