D6×C3

D6×C3 is the direct product of two smaller groups.

Statistics

Order of group18
GAP identifier18,3
Presentation< k,r,g | k3, r2, g3, (kr)2, [k,g], [r,g] >
Orders of elements1 of 1, 3 of 2, 2+2*1+2*2 of 3, 2*3 of 6
CentreC3
Derived subgroupC3
Automorphism groupD12
Inner automorphism groupC6
"Out" (quotient of above)C2
Schur multiplierC3
Sylow-3-subgroupC3×C3
 

Permutation Diagrams


Not transitive.

1-transitive on 6
points, odd.

1-transitive on 6
points, odd.

1-transitive on 6
points, odd.

1-transitive on 9
points, odd.

Cayley Graphs





Regular maps with D6×C3 symmetry

D6×C3 is the rotational symmetry group of the regular maps {3,6}(0,2),   {6,3}(0,2),   rectification of {6,3}(0,2).