D6×C3

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

Statistics
Order of group	18
GAP identifier	18,3
Presentation	< k,r,g \| k³, r², g³, (kr)², [k,g], [r,g] >
Orders of elements	1 of 1, 3 of 2, 2+21+22 of 3, 2*3 of 6
Centre	C3
Derived subgroup	C3
Automorphism group	D12
Inner automorphism group	C6
"Out" (quotient of above)	C2
Schur multiplier	C3
Sylow-3-subgroup	C3×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).

Index to regular maps