Also called  C5×C2.

C10 is Abelian, and is a direct product of two smaller groups.


Order of group10
GAP identifier10,2
Presentation< k | k10 >
Orders of elements1 of 1, 1 of 2, 4*1 of 5, 4*1 of 10
Derived subgroup1
Automorphism groupC4
Inner automorphism group1
"Out" (quotient of above)C4
Schur multiplier1

Permutation Diagrams

Sharply 1-transitive
on 10 points, odd.

Cayley Graphs

the di-decagon, type I

the 5-hosohedron, type IIa

Regular maps with C10 symmetry

C10 is the rotational symmetry group of the regular maps S2:{10,5},   S2:{5,10},   rectification of S2:{10,5}.

Index to regular maps