Also called  C10×C2.

C5×C2×C2 is Abelian, and is a direct product of two smaller groups.


Order of group20
GAP identifier20,5
Presentation< k,r | k10, r2, [k,r] >
Orders of elements1 of 1, 3*1 of 2, 4*1 of 5, 12*1 of 10
Derived subgroup1
Automorphism groupD6×C4
Inner automorphism group1
"Out" (quotient of above)D6×C4
Schur multiplierC2

Permutation Diagrams

Not transitive.

Not transitive.

Not transitive.

Not transitive.

Cayley Graphs

the 10-hosohedron, type IIa

Regular maps with C5×C2×C2 symmetry

C5×C2×C2 is the rotational symmetry group of the regular map S4:{10,10}.

Index to regular maps