C12×C2

Also called  C4×C3×C2,   C6×C4.

C12×C2 is Abelian, and is a direct product of two smaller groups.

Statistics

Order of group24
GAP identifier24,9
Presentation< k,r | k12, r2, [k,r] >
Orders of elements1 of 1, 1+2*1 of 2, 2*1 of 3, 4*1 of 4, 2*1+4*1 of 6, 8*1 of 12
CentreC12×C2
Derived subgroup1
Automorphism groupD8×C2
Inner automorphism group1
"Out" (quotient of above)D8×C2
Schur multiplierC2
Sylow-2-subgroupC4×C2
 

Permutation Diagrams


Not transitive.

Not transitive.

Not transitive.

Not transitive.

Not transitive.

Cayley Graphs


the 12-hosohedron, type IIa




Regular maps with C12×C2 symmetry

C12×C2 is the rotational symmetry group of the regular map S5:{12,12}.