Dihedral group of order 8

URI: https://gptkb.org/entity/Dihedral_group_of_order_8

GPTKB entity

Statements (48)

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people dihedral group
gptkbp:automorphismGroup	gptkb:GL(2,2)
gptkbp:centralTo	{1, r^2}
gptkbp:generation	reflection rotation of 90 degrees
gptkbp:has_1_identity_element	true
gptkbp:has_2_elements_of_order_4	true
gptkbp:has_4_elements_of_order_2	true
gptkbp:has_4_reflections	true
gptkbp:has_4_rotations	true
gptkbp:has_5_conjugacy_classes	true
gptkbp:has_5_irreducible_representations_over_C	true
gptkbp:has_8_elements	true
gptkbp:hasElementOrder	2 1 4
gptkbp:hasNormalSubgroup	gptkb:Klein_four-group
gptkbp:hasSubgroup	gptkb:Klein_four-group gptkb:symmetric_group_S_4 cyclic group of order 2 cyclic group of order 4
https://www.w3.org/2000/01/rdf-schema#label	Dihedral group of order 8
gptkbp:is_a_semidirect_product_of	cyclic group of order 4 and cyclic group of order 2
gptkbp:is_group_of_symmetries_of	gptkb:public_square
gptkbp:is_nilpotent	true
gptkbp:is_not_cyclic	true
gptkbp:is_not_isomorphic_to	gptkb:quaternion_group gptkb:cyclic_group_of_order_8 direct product of two Klein four-groups direct product of cyclic group of order 4 and cyclic group of order 2
gptkbp:is_not_simple	true
gptkbp:is_not_simple_group	true
gptkbp:is_solvable	true
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	gptkb:symmetry_group_of_the_square
gptkbp:notation	gptkb:D4 gptkb:D_4 gptkb:D_8 gptkb:D8
gptkbp:number_of_conjugacy_classes	5
gptkbp:number_of_elements	8
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:D_8
gptkbp:bfsLayer	7