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.