Group theory MOC Holomorph group Let 𝐺 be a group. The holomorph Hol𝐺 of 𝐺 is the semidirect product with its automorphism group group Hol𝐺=𝐺⋊Aut𝐺 Properties Hol𝐺 acts faithfully on 𝐺 by combining the regular group action with the canonical action of Aut𝐺. develop | en | SemBr