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 group	168
GAP identifier	168,42
Presentation
Orders of elements	1 of 1, 21 of 2, 228 of 3, 221 of 4, 2*28 of 7
Centre	1
Derived subgroup	PSL(2,7)
Automorphism group	PGL(2,7)
Inner automorphism group	PSL(2,7)
"Out" (quotient of above)	C2
Schur multiplier	C2
Sylow-2-subgroup	D8

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

o3/psl2-7

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