The $($one$-$dimensional$)$ matrices D$($Cs$)=1$ and D$($C$,)=1,$ and D$($C$,)=1$

and D$($C$,)=-1$ both represent the group multiplication C$,$C$,=$C in the group Cy with D$($C$6)=+1$ and $-1,$ respectively. Use the character tale to confirm these remarks. What are the representatives of o$,$ and o$,$ in each case?