SmallGroup(64,57)

Definition
This group can be defined by the following presentation:

$$G := \langle a,b,c \mid a^4 = b^4 = c^4 = e, ab = ba, ac = ca, cbc^{-1} = a^2b \rangle$$

Description by presentation
gap> F := FreeGroup(3);  gap> G := F/[F.1^4,F.2^4,F.3^4,F.1*F.3*F.1^(-1)*F.3^(-1),F.1*F.2*F.1^(-1)*F.2^(-1),F.2*F.3*F.2^(-1)*F.3^(-1)*F.1^2];  gap> IdGroup(G); [ 64, 57 ]