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Statistic identifier: St001945

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Collection: Finite Cartan types

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Description: The number of non-isomorphic subgroups of the Weyl group of a finite Cartan type.

This statistic returns the number of non-isomorphic abstract groups.

See [[St001155]] for the number of conjugacy classes of subgroups.

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References: [1]  [[oeis:A174511]]
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Code:
def statistic(ct):
    l = []
    for H in WeylGroup(ct).conjugacy_classes_subgroups():
        if not any(F.is_isomorphic(H) for F in l):
            l.append(H)
    return len(l)


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Statistic values:

['A',1]  => 2
['A',2]  => 4
['B',2]  => 5
['G',2]  => 7
['A',3]  => 9
['B',3]  => 16
['C',3]  => 16
['A',4]  => 16
['B',4]  => 54
['C',4]  => 54
['D',4]  => 27
['F',4]  => 78
['A',5]  => 29
['B',5]  => 140
['C',5]  => 140
['D',5]  => 78
['A',6]  => 55
['A',7]  => 137
['A',8]  => 241
['A',9]  => 453
['A',10] => 894
['A',11] => 2065
['A',12] => 3845

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Created: Apr 23, 2024 at 11:06 by Martin Rubey

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Last Updated: Apr 23, 2024 at 11:33 by Martin Rubey