Nontrivial semidirect product of Z7 and Z9

Definition
This group is defined as the external semidirect product of cyclic group:Z7 (the normal subgroup, which is being acted upon) and cyclic group:Z9 (the acting group) where the generator of the latter acts by an automorphism of order three. An explicit presentation (where $$e$$ is the identity element) is below:

$$G := \langle a,b \mid a^7 = b^9 = e, bab^{-1} = a^2 \rangle$$

Smallest of its kind
This group is the smallest odd-order group with an irreducible representation whose Schur index is strictly greater than 1 (the value of the Schur index is 3).

Description by presentation
gap> F := FreeGroup(2);; gap> G := F/[F.1^7,F.2^9,F.2*F.1*F.2^(-1)*F.1^(-2)];  gap> IdGroup(G); [ 63, 1 ]