Inmathematics, the Hessian group is a finite groupoforder 216, introduced by Jordan (1877) who named it for Otto Hesse. It may be represented as the groupofaffine transformations with determinant 1 of the affine plane over the finite field of 3 elements.[1] It has a normal subgroup that is an elementary abelian group of order 32, and the quotient by this subgroupisisomorphic to the group SL2(3) of order 24. It also acts on the Hesse pencilofelliptic 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, 3[3]3[3]3or
of order 648, and the product of this with a group of order 2 is another complex reflection group, 3[3]3[4]2or
of order 1296.
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