  In general quantum field theories (QFTs), ordinary (0-form) global symmetries
and 1-form symmetries can combine into 2-group global symmetries. We describe
this phenomenon in detail using the language of symmetry defects. We exhibit a
simple procedure to determine the (possible) 2-group global symmetry of a given
QFT, and provide a classification of the related 't Hooft anomalies (for
symmetries not acting on spacetime). We also describe how QFTs can be coupled
to extrinsic backgrounds for symmetry groups that differ from the intrinsic
symmetry acting faithfully on the theory. Finally, we provide a variety of
examples, ranging from TQFTs (gapped systems) to gapless QFTs. Along the way,
we stress that the "obstruction to symmetry fractionalization" discussed in
some condensed matter literature is really an instance of 2-group global
symmetry.
