|
gptkbp:instanceOf
|
gptkb:group_of_people
permutation group
|
|
gptkbp:actsOn
|
set of 4 elements
|
|
gptkbp:automorphismGroup
|
trivial group
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:characterTable
|
known
|
|
gptkbp:degree
|
4
|
|
gptkbp:firstAppearance
|
studied in 19th century
|
|
gptkbp:generation
|
(1 2), (1 2 3 4)
|
|
gptkbp:hasNormalSubgroup
|
gptkb:Klein_four-group
gptkb:alternating_group_A4
|
|
gptkbp:hasSubgroup
|
gptkb:Klein_four-group
gptkb:symmetric_group_S5
gptkb:alternating_group_A4
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S4
|
|
gptkbp:innerAutomorphismGroup
|
S4
|
|
gptkbp:isomorphicTo
|
automorphism group of the Klein four-group
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSolvable
|
true
|
|
gptkbp:minimalDegreeFaithfulRepresentation
|
3
|
|
gptkbp:notation
|
S4
|
|
gptkbp:numberOfConjugacyClasses
|
5
|
|
gptkbp:numberOfElementsOfOrder
|
1 (order 1)
3 (order 2, double transpositions)
6 (order 2)
6 (order 4)
8 (order 3)
|
|
gptkbp:numberOfIrreducibleRepresentationsOverC
|
5
|
|
gptkbp:order
|
24
|
|
gptkbp:permutationRepresentation
|
degree 4
|
|
gptkbp:presentedBy
|
⟨a, b | a^4 = b^2 = (ab)^3 = e⟩
|
|
gptkbp:quotientByA4
|
C2
|
|
gptkbp:usedIn
|
gptkb:algebra
gptkb:Galois_theory
group theory
combinatorics
symmetry analysis
permutation puzzles
|
|
gptkbp:bfsParent
|
gptkb:octahedral_group
gptkb:alternating_group_A4
|
|
gptkbp:bfsLayer
|
7
|