Hessian group

In mathematics, the Hessian group is a finite group of order 216, introduced by Jordan (1877) who named it for Otto Hesse, given by the group of determinant 1 affine transformations of the affine plane over the field of 3 elements. It acts on the Hesse pencil and the Hesse configuration. Its triple cover is a complex reflection group of order 648, and the product of this with a group of order 2 is another complex reflection group. It has a normal subgroup that is an elementary abelian group of order 32, and the quotient by this subgroup is isomorphic to the group SL2(3) of order 24.
References

Artebani, Michela; Dolgachev, Igor (2009), "The Hesse pencil of plane cubic curves", L'Enseignement Mathématique. Revue Internationale. 2e Série 55 (3): 235–273, doi:10.4171/lem/55-3-3, ISSN 0013-8584, MR 2583779
Coxeter, Harold Scott MacDonald (1956), "The collineation groups of the finite affine and projective planes with four lines through each point", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 20: 165–177, ISSN 0025-5858, MR 0081289
Grove, Charles Clayton (1906), The syzygetic pencil of cubics with a new geometrical development of its Hesse Group, Baltimore, Md.
Jordan, Camille (1877), "Mémoire sur les équations différentielles linéaires à intégrale algébrique.", Journal für die reine und angewandte Mathematik (in French) 84: 89–215, doi:10.1515/crll.1878.84.89, ISSN 0075-4102

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