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# 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.PSU_{4}(**F**_{3}).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.

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

References

Conway, J. H.; Sloane, N. J. A. (1983), "The Coxeter–Todd lattice, the Mitchell group, and related sphere packings", Math. Proc. Cambridge Philos. Soc. 93 (3): 421–440, 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, JSTOR 2370513

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