|
gptkbp:instanceOf
|
gptkb:group_of_people
permutation group
|
|
gptkbp:actsOn
|
set of 8 elements
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:degree
|
8
|
|
gptkbp:generation
|
(1 2)
(1 2 3 ... 8)
|
|
gptkbp:hasMaximalSubgroup
|
gptkb:symmetric_group_S_9
|
|
gptkbp:hasNormalSubgroup
|
gptkb:alternating_group_A_8
trivial group
itself
|
|
gptkbp:hasOuterAutomorphism
|
false
|
|
gptkbp:hasSubgroup
|
gptkb:Klein_four-group
gptkb:symmetric_group_S_6
gptkb:symmetric_group_S_5
gptkb:alternating_group_A_8
gptkb:alternating_group_A_7
alternating group A_5
cyclic group C_5
cyclic group C_2
cyclic group C_3
cyclic group C_4
cyclic group C_6
cyclic group C_7
cyclic group C_8
dihedral group D_8
symmetric group S_7
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S 8
|
|
gptkbp:isCompleteGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
automorphism group of A_8
|
|
gptkbp:isParentGroupOf
|
gptkb:alternating_group_A_8
|
|
gptkbp:isPermutationGroupOn
|
8 symbols
|
|
gptkbp:isPrimitive
|
true
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSolvable
|
false
|
|
gptkbp:isTransitiveOn
|
true
8 points
|
|
gptkbp:notation
|
gptkb:S_8
|
|
gptkbp:numberOfConjugacyClasses
|
22
|
|
gptkbp:numberOfElementsOfOrder2
|
784
|
|
gptkbp:numberOfElementsOfOrder3
|
1120
|
|
gptkbp:numberOfElementsOfOrder4
|
1680
|
|
gptkbp:numberOfElementsOfOrder5
|
1344
|
|
gptkbp:numberOfElementsOfOrder6
|
1344
|
|
gptkbp:numberOfElementsOfOrder7
|
576
|
|
gptkbp:numberOfElementsOfOrder8
|
504
|
|
gptkbp:order
|
40320
|
|
gptkbp:bfsParent
|
gptkb:symmetric_group_S_9
gptkb:A_7
gptkb:alternating_group_A_8
|
|
gptkbp:bfsLayer
|
8
|