Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:projective_special_linear_group |
| gptkbp:actsOn |
gptkb:projective_plane_of_order_2
|
| gptkbp:automorphismGroup |
gptkb:Fano_plane
trivial |
| gptkbp:centralTo |
trivial
|
| gptkbp:foundIn |
classification of finite simple groups
|
| gptkbp:hasSubgroup |
gptkb:S_4
gptkb:A_4 gptkb:D_14 gptkb:Z_2 gptkb:Z_3 gptkb:Z_7 |
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
gptkb:PSL(2,7)
gptkb:GL(3,2) gptkb:PGL(3,2) gptkb:PSigmaL(2,7) gptkb:group_of_automorphisms_of_the_Fano_plane gptkb:projective_linear_group_of_order_168 group of orientation-preserving symmetries of the Klein quartic |
| gptkbp:isPerfect |
true
|
| gptkbp:isSimple |
true
|
| gptkbp:isTransitiveOn |
7 lines of the Fano plane
7 points of the Fano plane |
| gptkbp:minimalDegreePermutationRepresentation |
7
|
| gptkbp:order |
168
|
| gptkbp:presentedBy |
⟨a,b|a^7=b^3=(ab)^2=1⟩
|
| gptkbp:SchurMultiplier |
trivial
|
| gptkbp:bfsParent |
gptkb:PSL(2,7)
|
| gptkbp:bfsLayer |
6
|
| https://www.w3.org/2000/01/rdf-schema#label |
PSL(3,2)
|