Sym(8)

URI: https://gptkb.org/entity/Sym(8)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people
gptkbp:actsOn	set of 8 elements
gptkbp:automorphismGroup	gptkb:Z/2Z
gptkbp:centralTo	trivial group
gptkbp:containsSimpleSubgroup	gptkb:A_8
gptkbp:degree	8
gptkbp:hasConjugacyClasses	22
gptkbp:hasElementOrder	2 3 4 5 6 7 8
gptkbp:hasExceptionalOuterAutomorphism	true
gptkbp:hasIrreducibleRepresentations	22
gptkbp:hasSubgroup	gptkb:A_2 gptkb:S_3 gptkb:S_4 gptkb:A_4 gptkb:A_8 gptkb:D_8 gptkb:S_6 gptkb:A_3 gptkb:A_5 gptkb:A_7 gptkb:A_6 gptkb:S_5 gptkb:S_7 gptkb:S_2 C_8
https://www.w3.org/2000/01/rdf-schema#label	Sym(8)
gptkbp:isCayleyGroup	true
gptkbp:isFullSymmetricGroup	true
gptkbp:isGroupOfPermutations	true
gptkbp:isMaximalIn	gptkb:S_9
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	Aut(A_8)
gptkbp:isPermutationGroup	true
gptkbp:isPrimitive	true
gptkbp:isSimple	false
gptkbp:isSolvable	false
gptkbp:isTransitiveOn	true
gptkbp:isWreathProduct	false
gptkbp:notation	gptkb:S_8
gptkbp:order	40320
gptkbp:bfsParent	gptkb:PGL(2,7)
gptkbp:bfsLayer	7