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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{2}=c^{8}=[b,c]=1, b^{a}=bc^{4}, c^{a}=bc^{5} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$\OD_{16}:C_4$ 1A $1$ $1$ $\OD_{16}:C_4$ 1A $1$
$\OD_{16}:C_4$ 2A $2$ $1$ $\OD_{16}:C_4$ 1A $c^{4}$
$\OD_{16}:C_4$ 2B $2$ $2$ $C_2\times \OD_{16}$ 1A $b$
$\OD_{16}:C_4$ 2C $2$ $2$ $C_2\times \OD_{16}$ 1A $a^{2}b$
$\OD_{16}:C_4$ 2D $2$ $2$ $C_4^2:C_2$ 1A $a^{2}$
$\OD_{16}:C_4$ 4A1 $4$ $1$ $\OD_{16}:C_4$ 2A $c^{2}$
$\OD_{16}:C_4$ 4A-1 $4$ $1$ $\OD_{16}:C_4$ 2A $c^{6}$
$\OD_{16}:C_4$ 4B $4$ $2$ $C_2\times \OD_{16}$ 2A $bc^{2}$
$\OD_{16}:C_4$ 4C $4$ $2$ $C_4^2:C_2$ 2A $a^{2}c^{2}$
$\OD_{16}:C_4$ 4D $4$ $2$ $C_2\times \OD_{16}$ 2A $a^{2}bc^{6}$
$\OD_{16}:C_4$ 4E1 $4$ $4$ $C_4^2$ 2D $a$
$\OD_{16}:C_4$ 4E-1 $4$ $4$ $C_4^2$ 2D $a^{3}$
$\OD_{16}:C_4$ 4F1 $4$ $4$ $C_4^2$ 2D $ac^{2}$
$\OD_{16}:C_4$ 4F-1 $4$ $4$ $C_4^2$ 2D $a^{3}c^{2}$
$\OD_{16}:C_4$ 8A1 $8$ $4$ $C_2\times C_8$ 4A1 $c$
$\OD_{16}:C_4$ 8A-1 $8$ $4$ $C_2\times C_8$ 4A-1 $c^{3}$
$\OD_{16}:C_4$ 8B1 $8$ $4$ $C_2\times C_8$ 4A-1 $a^{2}c$
$\OD_{16}:C_4$ 8B-1 $8$ $4$ $C_2\times C_8$ 4A1 $a^{2}c^{3}$
$\OD_{16}:C_4$ 8C1 $8$ $4$ $C_2\times C_8$ 4D $ac$
$\OD_{16}:C_4$ 8C-1 $8$ $4$ $C_2\times C_8$ 4D $a^{3}c^{3}$
$\OD_{16}:C_4$ 8D1 $8$ $4$ $C_2\times C_8$ 4D $ac^{3}$
$\OD_{16}:C_4$ 8D-1 $8$ $4$ $C_2\times C_8$ 4D $a^{3}c$
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