\ltimesThe \ltimes symbol represents the semidirect product in group theory, which is a way to construct a new group from two subgroups, one of which acts on the other.
The semidirect product of groups G and H.
G \ltimes HThe semidirect product of the integers with the cyclic group of order 2.
\mathbb{Z} \ltimes \mathbb{Z}_2A semidirect product where H acts on N via the homomorphism \phi.
N \ltimes_\phi H