Projective symplectic group:PSp(6,3)

Definition
This group is defined as follows: It is the member of family::projective symplectic group of degree six (i.e., arising from $$6 \times 6$$ matrices) over field:F3. This is denoted $$PSp(6,3)$$ and the Chevalley notation is $$C_3(3)$$.

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 Chevalley group of type B:B3(3), which is the kernel of the spinor norm from special orthogonal group:SO(7,3). 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.