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This group is defined as , 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 . In general, and have the same order, but are isomorphic only if or is a prime power.
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 4585351680#Arithmetic functions
|| Similar groups
| order (number of elements, equivalently, cardinality or size of underlying set)
|| groups with same order
|| As : which becomes