S 5

URI: https://gptkb.org/entity/S_5

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:permutation_group
gptkbp:automorphismGroup	gptkb:C_2 gptkb:S_5
gptkbp:centralTo	trivial group
gptkbp:degree	5
gptkbp:fullName	gptkb:symmetric_group_on_5_elements
gptkbp:generation	(1 2) (1 2 3 4 5)
gptkbp:hasElementOrder	2 3 4 5
gptkbp:hasNormalSubgroup	gptkb:A_5
gptkbp:hasSubgroup	gptkb:D_5 gptkb:S_4 gptkb:C_5 gptkb:S_6 gptkb:A_5
gptkbp:isGroupOfPermutationsOn	5 elements
gptkbp:isMaximalIn	gptkb:S_6
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	gptkb:Aut(A_5)
gptkbp:isPrimitive	true
gptkbp:isSimple	true
gptkbp:isSolvable	false
gptkbp:isTransitiveOn	true
gptkbp:notation	gptkb:S_5 gptkb:Sym(5) Σ_5
gptkbp:numberOfConjugacyClasses	7
gptkbp:numberOfElementsOfOrder2	25
gptkbp:numberOfElementsOfOrder3	20
gptkbp:numberOfElementsOfOrder4	30
gptkbp:numberOfElementsOfOrder5	24
gptkbp:order	120
gptkbp:quotientByA_5	gptkb:C_2
gptkbp:bfsParent	gptkb:PSL(2,_11) gptkb:symmetric_group_S_5 gptkb:Clebsch_diagonal_cubic_surface gptkb:S_6
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	S 5