In abstract algebra, the study of concrete groups is fundamentally important to beginners. Most commonly used groups as examples are integer addition modulo n, real number addition and multiplication, permutation groups, and groups of symmetry. The last two examples are finite non-abelian groups and can be investigated with the aid of concrete representations. This study presents a finite abelian group of inversions of two letter symbols with vertical and horizontal axes of symmetry and whose binary operation is established through motions like alternation, rotation, reflection, and a combination of two or all motions.