D16

Also called  dihedral(16).

Statistics

Order of group16
GAP identifier16,7
Presentation< k,r | k8, r2, (kr)2 >
Orders of elements1 of 1, 1+2*4 of 2, 2 of 4, 2+2 of 8
CentreC2
Derived subgroupC4
Automorphism groupa group of order 32
Inner automorphism groupD8
"Out" (quotient of above)C2×C2
Schur multiplierC2
 

Permutation Diagrams


1-transitive on 8
points, odd.

1-transitive on 8
points, odd.

1-transitive on 8
points, odd.

1-transitive on 16
points, even.

Cayley Graphs


S2:{8,3}, type I


the 8-hosohedron, type II



the 4-hosohedron, type IIIa



Regular maps with D16 symmetry

D16 is the rotational symmetry group of the regular maps the 8-hosohedron,   the di-octagon,   the hemi-8-hosohedron,   the hemi-di-octagon,   the 8-lucanicohedron,   the hemi-8-lucanicohedron.

D16 is the full symmetry group of the regular map S2:{8,8}.


Index to regular maps