D28

Also called C8 ⋊ _C2C4, Dihedral(28), D14.

Statistics
Order of group	28
GAP identifier	28,3
Presentation	< k,r \| k¹⁴, r², (kr)² >
Orders of elements	1 of 1, 1+27 of 2, 32 of 7, 3*2 of 14
Centre	C2
Derived subgroup	C7
Automorphism group	Frob42×C2
Inner automorphism group	D14
"Out" (quotient of above)	D6
Schur multiplier	C2
Sylow-2-subgroup	C2×C2

Permutation Diagrams

Not transitive.

Not transitive.

1-transitive on 14
points, odd.

1-transitive on 14
points, odd.

1-transitive on 14
points, odd.

Not transitive.

1-transitive on 28
points, even.

Cayley Graphs

the 14-hosohedron, type II

the 7-hosohedron, type III

the 7-hosohedron, type IIIa

Regular maps with D28 symmetry

D28 is the rotational symmetry group of the regular maps the 14-hosohedron, the hemi-di-14gon, the hemi-14-hosohedron, the 14-lucanicohedron, the hemi-14-lucanicohedron.

D28 is the full symmetry group of the regular maps S3:{14,7}, S3{7,14}, the 7-hosohedron, the di-heptagon, the 7-lucanicohedron, rectification of S3:{14,7}.

Index to regular maps