Also called  C3×C2.

C6 is Abelian, and is a direct product of two smaller groups.


Order of group6
GAP identifier6,2
Presentation< k | k6 >
Orders of elements1 of 1, 1 of 2, 2*1 of 3, 2*1 of 6
Derived subgroup1
Automorphism groupC2
Inner automorphism group1
"Out" (quotient of above)C2
Schur multiplier1

Permutation Diagrams

Not transitive.

Not transitive.

1-transitive on 5
points, odd.

Sharply 1-transitive
on 6 points, odd.

Cayley Graphs

the di-hexagon, type I

the 3-hosohedron, type IIa

Regular maps with C6 symmetry

C6 is the rotational symmetry group of the regular maps {3,6}(1,1),   {6,3}(1,1),   rectification of {6,3}(1,1).

Index to regular maps