I know this factor group is isomorphic to $C_2$, but I have tried calculating it and I only get one coset.
2026-03-25 17:44:04.1774460644
What is the factor group $C_{12}/C_{6}$?
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$C_6$, as a subgroup of $C_{12}$, contains $6$ of the $12$ elements. The remaining $6$ must make up the second coset.
Specifically, if $$ C_{12} = \{0,1,2,3,4,5,6,7,8,9,10,11\} $$ with addition modulo $12$ as the group operation, then the two cosets of $C_6$ are $$ C_6 = \{0,2,4,6,8,10\}\\ 1 + C_6 = \{1,3,5,7,9,11\} $$