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Hessian group

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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. It may be represented as the group of affine transformations with determinant 1 of the affine plane over the finite field of 3 elements. It has a normal subgroup that is an elementary abelian group of order 3, and the quotient by this subgroup is isomorphic to the group SL2(3) of order 24. It also acts on the Hesse pencil of elliptic curves, and forms the automorphism group of the Hesse configuration of the 9 inflection points of these curves and the 12 lines through triples of these points.

The triple cover of this group is a complex reflection group, 333 or of order 648, and the product of this with a group of order 2 is another complex reflection group, 332 or of order 1296.

References

External links

  1. Hessian group on GroupNames


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