C18

Also called  C9×C2.

C18 is Abelian, and is a direct product of two smaller groups.

Statistics

Order of group18
GAP identifier18,2
Presentation< k | k18 >
Orders of elements1 of 1, 1 of 2, 2*1 of 3, 2*1 of 6, 6*1 of 9, 6*1 of 18
CentreC18
Derived subgroup1
Automorphism groupC6
Inner automorphism group1
"Out" (quotient of above)C6
Schur multiplier1
Sylow-3-subgroupC9
 

Permutation Diagrams


Not transitive.

Not transitive.

Sharply 1-transitive
on 18 points, odd.

Cayley Graphs



the 9-hosohedron, type IIa




Regular maps with C18 symmetry

C18 is the rotational symmetry group of the regular maps S4:{9,18},   S4:{18,9}.