projective special unitary group PSU(2)

Target entity: projective special unitary group PSU(2)
Context triple: [SO(3), isIsomorphicTo, projective special unitary group PSU(2)]

• 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. special unitary group SU(n)
  The special unitary group SU(n) is a fundamental compact Lie group consisting of n×n unitary matrices with determinant 1, central in mathematics and physics, especially in quantum theory and gauge symmetries.
• C. SL(2,7)
  SL(2,7) is the special linear group of 2×2 matrices with determinant 1 over the finite field with 7 elements, a non-abelian finite group of order 336 that plays an important role in group theory and geometry.
• D. PSL(2,\mathbb{C})
  PSL(2,ℂ) is the group of Möbius transformations acting as all biholomorphic automorphisms of the Riemann sphere.
• E. PGL(2,7)
  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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: projective special unitary group PSU(2)
Target entity description: The projective special unitary group PSU(2) is a simple Lie group that can be realized as the group of orientation-preserving rotations of three-dimensional Euclidean space.

• 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. special unitary group SU(n)
  The special unitary group SU(n) is a fundamental compact Lie group consisting of n×n unitary matrices with determinant 1, central in mathematics and physics, especially in quantum theory and gauge symmetries.
• C. SL(2,7)
  SL(2,7) is the special linear group of 2×2 matrices with determinant 1 over the finite field with 7 elements, a non-abelian finite group of order 336 that plays an important role in group theory and geometry.
• D. PSL(2,\mathbb{C})
  PSL(2,ℂ) is the group of Möbius transformations acting as all biholomorphic automorphisms of the Riemann sphere.
• E. PGL(2,7)
  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.
• F. None of above. chosen