go to next tab: ctrl+pgdown
go to previous tab: ctrl+pgup
Key commands in Terminator

Toggle fullscreen: F11
Split terminals horizontally: Ctrl + Shift + O
Split terminals vertically: Ctrl + Shift + E
Close current Panel: Ctrl + Shift + W
Open new tab: Ctrl + Shift + T
Move to the terminal above the current one: Alt + ↑
Move to the terminal below the current one: Alt + ↓
Move to the terminal left of the current one: Alt + ←
Move to the terminal right of the current one: Alt + →