Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
set of 2^n elements
|
| gptkbp:centralTo |
trivial (identity only) for n > 1
|
| gptkbp:conjugacy_classes |
indexed by partitions of 2^n
|
| gptkbp:contains |
A_{2^n}
|
| gptkbp:contains_elements_of_order |
any integer up to 2^n
|
| gptkbp:generation |
transpositions
|
| gptkbp:hasSubgroup |
S_{2^{n+1}}
S_{m} (for m > 2^n) |
| https://www.w3.org/2000/01/rdf-schema#label |
S {2^n}
|
| gptkbp:is_a_Coxeter_group |
true
|
| gptkbp:is_a_permutation_group |
true
|
| gptkbp:is_a_transitive_group |
true
|
| gptkbp:is_a_Weyl_group |
of type A_{2^n-1}
|
| gptkbp:is_finite |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isSimple |
false (for n > 1)
|
| gptkbp:name |
symmetric group on 2^n elements
|
| gptkbp:notation |
gptkb:S_{2^n}
|
| gptkbp:order |
(2^n)!
|
| gptkbp:representation_theory |
well-studied
|
| gptkbp:bfsParent |
gptkb:symmetric_group_S_{2^n}
|
| gptkbp:bfsLayer |
8
|