Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: symmetric group S5 | Statement: [Clebsch diagonal surface, hasAutomorphismGroup, symmetric group S5]

Target entity: symmetric group S5
Context triple: [Clebsch diagonal surface, hasAutomorphismGroup, symmetric group S5]

• A. Burnside's lemma
  Burnside's lemma is a result in group theory and combinatorics that counts distinct configurations under symmetries by averaging the number of fixed points of group actions.
• B. 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.
• C. Harada–Norton group
  The Harada–Norton group is one of the 26 sporadic simple groups in finite group theory, notable for its large order and close relationship to the Monster group.
• D. Galois group
  A Galois group is the group of field automorphisms of a field extension that captures the symmetries of its algebraic equations and underpins much of modern algebra and number theory.
• E. Carian-Sidetic-Pisidian group
  The Carian-Sidetic-Pisidian group is a subgroup of the Luwic branch of the Anatolian Indo-European languages, encompassing the closely related ancient languages Carian, Sidetic, and Pisidian once spoken in southwestern Anatolia.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: symmetric group S5
Triple: [Clebsch diagonal surface, hasAutomorphismGroup, symmetric group S5]

The symmetric group S5 is the group of all permutations of five elements, a fundamental finite group of order 120 that plays a key role in group theory and Galois theory.

Target entity: symmetric group S5
Target entity description: The symmetric group S5 is the group of all permutations of five elements, a fundamental finite group of order 120 that plays a key role in group theory and Galois theory.

• A. Burnside's lemma
  Burnside's lemma is a result in group theory and combinatorics that counts distinct configurations under symmetries by averaging the number of fixed points of group actions.
• B. 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.
• C. Harada–Norton group
  The Harada–Norton group is one of the 26 sporadic simple groups in finite group theory, notable for its large order and close relationship to the Monster group.
• D. Galois group
  A Galois group is the group of field automorphisms of a field extension that captures the symmetries of its algebraic equations and underpins much of modern algebra and number theory.
• E. Carian-Sidetic-Pisidian group
  The Carian-Sidetic-Pisidian group is a subgroup of the Luwic branch of the Anatolian Indo-European languages, encompassing the closely related ancient languages Carian, Sidetic, and Pisidian once spoken in southwestern Anatolia.
• F. None of above. chosen