  We determine the 2-group structure constants for all the six-dimensional
little string theories (LSTs) geometrically engineered in F-theory without
frozen singularities. We use this result as a consistency check for T-duality:
the 2- groups of a pair of T-dual LSTs have to match. When the T-duality
involves a discrete symmetry twist the 2-group used in the matching is
modified. We demonstrate the matching of the 2-groups in several examples.
