C12

Also called C4×C3.

C12 is Abelian, and is a direct product of two smaller groups.

Statistics
Order of group	12
GAP identifier	12,2
Presentation	< k \| k¹² >
Orders of elements	1 of 1, 21 of 3, 21 of 4, 21 of 6, 41 of 12
Centre	C12
Derived subgroup	1
Automorphism group	C2×C2
Inner automorphism group	1
"Out" (quotient of above)	C2×C2
Schur multiplier	1
Sylow-2-subgroup	C4

Permutation Diagrams

Not transitive.

Not transitive.

Sharply 1-transitive
on 12 points, odd.

Cayley Graphs

the di-dodecagon, type I

Regular maps with C12 symmetry

C12 is the rotational symmetry group of the regular map S3{12,12}.