List of practice Questions

Which of the following statements is/are TRUE for a group \( G \)?

Let \( G \) be a group of order \(6\), and \( H \) be a subgroup of \( G \) such that \( 1 < |H| < 6 \). Which one of the following options is correct?

Let \( G \) be a group of order \( 5^4 \) with center having \( 5^2 \) elements. Then the number of conjugacy classes in \( G \) is \(\underline{\hspace{1cm}}\) .