 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-3/1d/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Such a group does exist. Take

H = S_{3}

. Its center is trivial, so

H / Z (H) ≅ S_{3}

has order six. Therefore

H = S_{3} is an example .

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