D8

Also called  C4 ⋊ C2.

Statistics

Order of group8
GAP identifier8,3
Presentation< k,r | r4, r2, (kr)2 >
Orders of elements1 of 1, 1+2*2 of 2, 2 of 4
CentreC2
Derived subgroupC2
Automorphism groupD8
Inner automorphism groupC2×C2
"Out" (quotient of above)C2
Schur multiplierC2
 

Permutation Diagrams


1-transitive on 4
points, odd.

1-transitive on 4
points, odd.

1-transitive on 4
points, odd.

1-transitive on 4
points, odd.

1-transitive on 8
points, even.

Cayley Graphs


the cube, type I

the di-square, type II

the cube, type I




Regular maps with D8 symmetry

D8 is the rotational symmetry group of the regular maps the 4-hosohedron,   the di-square,   the hemi-4-hosohedron,   the hemi-di-square,   the 4-lucanicohedron,   the hemi-4-lucanicohedron.