C5×C2×C2

Also called  C10×C2.

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

Statistics

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
CentreC5×C2×C2
Derived subgroup1
Automorphism groupD6×C4
Inner automorphism group1
"Out" (quotient of above)D6×C4
Schur multiplierC2
Sylow-2-subgroupC2×C2
 

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

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