S5

Also called PGL(2,5).

Statistics
Order of group	120
GAP identifier	120,34
Presentation
Orders of elements	1 of 1, 10+15 of 2, 20 of 3, 30 of 4, 24 of 5, 20 of 6
Centre	1
Derived subgroup	A5
Automorphism group	S5
Inner automorphism group	S5
"Out" (quotient of above)	1
Schur multiplier	C2
Sylow-2-subgroup	D8

Permutation Diagrams

Sharply 5-transitive
on 5 points, odd.

Sharply 5-transitive
on 5 points, odd.

Sharply 5-transitive
on 5 points, odd.

Sharply 5-transitive
on 5 points, odd.

Sharply 5-transitive
on 5 points, odd.

Sharply 3-transitive
on 6 points, odd.

3-transitive on 6
points, odd.

Sharply 3-transitive
on 6 points, odd.

Sharply 3-transitive
on 6 points, odd.

Sharply 3-transitive
on 6 points, odd.

Sharply 3-transitive
on 6 points, odd.

Regular maps with S5 symmetry

S5 is the rotational symmetry group of the regular maps N5:{4,5}, S4:{4,5}, S6:{4,6}, N7:{4,6}.

Index to regular maps