D24

Also called  (C3,C4) ⋊ C2.

Statistics

Order of group24
GAP identifier24,6
Presentation< k,r | k12, r2, (kr)2>
Orders of elements1 of 1, 1+12 of 2, 2 of 3, 2 of 4, 2 of 6, 4 of 12
CentreC2
Derived subgroupC6
Automorphism groupD8×D6
Inner automorphism groupD12
"Out" (quotient of above)C4
Schur multiplierC2
 

Permutation Diagrams


Not transitive.

Not transitive.

Not transitive.

1-transitive on 12
points, odd.

1-transitive on 12
points, odd.

1-transitive on 12
points, odd.

1-transitive on 24
points, even.

Cayley Graphs



the 12-hosohedron, type II


the 6-hosohedron, type IIIa



Regular maps with D24 symmetry

D24 is the rotational symmetry group of the regular maps the hemi-di-dodecagon,   the hemi-12-hosohedron,   the di-dodecagon,   the 12-hosohedron,   the 12-lucanicohedron,   the hemi-12-lucanicohedron.

D24 is the full symmetry group of the regular map S3{12,12}.


Index to regular maps

Orientable sphere | torus | 2 | 3 | 4 | 5 | 6
Non-orientable projective plane | 4 | 5 | 6 | 7