Also called  C4×C3.

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


Order of group12
GAP identifier12,2
Presentation< k | k12 >
Orders of elements1 of 1, 2*1 of 3, 2*1 of 4, 2*1 of 6, 4*1 of 12
Derived subgroup1
Automorphism groupC2×C2
Inner automorphism group1
"Out" (quotient of above)C2×C2
Schur multiplier1

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}.

Index to regular maps