dihedral group of order 6

URI: https://gptkb.org/entity/dihedral_group_of_order_6
GPTKB entity
Statements (45)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
dihedral group
gptkbp:actsOn gptkb:equilateral_triangle
gptkbp:alsoKnownAs gptkb:D3
gptkb:D6
gptkb:D_3
gptkbp:automorphismGroup trivial group
S3
gptkbp:Cayley_table available
gptkbp:centralTo trivial group
gptkbp:generation reflection of order 2
rotation of order 3
gptkbp:has_1_identity_element true
gptkbp:has_2_elements_of_order_3 true
gptkbp:has_3_elements_of_order_2 true
gptkbp:hasElementOrder 2
1
3
gptkbp:hasNormalSubgroup trivial group
cyclic group of order 3
whole group
gptkbp:hasSubgroup cyclic group of order 2
cyclic group of order 3
https://www.w3.org/2000/01/rdf-schema#label dihedral group of order 6
gptkbp:isNonAbelian true
gptkbp:isomorphicTo gptkb:symmetric_group_S3
permutation group of 3 elements
gptkbp:isSimple false
gptkbp:isSolvable true
gptkbp:number_of_conjugacy_classes 3
gptkbp:number_of_elements 6
gptkbp:number_of_irreducible_representations_over_C 3
gptkbp:number_of_reflections 3
gptkbp:number_of_rotations 3
gptkbp:order 6
gptkbp:order_of_automorphism_group 6
gptkbp:presentedBy <a, b | a^3 = b^2 = 1, b a b^{-1} = a^{-1}>
<r, s | r^3 = s^2 = 1, s r s^{-1} = r^{-1}>
gptkbp:Schur_multiplier gptkb:cyclic_group_of_order_6
gptkbp:used_in gptkb:algebra
gptkb:geometry
group theory
symmetry studies
gptkbp:bfsParent gptkb:icosahedral_group
gptkbp:bfsLayer 5