[1] Complete each ofthe following multiplication tables,so that the resulting table isthe multiplication rule for a group G. In each case, what group do you get? ∗ 1 2 3 4 1 1 2 3 4 2 2 1 3 3 1 4 4 ∗ 1 2 3 4 1 1 2 3 4 2 2 1 3 3 4 4 1 ∗ 1 2 3 4 5 6 1 1 2 3 4 5 6 2 2 3 1 5 4 3 3 1 2 6 5 4 4 6 5 2 5 5 3 6 6 5 4 3 2 [2] For each of the groups found in problem 1, let the group act on itself by right multiplication. Use these actionsto find permutation representationsfor each group.

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