Projective Special Linear Group of 3x3 matrices over field with 2 elements
URI: https://gptkb.org/entity/Projective_Special_Linear_Group_of_3x3_matrices_over_field_with_2_elements
GPTKB entity
Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:abbreviation |
gptkb:PSL(3,2)
|
| gptkbp:actsOn |
gptkb:projective_plane_of_order_2
|
| gptkbp:automorphismGroup |
gptkb:Fano_plane
cyclic group of order 2 |
| gptkbp:centralTo |
trivial group
|
| gptkbp:field |
finite field with 2 elements
|
| gptkbp:generation |
2
|
| gptkbp:hasSubgroup |
gptkb:symmetric_group_S4
gptkb:dihedral_group_of_order_8 cyclic group of order 7 alternating group A7 |
| https://www.w3.org/2000/01/rdf-schema#label |
Projective Special Linear Group of 3x3 matrices over field with 2 elements
|
| gptkbp:isomorphicTo |
gptkb:PSL(2,7)
gptkb:GL(3,2) gptkb:projective_linear_group_of_order_168 automorphism group of the Fano plane |
| gptkbp:isSimple |
true
|
| gptkbp:minimalDegreeOfFaithfulPermutationRepresentation |
7
|
| gptkbp:notation |
gptkb:PSL(3,2)
|
| gptkbp:order |
168
|
| gptkbp:presentedBy |
⟨a,b | a^2 = b^3 = (ab)^7 = [a,b]^4 = 1⟩
|
| gptkbp:SchurMultiplier |
cyclic group of order 3
|
| gptkbp:bfsParent |
gptkb:PSL_3(2)
|
| gptkbp:bfsLayer |
8
|