Sylow subgroup of holomorph of Z27

Definition
This group is defined as the $$3$$-Sylow subgroup of the holomorph of the cyclic group of order 27. Equivalently, it is the semidirect product of the cyclic group of order 27 and the cyclic group of order 9, where the generator of the latter acts on the former by the $$4^{th}$$ power map.

It is a particular case of a member of family::Sylow subgroup of holomorph of cyclic group of prime-cube order.

Other descriptions
The group can be constructed as the group G using the following commands, that involve CyclicGroup, Automorphism, SylowSubgorup, and SemidirectProduct.

gap> C := CyclicGroup(27);  gap> A := AutomorphismGroup(C);  gap> S := SylowSubgroup(A,3); gap> G := SemidirectProduct(S,C); 