D6×C2×C2

D6×C2×C2 is the direct product of two smaller groups.

Statistics

Order of group24
GAP identifier24,14
Presentation< k,r,g | k6, r2, g2, (kr)2, [k,g], [r,g] >
Orders of elements1 of 1, 3*1+4*3 of 2, 2 of 3, 3*2 of 6
CentreC2×C2
Derived subgroupC3
Automorphism groupD6 ⋊ S4
Inner automorphism groupD6
"Out" (quotient of above)S4
Schur multiplierC2×C2×C2
Sylow-2-subgroupC2×C2×C2
 

Permutation Diagrams


Not transitive.

Not transitive.

1-transitive on 12
points, even.

Cayley Graphs


the 6-hosohedron, type III



Regular maps with D6×C2×C2 symmetry

D6×C2×C2 is the full symmetry group of the regular maps S2:{6,6},   the 6-hosohedron,   the di-hexagon,   the 6-lucanicohedron.


Index to regular maps

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