PGL(2,7)

Target entity: PGL(2,7)
Context triple: [PSL(2,7), automorphismGroup, PGL(2,7)]

• A. PSL(2,7)
  PSL(2,7) is a finite simple group of order 168, notable as the full automorphism group of the Klein quartic and as a key example in the theory of projective linear groups over finite fields.
• B. PSL(2,ℤ/Nℤ)
  PSL(2,ℤ/Nℤ) is the projective special linear group of 2×2 matrices with entries in the ring of integers modulo N, modulo scalar matrices, forming a fundamental example of a finite (or, for composite N, generally non-simple) group in algebra and number theory.
• C. SL(2,ℤ)
  SL(2,ℤ) is the group of 2×2 integer matrices with determinant 1, fundamental in number theory, geometry, and the theory of modular forms.
• D. PSL(2,\mathbb{C})
  PSL(2,ℂ) is the group of Möbius transformations acting as all biholomorphic automorphisms of the Riemann sphere.
• E. modular group PSL(2,Z)
  The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: PGL(2,7)
Target entity description: PGL(2,7) is the projective general linear group of 2×2 invertible matrices over the finite field with 7 elements, a finite group of order 336 that acts as the full collineation group of the projective line over that field.

• A. PSL(2,7)
  PSL(2,7) is a finite simple group of order 168, notable as the full automorphism group of the Klein quartic and as a key example in the theory of projective linear groups over finite fields.
• B. PSL(2,ℤ/Nℤ)
  PSL(2,ℤ/Nℤ) is the projective special linear group of 2×2 matrices with entries in the ring of integers modulo N, modulo scalar matrices, forming a fundamental example of a finite (or, for composite N, generally non-simple) group in algebra and number theory.
• C. SL(2,ℤ)
  SL(2,ℤ) is the group of 2×2 integer matrices with determinant 1, fundamental in number theory, geometry, and the theory of modular forms.
• D. PSL(2,\mathbb{C})
  PSL(2,ℂ) is the group of Möbius transformations acting as all biholomorphic automorphisms of the Riemann sphere.
• E. modular group PSL(2,Z)
  The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
• F. None of above. chosen