PSL(2,7)

Also called  PSL(3,2),   A1(7),   A2(2),   GL(3,2),   SL(3,2),   PGL(3,2).

PSL(2,7) is simple.

Statistics

Order of group168
GAP identifier168,42
Presentation
Orders of elements1 of 1, 21 of 2, 2*28 of 3, 2*21 of 4, 2*28 of 7
Centre1
Derived subgroupPSL(2,7)
Automorphism groupPGL(2,7)
Inner automorphism groupPSL(2,7)
"Out" (quotient of above)C2
Schur multiplierC2
Sylow-2-subgroupD8
 

Permutation Diagrams


2-transitive on 7
points, even.

Transitive on 7 points, even.

Transitive on 8 points, even.

Transitive on 8 points, even.

Cayley Graphs


the Klein map, type II

Regular maps with PSL(2,7) symmetry

PSL(2,7) is the rotational symmetry group of the regular maps the Klein map,   the dual Klein map.


Index to regular maps