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Elements of the group are displayed as words in the presentation $\langle a, b \mid b^{4}=1, a^{2}=b^{2}, b^{a}=b^{3} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$Q_8$ 1A $1$ $1$ $Q_8$ 1A $1$
$Q_8$ 2A $2$ $1$ $Q_8$ 1A $b^{2}$
$Q_8$ 4A $4$ $2$ $C_4$ 2A $b$
$Q_8$ 4B $4$ $2$ $C_4$ 2A $a$
$Q_8$ 4C $4$ $2$ $C_4$ 2A $ab$
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