D16

Also called dihedral(16).

Statistics
Order of group	16
GAP identifier	16,7
Presentation	< k,r \| k⁸, r², (kr)² >
Orders of elements	1 of 1, 1+2*4 of 2, 2 of 4, 2+2 of 8
Centre	C2
Derived subgroup	C4
Automorphism group	a group of order 32
Inner automorphism group	D8
"Out" (quotient of above)	C2×C2
Schur multiplier	C2

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.