dihedral group of order 2^{n+1}

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:dihedral_group
gptkbp:centralTo	\langle r^{2^{n-1}} \rangle
gptkbp:hasNormalSubgroup	\langle r \rangle
gptkbp:hasOrderDivisibleBy	4
gptkbp:hasSubgroup	gptkb:cyclic_group_of_order_2^n elementary abelian group of order 4
gptkbp:isDiscrete	true
gptkbp:isFinite	true
gptkbp:isGeneratedBy	two elements
gptkbp:isGroupOfSymmetriesOf	regular 2^n-gon
gptkbp:isMetacyclic	true
gptkbp:isNilpotent	false
gptkbp:isNonAbelian	true
gptkbp:isNonAbelianForNGeq2	true
gptkbp:isNonCyclic	true
gptkbp:isNonSimple	true
gptkbp:isSemidirectProduct	cyclic group of order 2^n and cyclic group of order 2
gptkbp:isSolvable	true
gptkbp:notation	D_{2^{n+1}}
gptkbp:numberOfElementsOfOrder2	2^{n+1} - 2^n
gptkbp:order	2^{n+1}
gptkbp:presentedBy	\langle r, s \mid r^{2^n} = s^2 = 1, srs = r^{-1} \rangle
gptkbp:bfsParent	gptkb:symmetric_group_S_{2^n}
gptkbp:bfsLayer	8
https://www.w3.org/2000/01/rdf-schema#label	dihedral group of order 2^{n+1}