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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{7}=1, b^{a}=b^{6} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 7P
$D_7$ 1A $1$ $1$ $D_7$ 1A 1A $1$
$D_7$ 2A $2$ $7$ $C_2$ 1A 2A $ab^{3}$
$D_7$ 7A1 $7$ $2$ $C_7$ 7A2 7A3 $b$
$D_7$ 7A2 $7$ $2$ $C_7$ 7A3 7A1 $b^{2}$
$D_7$ 7A3 $7$ $2$ $C_7$ 7A1 7A2 $b^{3}$
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