D6

Also called C3 ⋊ C2, S3.

Statistics
Order of group	6
GAP identifier	6,1
Presentation	< k,r \| k³, r², (rk)² >
Orders of elements	1 of 1, 3 of 2, 2 of 3
Centre	1
Derived subgroup	C3
Automorphism group	D6
Inner automorphism group	D6
"Out" (quotient of above)	1
Schur multiplier	1

Permutation Diagrams

Sharply 3-transitive
on 3 points, odd.

Sharply 3-transitive
on 3 points, odd.

Sharply 1-transitive
on 6 points, even.

Sharply 1-transitive
on 6 points, even.

Sharply 1-transitive
on 6 points, odd.

Sharply 1-transitive
on 6 points, odd.

Cayley Graphs

the di-hexagon, type I

the 3-hosohedron, type II

the octahedron, type I

Regular maps with D6 symmetry

D6 is the rotational symmetry group of the regular maps the 3-hosohedron, the di-triangle, the 3-lucanicohedron.

Index to regular maps