SmallGroup(81,3)

Definition
This group is defined by the following presentation:

$$G := \langle a,b,c \mid a^9 = b^3 = c^3 = e, ab = ba, bc = cb, cac^{-1} = ab \rangle$$

Families
This group is part of the family SmallGroup(p^4,3).

Other descriptions
gap> F := FreeGroup(3);  gap> G := F/[F.1^9,F.2^3,F.3^3,F.1*F.2*F.1^(-1)*F.2^(-1),F.2*F.3*F.2^(-1)*F.3^(-1),F.3*F.1*F.3^(-1)*F.1^(-1)*F.2^(-1)]; 