Chevalley group of type B:B3(3)

Definition
This group is defined as $$B_3(3)$$, the Chevalley group of type B and parameter value 3 for field:F3. Explicitly, it is the kernel of the spinor norm map from special orthogonal group:SO(7,3).

It is an example of a simple non-abelian group that is not the only simple non-abelian group of its order. There are at most two finite simple groups of any order. The other group in this case is projective symplectic group:PSp(6,3), which in the Chevalley notation is $$C_3(3)$$. In general, $$B_n(q)$$ and $$C_n(q)$$ have the same order, but are isomorphic only if $$n = 2$$ or $$q$$ is a prime power.