Unlocking Symmetry: A Group Theory Quiz
Published Jul 9, 2026 · Updated Jul 31, 2026 · Editorial Team
Test your understanding of group theory concepts, from symmetry groups to fundamental theorems, with these engaging mathematical puzzles.
❓ 10 Questions
⏱️ 5 Minutes
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Question 1 of 100 correct
⏱️ 05:00
QUESTION 1
What is the order of the symmetry group of a regular pentagon (the dihedral group D₅)?
All Questions in This Quiz
Here is every question waiting for you in this 10-question mathematics puzzles and theorems quiz. Play it in the interactive player above to lock in your answers, see your score and read the explanations.
What is the order of the symmetry group of a regular pentagon (the dihedral group D₅)?
- A. 5
- B. 8
- C. 10
- D. 12
Which of the following groups is isomorphic to the Klein four-group V₄?
- A. ℤ₄
- B. ℤ₂ × ℤ₂
- C. S₃
- D. D₄
What is the smallest non-abelian group?
- A. S₃
- B. D₄
- C. Q₈
- D. A₄
By Lagrange's Theorem, which of the following cannot be the order of a subgroup of a group of order 30?
- A. 5
- B. 6
- C. 8
- D. 15
Which group represents the rotational symmetries of a cube?
- A. S₄
- B. A₄
- C. S₅
- D. D₄
What is the center of the dihedral group D₄ (symmetries of a square)?
- A. {e}
- B. {e, r²}
- C. {e, r, r², r³}
- D. D₄
How many elements of order 2 are in the symmetric group S₄?
- A. 6
- B. 9
- C. 12
- D. 15
Which statement about the alternating group A₄ is true?
- A. A₄ is abelian
- B. A₄ has a subgroup of order 6
- C. A₄ has no subgroup of order 6
- D. A₄ is isomorphic to D₆
What is the number of conjugacy classes in the symmetric group S₄?
- A. 4
- B. 5
- C. 6
- D. 7
If G is a finite group and H is a subgroup of index 2, which statement is always true?
- A. H is abelian
- B. H is normal in G
- C. G is abelian
- D. H is the center of G
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