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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b, c, d \mid a^{2}=b^{2}=c^{2}=d^{4}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$C_2^3\times C_4$ 1A $1$ $1$ $C_2^3\times C_4$ 1A $1$
$C_2^3\times C_4$ 2A $2$ $1$ $C_2^3\times C_4$ 1A $c$
$C_2^3\times C_4$ 2B $2$ $1$ $C_2^3\times C_4$ 1A $b$
$C_2^3\times C_4$ 2C $2$ $1$ $C_2^3\times C_4$ 1A $a$
$C_2^3\times C_4$ 2D $2$ $1$ $C_2^3\times C_4$ 1A $cd^{2}$
$C_2^3\times C_4$ 2E $2$ $1$ $C_2^3\times C_4$ 1A $bd^{2}$
$C_2^3\times C_4$ 2F $2$ $1$ $C_2^3\times C_4$ 1A $bc$
$C_2^3\times C_4$ 2G $2$ $1$ $C_2^3\times C_4$ 1A $ad^{2}$
$C_2^3\times C_4$ 2H $2$ $1$ $C_2^3\times C_4$ 1A $ac$
$C_2^3\times C_4$ 2I $2$ $1$ $C_2^3\times C_4$ 1A $ab$
$C_2^3\times C_4$ 2J $2$ $1$ $C_2^3\times C_4$ 1A $bcd^{2}$
$C_2^3\times C_4$ 2K $2$ $1$ $C_2^3\times C_4$ 1A $acd^{2}$
$C_2^3\times C_4$ 2L $2$ $1$ $C_2^3\times C_4$ 1A $abd^{2}$
$C_2^3\times C_4$ 2M $2$ $1$ $C_2^3\times C_4$ 1A $abc$
$C_2^3\times C_4$ 2N $2$ $1$ $C_2^3\times C_4$ 1A $abcd^{2}$
$C_2^3\times C_4$ 2O $2$ $1$ $C_2^3\times C_4$ 1A $d^{2}$
$C_2^3\times C_4$ 4A1 $4$ $1$ $C_2^3\times C_4$ 2O $d$
$C_2^3\times C_4$ 4A-1 $4$ $1$ $C_2^3\times C_4$ 2O $d^{3}$
$C_2^3\times C_4$ 4B1 $4$ $1$ $C_2^3\times C_4$ 2O $cd$
$C_2^3\times C_4$ 4B-1 $4$ $1$ $C_2^3\times C_4$ 2O $cd^{3}$
$C_2^3\times C_4$ 4C1 $4$ $1$ $C_2^3\times C_4$ 2O $bd$
$C_2^3\times C_4$ 4C-1 $4$ $1$ $C_2^3\times C_4$ 2O $bd^{3}$
$C_2^3\times C_4$ 4D1 $4$ $1$ $C_2^3\times C_4$ 2O $ad$
$C_2^3\times C_4$ 4D-1 $4$ $1$ $C_2^3\times C_4$ 2O $ad^{3}$
$C_2^3\times C_4$ 4E1 $4$ $1$ $C_2^3\times C_4$ 2O $bcd$
$C_2^3\times C_4$ 4E-1 $4$ $1$ $C_2^3\times C_4$ 2O $bcd^{3}$
$C_2^3\times C_4$ 4F1 $4$ $1$ $C_2^3\times C_4$ 2O $acd$
$C_2^3\times C_4$ 4F-1 $4$ $1$ $C_2^3\times C_4$ 2O $acd^{3}$
$C_2^3\times C_4$ 4G1 $4$ $1$ $C_2^3\times C_4$ 2O $abd$
$C_2^3\times C_4$ 4G-1 $4$ $1$ $C_2^3\times C_4$ 2O $abd^{3}$
$C_2^3\times C_4$ 4H1 $4$ $1$ $C_2^3\times C_4$ 2O $abcd$
$C_2^3\times C_4$ 4H-1 $4$ $1$ $C_2^3\times C_4$ 2O $abcd^{3}$
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