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

Group Label Order Size Centralizer Powers Representative
2P
$C_2^3\times C_{16}$ 1A $1$ $1$ $C_2^3\times C_{16}$ 1A $1$
$C_2^3\times C_{16}$ 2A $2$ $1$ $C_2^3\times C_{16}$ 1A $c$
$C_2^3\times C_{16}$ 2B $2$ $1$ $C_2^3\times C_{16}$ 1A $b$
$C_2^3\times C_{16}$ 2C $2$ $1$ $C_2^3\times C_{16}$ 1A $a$
$C_2^3\times C_{16}$ 2D $2$ $1$ $C_2^3\times C_{16}$ 1A $cd^{8}$
$C_2^3\times C_{16}$ 2E $2$ $1$ $C_2^3\times C_{16}$ 1A $bd^{8}$
$C_2^3\times C_{16}$ 2F $2$ $1$ $C_2^3\times C_{16}$ 1A $bc$
$C_2^3\times C_{16}$ 2G $2$ $1$ $C_2^3\times C_{16}$ 1A $ad^{8}$
$C_2^3\times C_{16}$ 2H $2$ $1$ $C_2^3\times C_{16}$ 1A $ac$
$C_2^3\times C_{16}$ 2I $2$ $1$ $C_2^3\times C_{16}$ 1A $ab$
$C_2^3\times C_{16}$ 2J $2$ $1$ $C_2^3\times C_{16}$ 1A $bcd^{8}$
$C_2^3\times C_{16}$ 2K $2$ $1$ $C_2^3\times C_{16}$ 1A $acd^{8}$
$C_2^3\times C_{16}$ 2L $2$ $1$ $C_2^3\times C_{16}$ 1A $abd^{8}$
$C_2^3\times C_{16}$ 2M $2$ $1$ $C_2^3\times C_{16}$ 1A $abc$
$C_2^3\times C_{16}$ 2N $2$ $1$ $C_2^3\times C_{16}$ 1A $abcd^{8}$
$C_2^3\times C_{16}$ 2O $2$ $1$ $C_2^3\times C_{16}$ 1A $d^{8}$
$C_2^3\times C_{16}$ 4A1 $4$ $1$ $C_2^3\times C_{16}$ 2O $cd^{4}$
$C_2^3\times C_{16}$ 4A-1 $4$ $1$ $C_2^3\times C_{16}$ 2O $cd^{12}$
$C_2^3\times C_{16}$ 4B1 $4$ $1$ $C_2^3\times C_{16}$ 2O $bd^{4}$
$C_2^3\times C_{16}$ 4B-1 $4$ $1$ $C_2^3\times C_{16}$ 2O $bd^{12}$
$C_2^3\times C_{16}$ 4C1 $4$ $1$ $C_2^3\times C_{16}$ 2O $ad^{4}$
$C_2^3\times C_{16}$ 4C-1 $4$ $1$ $C_2^3\times C_{16}$ 2O $ad^{12}$
$C_2^3\times C_{16}$ 4D1 $4$ $1$ $C_2^3\times C_{16}$ 2O $bcd^{4}$
$C_2^3\times C_{16}$ 4D-1 $4$ $1$ $C_2^3\times C_{16}$ 2O $bcd^{12}$
$C_2^3\times C_{16}$ 4E1 $4$ $1$ $C_2^3\times C_{16}$ 2O $acd^{4}$
$C_2^3\times C_{16}$ 4E-1 $4$ $1$ $C_2^3\times C_{16}$ 2O $acd^{12}$
$C_2^3\times C_{16}$ 4F1 $4$ $1$ $C_2^3\times C_{16}$ 2O $abd^{4}$
$C_2^3\times C_{16}$ 4F-1 $4$ $1$ $C_2^3\times C_{16}$ 2O $abd^{12}$
$C_2^3\times C_{16}$ 4G1 $4$ $1$ $C_2^3\times C_{16}$ 2O $abcd^{4}$
$C_2^3\times C_{16}$ 4G-1 $4$ $1$ $C_2^3\times C_{16}$ 2O $abcd^{12}$
$C_2^3\times C_{16}$ 4H1 $4$ $1$ $C_2^3\times C_{16}$ 2O $d^{4}$
$C_2^3\times C_{16}$ 4H-1 $4$ $1$ $C_2^3\times C_{16}$ 2O $d^{12}$
$C_2^3\times C_{16}$ 8A1 $8$ $1$ $C_2^3\times C_{16}$ 4H1 $cd^{2}$
$C_2^3\times C_{16}$ 8A-1 $8$ $1$ $C_2^3\times C_{16}$ 4H-1 $cd^{14}$
$C_2^3\times C_{16}$ 8A3 $8$ $1$ $C_2^3\times C_{16}$ 4H-1 $cd^{6}$
$C_2^3\times C_{16}$ 8A-3 $8$ $1$ $C_2^3\times C_{16}$ 4H1 $cd^{10}$
$C_2^3\times C_{16}$ 8B1 $8$ $1$ $C_2^3\times C_{16}$ 4H1 $bd^{2}$
$C_2^3\times C_{16}$ 8B-1 $8$ $1$ $C_2^3\times C_{16}$ 4H-1 $bd^{14}$
$C_2^3\times C_{16}$ 8B3 $8$ $1$ $C_2^3\times C_{16}$ 4H-1 $bd^{6}$
$C_2^3\times C_{16}$ 8B-3 $8$ $1$ $C_2^3\times C_{16}$ 4H1 $bd^{10}$
$C_2^3\times C_{16}$ 8C1 $8$ $1$ $C_2^3\times C_{16}$ 4H1 $ad^{2}$
$C_2^3\times C_{16}$ 8C-1 $8$ $1$ $C_2^3\times C_{16}$ 4H-1 $ad^{14}$
$C_2^3\times C_{16}$ 8C3 $8$ $1$ $C_2^3\times C_{16}$ 4H-1 $ad^{6}$
$C_2^3\times C_{16}$ 8C-3 $8$ $1$ $C_2^3\times C_{16}$ 4H1 $ad^{10}$
$C_2^3\times C_{16}$ 8D1 $8$ $1$ $C_2^3\times C_{16}$ 4H1 $bcd^{2}$
$C_2^3\times C_{16}$ 8D-1 $8$ $1$ $C_2^3\times C_{16}$ 4H-1 $bcd^{14}$
$C_2^3\times C_{16}$ 8D3 $8$ $1$ $C_2^3\times C_{16}$ 4H-1 $bcd^{6}$
$C_2^3\times C_{16}$ 8D-3 $8$ $1$ $C_2^3\times C_{16}$ 4H1 $bcd^{10}$
$C_2^3\times C_{16}$ 8E1 $8$ $1$ $C_2^3\times C_{16}$ 4H1 $acd^{2}$
$C_2^3\times C_{16}$ 8E-1 $8$ $1$ $C_2^3\times C_{16}$ 4H-1 $acd^{14}$
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