Mitchell's group
Encyclopedia
In mathematics, Mitchell's group is a complex reflection group
in 6 complex dimensions of order 108 × 9!, introduced by . 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.
Mitchell's group is an index 2 subgroup of the automorphism group of the
Coxeter–Todd lattice
.
Complex reflection group
In mathematics, a complex reflection group is a group acting on a finite-dimensional complex vector space, that is generated by complex reflections: non-trivial elements that fix a complex hyperplane in space pointwise...
in 6 complex dimensions of order 108 × 9!, introduced by . 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.
Mitchell's group is an index 2 subgroup of the automorphism group of the
Coxeter–Todd lattice
Coxeter–Todd lattice
In mathematics, the Coxeter–Todd lattice K12, discovered by , is a the 12-dimensional even integral lattice of discriminant 36 with no norm-2 vectors...
.