In mathematics, Mitchell's group is a complex reflection group in 6 complex dimensions of order 108 ÃÂ 9!, introduced by . It has the structure 6.PSU<sub>4</sub>(F<sub>3</sub>).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]<sup>3</sup> and Coxeter-Dynkin diagram .
Mitchell's group is an index 2 subgroup of the automorphism group of the CoxeterâÂÂTodd lattice.