D18

Also called C9 ⋊ C2.

Statistics
Order of group	18
GAP identifier	18,1
Presentation	< k,r \| k⁹, r², (kr)² >
Orders of elements	1 of 1, 9 of 2, 2 of 3, 3*2 of 9
Centre	1
Derived subgroup	C9
Automorphism group	a group of order 54
Inner automorphism group	D18
"Out" (quotient of above)	C9
Schur multiplier	1
Sylow-3-subgroup	C9

Permutation Diagrams

1-transitive on 9
points, even.

1-transitive on 9
points, even.

Sharply 1-transitive
on 18 points, odd.

Cayley Graphs

the 9-hosohedron, type II

Regular maps with D18 symmetry

D18 is the rotational symmetry group of the regular maps the 9-hosohedron, the di-nonagon, the 9-lucanicohedron.

Index to regular maps