D28

Also called  C8 ⋊ C2C4,   Dihedral(28),   D14.

Statistics

Order of group28
GAP identifier28,3
Presentation< k,r | k14, r2, (kr)2 >
Orders of elements1 of 1, 1+2*7 of 2, 3*2 of 7, 3*2 of 14
CentreC2
Derived subgroupC7
Automorphism groupFrob42×C2
Inner automorphism groupD14
"Out" (quotient of above)D6
Schur multiplierC2
Sylow-2-subgroupC2×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