You have only yourselves to blame, that you have to listen to me yet again.
A construction of the small Ree groups from 7 coordinates labelled by 0 and the complex 6th roots of unity, using a dot product, a cross product, and a star product. The dot/scalar/inner product is defined by pairs of labels adding to zero, and the cross/vector/outer product is defined by triples of labels adding to zero. The star product is defined by pairs of labels adding to a complex number of absolute value 3. There are q^3+1 points P defined by P=P*x, on which the automorphism group acts 2-transitively. The stabilizer of two distinct points is a diagonal matrix determined by one non-zero scalar. Hence the group has order (q^3+1)q^3(q-1).
Possibly followed by drinks and mince pies in the Common Room (102).