C7×C2×C2

C7×C2×C2 is Abelian, and is a direct product of two smaller groups.

Statistics

Order of group28
GAP identifier28,4
Presentation< k,r | k14, r2, [k,r] >
Orders of elements1 of 1, 3*1 of 2, 6*1 of 7, 18*1 of 14
CentreC7×C2×C2
Derived subgroup1
Automorphism groupD6×C6
Inner automorphism group1
"Out" (quotient of above)D6×C6
Schur multiplierC2
Sylow-2-subgroupC2×C2
 

Permutation Diagrams


Not transitive.

Not transitive.

Cayley Graphs


the 14-hosohedron, type IIa



Regular maps with C7×C2×C2 symmetry

C7×C2×C2 is the rotational symmetry group of the regular map S6:{14,14}.


Index to regular maps

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