symmetry group of the square

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people dihedral group
gptkbp:actsOn	gptkb:public_square
gptkbp:automorphismGroup	gptkb:public_square
gptkbp:centralTo	{identity, rotation by 180 degrees}
gptkbp:containsElement	gptkb:identity reflection over horizontal axis reflection over vertical axis rotation by 180 degrees rotation by 270 degrees rotation by 90 degrees reflection over anti-diagonal reflection over main diagonal
gptkbp:hasCayleyTable	available
gptkbp:hasCharacterTable	available
gptkbp:hasConjugacyClasses	5
gptkbp:hasElementOrder	2 1 4
gptkbp:hasGenerators	reflection over vertical axis rotation by 90 degrees
gptkbp:hasReflection	horizontal axis vertical axis diagonal (anti-main) diagonal (main)
gptkbp:hasRotation	90 degrees 0 degrees 180 degrees 270 degrees
gptkbp:hasSubgroup	gptkb:Klein_four-group gptkb:symmetric_group_S4 cyclic group of order 4
https://www.w3.org/2000/01/rdf-schema#label	symmetry group of the square
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	gptkb:dihedral_group_of_order_8
gptkbp:isPointGroupIn2D	true
gptkbp:order	8
gptkbp:presentedBy	<r, s \| r^4 = s^2 = 1, s r = r^{-1} s>
gptkbp:standardizedBy	gptkb:D4
gptkbp:bfsParent	gptkb:Dihedral_group_of_order_8
gptkbp:bfsLayer	8