|
gptkbp:instanceOf
|
gptkb:group_of_people
permutation group
|
|
gptkbp:alternatingSubgroup
|
alternating group A_5
|
|
gptkbp:automorphismGroup
|
trivial group
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:degree
|
5
|
|
gptkbp:generation
|
(1 2)
(1 2 3 4 5)
|
|
gptkbp:hasElementOrder
|
2
10
3
4
5
6
|
|
gptkbp:hasSubgroup
|
gptkb:Klein_four-group
gptkb:symmetric_group_S_4
2
12
20
24
4
5
6
60
alternating group A_5
cyclic group C_5
dihedral group D_5
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S 5
|
|
gptkbp:isFirstNonabelianSimpleGroup
|
true
|
|
gptkbp:isGaloisGroupOf
|
general quintic polynomial
|
|
gptkbp:isGroupOfPermutationsOn
|
5 elements
|
|
gptkbp:isNonAbelian
|
false
|
|
gptkbp:isNonabelianSimpleGroup
|
true
|
|
gptkbp:isNotIsomorphicTo
|
gptkb:Klein_four-group
gptkb:symmetric_group_S_4
alternating group A_5
cyclic group C_5
dihedral group D_5
|
|
gptkbp:isomorphicTo
|
automorphism group of A_5
|
|
gptkbp:isPrimitive
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:isSolvable
|
false
|
|
gptkbp:isTransitiveOn
|
true
|
|
gptkbp:minimalDegreeFaithfulRepresentation
|
5
|
|
gptkbp:notation
|
gptkb:S_5
|
|
gptkbp:numberOfConjugacyClasses
|
7
|
|
gptkbp:order
|
120
|
|
gptkbp:bfsParent
|
gptkb:Conway's_icosian_automorphism_group
|
|
gptkbp:bfsLayer
|
6
|