dihedral group of order 10

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:dihedral_group
gptkbp:abelianization	cyclic group of order 2 × cyclic group of order 5
gptkbp:automorphismGroup	gptkb:dihedral_group_of_order_10 cyclic group of order 2
gptkbp:centralTo	trivial group
gptkbp:derivedSubgroup	gptkb:cyclic_group_of_order_5
gptkbp:hasCyclicSubgroupOfOrder	2 5
gptkbp:hasElementOrder	2 1 5
gptkbp:hasNormalSubgroup	gptkb:cyclic_group_of_order_5 trivial group whole group
gptkbp:hasSubgroup	2 1 10 5
gptkbp:isFrobeniusGroup	true
gptkbp:isGroupOfSymmetriesOf	regular pentagon
gptkbp:isMetacyclic	true
gptkbp:isNilpotent	false
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	gptkb:symmetry_group_of_regular_pentagon
gptkbp:isSimple	false
gptkbp:isSolvable	true
gptkbp:isSplitExtension	cyclic group of order 5 by cyclic group of order 2
gptkbp:isSupersolvable	true
gptkbp:minimalFaithfulLinearDegree	2
gptkbp:minimalFaithfulPermutationDegree	5
gptkbp:notation	gptkb:D10 gptkb:D_5 gptkb:D5
gptkbp:numberOfConjugacyClasses	4
gptkbp:numberOfElementsOfOrder1	1
gptkbp:numberOfElementsOfOrder2	5
gptkbp:numberOfElementsOfOrder5	4
gptkbp:numberOfIrreducibleRepresentations	4
gptkbp:order	10
gptkbp:presentedBy	⟨r, s \| r^5 = s^2 = 1, s r s^{-1} = r^{-1}⟩
gptkbp:bfsParent	gptkb:icosahedral_group
gptkbp:bfsLayer	8
https://www.w3.org/2000/01/rdf-schema#label	dihedral group of order 10