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## Compute a permutation representation of Dihedral group of order 8

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.6 Solution: We compute the permutation representation of $G$ in $D_{G/N}$.$$1 \mapsto 1$$ r(N) = rN, r(rN)…

## Exhibit the Klein 4-group as a subgroup of Sym(4) using the left regular representation

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.1 Solution: The multiplication table for $G$ is as follows.    1 a b c 1 1…