1690s, originally an art criticism term, "assemblage of figures or objects forming a harmonious whole in a painting or design," from French groupe "cluster, group" (17c.), from Italian gruppo "group, knot," which probably is, with Spanish grupo, from a Germanic source, from Proto-Germanic *kruppaz "round mass, lump," part of the general group of Germanic kr- words with the sense "rounded mass" (such as crop (n.).
Extended to "any assemblage, a number of individuals related in some way" by 1736. Meaning "pop music combo" is from 1958. As it was borrowed after the Great Vowel Shift in English, the pronunciation of the -ou- follows French rather than English models.
think v.
Old English þencan "imagine, conceive in the mind; consider, meditate, remember; intend, wish, desire" (past tense þohte, past participle geþoht), probably originally "cause to appear to oneself," from Proto-Germanic *thankjan (source also of Old Frisian thinka, Old Saxon thenkian, Old High German denchen, German denken, Old Norse þekkja, Gothic þagkjan).
Old English þencan is the causative form of the distinct Old English verb þyncan "to seem, to appear" (past tense þuhte, past participle geþuht), from Proto-Germanic *thunkjan (source also of German dünken, däuchte). Both are from PIE *tong- "to think, feel" which also is the root of thought and thank.
The two Old English words converged in Middle English and þyncan "to seem" was absorbed, except for its preservation in archaic methinks "it seems to me."
As a noun, think, "act of prolonged thinking," is attested by 1834. The figurative thinking cap is attested from 1839.