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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{20}=1, b^{a}=b^{9} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P
$C_4\times D_5$ 2A $2$ $1$ $C_4\times D_5$ 1A 2A $b^{10}$
$C_4\times D_5$ 2B $2$ $5$ $C_2\times C_4$ 1A 2B $a$
$C_4\times D_5$ 2C $2$ $5$ $C_2\times C_4$ 1A 2C $ab^{2}$
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