dihedral group of order 10

URI: https://gptkb.org/entity/dihedral_group_of_order_10
GPTKB entity
Statements (44)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
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
https://www.w3.org/2000/01/rdf-schema#label dihedral group of order 10
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 5