This is an exercise problem from book on group theory by Dixon.
Exercise: Find all the blocks containing 1 for the group
$$G=\langle(123456),(26)(35)\rangle \le S_6$$
where $\le $ is used for subgroup notation. One of the possible way is to compute all possible blocks (brute force way) and then check the membership of element 1 in all such blocks. Is there a better way to solve the exercise?
I am not getting from where to start please help or just provide a higher level idea how to proceed.