Soul-oriented band formed in Melbourne in 1967. The Groove was something of a supergroup, its members having worked with The Clefs (Tweed Harris), Max Merritt & the Meteors (Peter Williams), The Librettos and The Playboys (Rod Stone), Black Pearls and Running Jumping Standing Still (Jamie Byrne), and Steve & the Board (Geoff Bridgford).
For a thorough account of The Groove, see Paul Culnane's article at Milesago which draws on the recollections of Groove guitarist Rod Stone.
See also Simon Says and You are The One I Love.
Single on Stax label.
This is the version known to The Groove when they recorded Soothe Me. Rod Stone, for example, had not heard Sam Cooke's version at the time (or the original) but had seen Sam & Dave perform it in London in 1967, and Soothe Me became The Groove's most popular song on stage.
Thanks to Rod Stone.