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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{2}=b^{2}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$C_2^2$ 1A $1$ $1$ $C_2^2$ 1A $1$
$C_2^2$ 2A $2$ $1$ $C_2^2$ 1A $b$
$C_2^2$ 2B $2$ $1$ $C_2^2$ 1A $a$
$C_2^2$ 2C $2$ $1$ $C_2^2$ 1A $ab$
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