Is Capella a giant star?

Yes, but technically Capella isn't just no because it is actually a star system consisting of 4 stars in 2 binary pairs. For the first pair they are type-G GIANT stars, with a radius 10x the Sun's in a close orbit around each other, they are thought to be cooling by many astronomers and are on their path to becoming a red giant. The second pair are small, cool (compared to other stars), red dwarfs. The two pairs are about 10,000 astronomical units apart (1,500,000 km./930,000 mi.).