D10

Also called H₂.

Statistics
Order of group	10
GAP identifier	10,1
Presentation	< k,r \| k⁵, r², (kr)² >
Orders of elements	1 of 1, 5 of 2, 2*2 of 5
Centre	1
Derived subgroup	C5
Automorphism group	Frob(20)
Inner automorphism group	D10
"Out" (quotient of above)	C2
Schur multiplier	1

Permutation Diagrams

1-transitive on 5
points, even.

1-transitive on 5
points, even.

1-transitive on 5
points, even.

1-transitive on 10
points, odd.

Cayley Graphs

the 5-hosohedron, type II

the di-decagon, type I

Regular maps with D10 symmetry

D10 is the rotational symmetry group of the regular maps the 5-hosohedron, the di-pentagon, the 5-lucanicohedron.

Index to regular maps