Also called  C9 ⋊ C2.


Order of group18
GAP identifier18,1
Presentation< k,r | k9, r2, (kr)2 >
Orders of elements1 of 1, 9 of 2, 2 of 3, 3*2 of 9
Derived subgroupC9
Automorphism groupa group of order 54
Inner automorphism groupD18
"Out" (quotient of above)C9
Schur multiplier1

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