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Statistic identifier: St001155

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Collection: Finite Cartan types

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Description: The number of conjugacy classes of subgroups of the Weyl group of given type.

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References: [1]   Number of permutation groups of degree n; also number of conjugacy classes of subgroups of symmetric group S_n; also number of molecular species of degree n. [[OEIS:A000638]]
[2]   Number of conjugacy classes of subgroups of the hyperoctahedral group. [[OEIS:A269890]]

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Code:
def statistic(C):
    return len(WeylGroup(C).as_permutation_group().conjugacy_classes_subgroups())


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Statistic values:

['A',1]  => 2
['A',2]  => 4
['B',2]  => 8
['G',2]  => 10
['A',3]  => 11
['B',3]  => 33
['C',3]  => 33
['A',4]  => 19
['B',4]  => 193
['C',4]  => 193
['D',4]  => 98
['F',4]  => 246
['A',5]  => 56
['B',5]  => 953
['C',5]  => 953
['D',5]  => 197
['A',6]  => 96
['B',6]  => 7440
['C',6]  => 7440
['D',6]  => 1916
['E',6]  => 350
['A',7]  => 296
['A',8]  => 554
['A',9]  => 1593
['A',10] => 3094

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Created: Apr 21, 2018 at 23:43 by Martin Rubey

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Last Updated: Oct 18, 2020 at 17:52 by Martin Rubey