Thread: Find the no. of distinct left cosets of H = { e, (16), (23), (16)(23)} in H6.

Hi anyone knows how to solve this?

find the number of distinct left cosets of H ={e, (16), (23), (16)(23)} in H₆?

My workings as below,
Since H₆, 6!= 1x2x3x4x5x6=720
Since H has 4 elements, i take 720/4=180 (Answer)

Please correct me if i am wrong.

Thanks.

By H6, I assume you mean the symmetric group on 6 elements. I've seen that denoted or , but never .
With that assumption, your reasoning and answer are correct.