C6×C2

Also called  C3×C2×C2.

C6×C2 is Abelian, and is a direct product of two smaller groups.

Statistics

Order of group12
GAP identifier12,5
Presentation< k,r | k6, r2, [k,r] >
Orders of elements1 of 1, 3*1 of 2, 2*1 of 3, 6*1 of 6
CentreC6×C2
Derived subgroup1
Automorphism groupD12
Inner automorphism group1
"Out" (quotient of above)D12
Schur multiplierC2
Sylow-2-subgroupC2×C2
 

Permutation Diagrams


Not transitive.

Not transitive.

Not transitive.

Not transitive.

Not transitive.

Cayley Graphs


the 6-hosohedron, type IIa



Regular maps with C6×C2 symmetry

C6×C2 is the rotational symmetry group of the regular map S2:{6,6}.


Index to regular maps

Orientable sphere | torus | 2 | 3 | 4 | 5 | 6
Non-orientable projective plane | 4 | 5 | 6 | 7