S6

Statistics

Order of group720
GAP identifier720,763
Presentation
Orders of elements1 of 1, 2*15+45 of 2, 2*40 of 3, 2*90 of 4, 144 of 5, 2*120 of 6
Centre1
Derived subgroupA6
Automorphism groupPΓL(2,9)
Inner automorphism groupS6
"Out" (quotient of above)C2
Schur multiplierC2
Sylow-2-subgroupD8×C2
 

Permutation Diagrams


Sharply 6-transitive
on 6 points, odd.

Sharply 6-transitive
on 6 points, odd.

Sharply 6-transitive
on 6 points, odd.

Sharply 6-transitive
on 6 points, odd.

Sharply 6-transitive
on 6 points, odd.

Index to regular maps

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