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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{2}=b^{16}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$C_2\times C_{16}$ 1A $1$ $1$ $C_2\times C_{16}$ 1A $1$
$C_2\times C_{16}$ 2A $2$ $1$ $C_2\times C_{16}$ 1A $a$
$C_2\times C_{16}$ 2B $2$ $1$ $C_2\times C_{16}$ 1A $ab^{8}$
$C_2\times C_{16}$ 2C $2$ $1$ $C_2\times C_{16}$ 1A $b^{8}$
$C_2\times C_{16}$ 4A1 $4$ $1$ $C_2\times C_{16}$ 2C $ab^{4}$
$C_2\times C_{16}$ 4A-1 $4$ $1$ $C_2\times C_{16}$ 2C $ab^{12}$
$C_2\times C_{16}$ 4B1 $4$ $1$ $C_2\times C_{16}$ 2C $b^{4}$
$C_2\times C_{16}$ 4B-1 $4$ $1$ $C_2\times C_{16}$ 2C $b^{12}$
$C_2\times C_{16}$ 8A1 $8$ $1$ $C_2\times C_{16}$ 4B1 $ab^{2}$
$C_2\times C_{16}$ 8A-1 $8$ $1$ $C_2\times C_{16}$ 4B-1 $ab^{14}$
$C_2\times C_{16}$ 8A3 $8$ $1$ $C_2\times C_{16}$ 4B-1 $ab^{6}$
$C_2\times C_{16}$ 8A-3 $8$ $1$ $C_2\times C_{16}$ 4B1 $ab^{10}$
$C_2\times C_{16}$ 8B1 $8$ $1$ $C_2\times C_{16}$ 4B1 $b^{2}$
$C_2\times C_{16}$ 8B-1 $8$ $1$ $C_2\times C_{16}$ 4B-1 $b^{14}$
$C_2\times C_{16}$ 8B3 $8$ $1$ $C_2\times C_{16}$ 4B-1 $b^{6}$
$C_2\times C_{16}$ 8B-3 $8$ $1$ $C_2\times C_{16}$ 4B1 $b^{10}$
$C_2\times C_{16}$ 16A1 $16$ $1$ $C_2\times C_{16}$ 8B1 $b$
$C_2\times C_{16}$ 16A-1 $16$ $1$ $C_2\times C_{16}$ 8B-1 $b^{15}$
$C_2\times C_{16}$ 16A3 $16$ $1$ $C_2\times C_{16}$ 8B3 $b^{3}$
$C_2\times C_{16}$ 16A-3 $16$ $1$ $C_2\times C_{16}$ 8B-3 $b^{13}$
$C_2\times C_{16}$ 16A5 $16$ $1$ $C_2\times C_{16}$ 8B-3 $b^{5}$
$C_2\times C_{16}$ 16A-5 $16$ $1$ $C_2\times C_{16}$ 8B3 $b^{11}$
$C_2\times C_{16}$ 16A7 $16$ $1$ $C_2\times C_{16}$ 8B-1 $b^{7}$
$C_2\times C_{16}$ 16A-7 $16$ $1$ $C_2\times C_{16}$ 8B1 $b^{9}$
$C_2\times C_{16}$ 16B1 $16$ $1$ $C_2\times C_{16}$ 8B1 $ab$
$C_2\times C_{16}$ 16B-1 $16$ $1$ $C_2\times C_{16}$ 8B-1 $ab^{15}$
$C_2\times C_{16}$ 16B3 $16$ $1$ $C_2\times C_{16}$ 8B3 $ab^{3}$
$C_2\times C_{16}$ 16B-3 $16$ $1$ $C_2\times C_{16}$ 8B-3 $ab^{13}$
$C_2\times C_{16}$ 16B5 $16$ $1$ $C_2\times C_{16}$ 8B-3 $ab^{5}$
$C_2\times C_{16}$ 16B-5 $16$ $1$ $C_2\times C_{16}$ 8B3 $ab^{11}$
$C_2\times C_{16}$ 16B7 $16$ $1$ $C_2\times C_{16}$ 8B-1 $ab^{7}$
$C_2\times C_{16}$ 16B-7 $16$ $1$ $C_2\times C_{16}$ 8B1 $ab^{9}$
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