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Consider the group of permutation matrices $G =\{I_3, P_1, P_2, P_3, P_4, P_5\}$ For $n=3$ the permutation matrices are $I_3$ and the five matrices are:

\begin{equation*} P_1 = [1,0,0;0,0,1;0,1,0] \\ P_2 = [0,1,0;1,0,0;0,0,1] \\ P_3 = [0,1,0;0,0,1;1,0,0] \\ P_4 = [0,0,1;0,1,0;1,0,0] \\ P_5 = [0,0,1;1,0,0;0,1,0] \end{equation*}

Write out the elements of a group of permutations that is isomorphic to $G$, and exhibit an isomorphism from $G$ to this group!

I think it has to do with Cayley's Theorem. With $f_a:G\to G$ defined by $f_a(x) = ax$ for each $a$ that exists in $G$...

I thought about making a table, but realize I don't know how to since I am dealing with matrices.

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HINT: Look at the result of multiplying each of those matrices by the vector $(1,2,3)^T$.

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    Oh ok so P1=[132] P2=[213] P3=[231] P4=[321] P5=[312]2010-10-22
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    SO now... Isomorphism would be the mapping of G->G' ?2010-10-22
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    Well, you have to check that it's an homomorphism.2010-10-22
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    Multiplying each of those by the vector did not come out to the isomorphisms...2010-10-27
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    check out how i solved this problem... this one i then solved similar2010-10-27
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    http://math.stackexchange.com/questions/7475/find-elements-of-group-permutation-that-is-isomorphic-to-u142010-10-27