Find both the center Z(D₄) and the commutator subgroup C of the group D₄ of symmetries of the square in Table 8.12.

Data from Table 8.12

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Po PI P2 P3 f| f2 8₁ 82 Po Po P₁ P2 fy 12. 8₁ P3 Po PI 8₂ P2 P₁ P2 P3 82 P2 P3 Po 8₁ fi P3 fl2 8₁ fly 8₂ M2 8₁ P3 Po Pi fl2 fl P2 इ μ1 3 3 fly 12 PI M₂ 3 12 P3 82 8₂ 8₁ P3 8₁ PI 8₁ 12 8₂ flj 8₂ 8₁ Po P2 P3 PI 8₂ P2 Po PI P3 8₂ fl 8₁ ळ fl2 Po P2 P₂ Po