1. The problem statement, all variables and given/known data I need to determine [tex]dad^1[/tex] for each element d in the left-coset formed by acting on the elements in [tex]C_G(a)[/tex] with the element c such that c is not an element of the subgroup [tex]C_G(a)[/tex] 2. Relevant equations 3. The attempt at a solution I don't really understand what the question is asking me to do? I'm fairly new to group theory and understand that d are the elements in the left-coset of the subgroup and that a is the fixed element of the group G but I'm not really familiar with [tex]d^1[/tex], why is there a 1 in the exponent of the element? Can anyone start me off here? Or at least give me an outline of the goal?