Kernel: SageMath (stable)
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We'll be looking at the Complex reflection group which are the matrices with entries in such that the entires are in where is a cube root of unity. In addition each row and each column must have at most one non-zero entry. In particular the group will have the following set of elements:
According to wikipedia, this should have elements and should have order reflections and order pseudo-reflections.
Note that a pseudo-reflections are the matrices such that the eigenvalues of contain exactly one .
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Number of elements:
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Number of reflections:
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Reflections by order:
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Number of generating sets:
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All possible generating sets:
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We're using the following generating set:
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