Mitchell's group

In mathematics, Mitchell's group is a complex reflection group in 6 complex dimensions of order 108 × 9!, introduced by Mitchell (1914). It has the structure 6.PSU₄(F₃).2. As a complex reflection group it has 126 reflections of order 2, and its ring of invariants is a polynomial algebra with generators of degrees 6, 12, 18, 24, 30, 42. Coxeter gives it group symbol [1 2 3]³ and Coxeter-Dynkin diagram .^[1]

Mitchell's group is an index 2 subgroup of the automorphism group of the Coxeter–Todd lattice.

References

^ Coxeter, Finite Groups Generated by Unitary Reflections, 1966, 4. The Graphical Notation, Table of n-dimensional groups generated by n Unitary Reflections. pp. 422–423

Conway, J. H.; Sloane, N. J. A. (1983), "The Coxeter–Todd lattice, the Mitchell group, and related sphere packings", Mathematical Proceedings of the Cambridge Philosophical Society, 93 (3): 421–440, Bibcode:1983MPCPS..93..421C, doi:10.1017/S0305004100060746, MR 0698347
Mitchell, Howard H. (1914), "Determination of All Primitive Collineation Groups in More than Four Variables which Contain Homologies", American Journal of Mathematics, 36 (1): 1–12, doi:10.2307/2370513, JSTOR 2370513

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[1] Coxeter, Finite Groups Generated by Unitary Reflections, 1966, 4. The Graphical Notation, Table of n-dimensional groups generated by n Unitary Reflections. pp. 422–423

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