S5

Also called  PGL(2,5).

Statistics

Order of group120
GAP identifier120,34
Presentation
Orders of elements1 of 1, 10+15 of 2, 20 of 3, 30 of 4, 24 of 5, 20 of 6
Centre1
Derived subgroupA5
Automorphism groupS5
Inner automorphism groupS5
"Out" (quotient of above)1
Schur multiplierC2
Sylow-2-subgroupD8
 

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 C5:{4,5},   S4:{4,5},   S6:{4,6},   C7:{4,6}.


Index to regular maps