M27

Definition
This group, sometimes denoted $$M_{27}$$ or $$M_3(3)$$, is defined as the semidirect product of the cyclic group of order nine and a cyclic group of order three, acting on it by nontrivial automorphisms.

It is given by the presentation:

$$\langle a,b \mid a^9 = b^3 = e, bab^{-1} = a^4 \rangle$$