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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.

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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

Mathematics Encyclopedia

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