Group of 2x2 invertible matrices over GF(7) modulo scalar matrices
GPTKB entity
Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
projective linear group |
| gptkbp:actsOn |
gptkb:projective_line_over_GF(7)
|
| gptkbp:automorphismGroup |
C2
|
| gptkbp:centralTo |
trivial group
|
| gptkbp:hasElementOrder |
2
1 12 14 21 24 3 4 6 7 8 |
| gptkbp:hasSubgroup |
gptkb:PSL(2,7)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Group of 2x2 invertible matrices over GF(7) modulo scalar matrices
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
gptkb:PGL(2,7)
automorphism group of the Fano plane orientation-preserving symmetry group of the Klein quartic orientation-preserving symmetry group of the Heptagonal tiling |
| gptkbp:isQuotientOf |
GL(2,7)
center of GL(2,7) |
| gptkbp:isSimple |
false
|
| gptkbp:isTransitiveOn |
gptkb:projective_line_over_GF(7)
|
| gptkbp:name |
gptkb:PGL(2,7)
|
| gptkbp:order |
336
|
| gptkbp:PSL(2,7)_index |
2
|
| gptkbp:PSL(2,7)_is_normal_subgroup |
true
|
| gptkbp:bfsParent |
gptkb:PGL(2,7)
|
| gptkbp:bfsLayer |
7
|