M81

Definition
This group is defined as the semidirect product of the cyclic group of order 27 with the unique cyclic subgroup of order 3 in its automorphism group.

Other descriptions
The group can be constructed using the following series of GAP instructions (note that double semicolons are to suppress output display after each command):

gap> H := CyclicGroup(27);; gap> A := AutomorphismGroup(H);; gap> B := Filtered(NormalSubgroups(A),K->Order(K) = 3)[1];; gap> G := SemidirectProduct(B,H);