dihedral group of order 8

URI: https://gptkb.org/entity/dihedral_group_of_order_8

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people dihedral group
gptkbp:automorphismGroup	gptkb:dihedral_group_of_order_8
gptkbp:centralTo	{identity, r^2}
gptkbp:has_elements_of_order_1	true
gptkbp:has_elements_of_order_2	true
gptkbp:has_elements_of_order_4	true
gptkbp:hasNormalSubgroup	gptkb:Klein_four-group cyclic group of order 4
gptkbp:hasSubgroup	gptkb:symmetric_group_S_4 general linear group GL(2,3) quaternion group Q_8
https://www.w3.org/2000/01/rdf-schema#label	dihedral group of order 8
gptkbp:is_nilpotent	true
gptkbp:is_not_cyclic	true
gptkbp:is_not_simple	true
gptkbp:is_solvable	true
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	symmetries of square
gptkbp:notation	gptkb:D4 gptkb:D_4 gptkb:D_8 gptkb:D8
gptkbp:number_of_conjugacy_classes	5
gptkbp:number_of_elements_of_order_1	1
gptkbp:number_of_elements_of_order_2	5
gptkbp:number_of_elements_of_order_4	2
gptkbp:number_of_subgroups	10
gptkbp:order	8
gptkbp:order_of_center	2
gptkbp:presentedBy	⟨r, s \| r^4 = s^2 = 1, s r s^{-1} = r^{-1}⟩
gptkbp:bfsParent	gptkb:quaternion_group
gptkbp:bfsLayer	6