The correct spelling for the phrase "in groups" is /ɪn ɡruːps/. The first sound in "in" is the short "i" sound, followed by the "n" sound. The word "groups" starts with the "gr" blend, followed by a long "u" sound as in "soup", and instead of the "oo" sound as in "loop", it has a short "u" sound as in "put". Finally, the "ps" at the end of the word is pronounced like "s" with a puff of air.
The term in groups does not have a separate etymology as it is a combination of two separate words. In is a preposition that originated from Old English in or inn meaning inside or within. Groups is a noun that comes from Middle English group or groupe, which was borrowed from French groupe meaning cluster or crowd.