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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{2}=c^{8}=d^{6}=[a,d]=[b,d]=1, b^{a}=bd^{3}, c^{a}=c^{3}d^{3}, c^{b}=c^{5}, d^{c}=d^{5} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_{12}.(C_2\times D_4)$ 1A $1$ $1$ $C_{12}.(C_2\times D_4)$ 1A 1A $1$
$C_{12}.(C_2\times D_4)$ 2A $2$ $1$ $C_{12}.(C_2\times D_4)$ 1A 2A $c^{4}d^{3}$
$C_{12}.(C_2\times D_4)$ 2B $2$ $1$ $C_{12}.(C_2\times D_4)$ 1A 2B $c^{4}$
$C_{12}.(C_2\times D_4)$ 2C $2$ $1$ $C_{12}.(C_2\times D_4)$ 1A 2C $d^{3}$
$C_{12}.(C_2\times D_4)$ 2D $2$ $4$ $C_2^2\times C_{12}$ 1A 2D $b$
$C_{12}.(C_2\times D_4)$ 2E $2$ $8$ $C_2^2\times C_6$ 1A 2E $a$
$C_{12}.(C_2\times D_4)$ 2F $2$ $24$ $C_2^3$ 1A 2F $abc^{7}d^{5}$
$C_{12}.(C_2\times D_4)$ 3A $3$ $2$ $C_{12}:D_4$ 3A 1A $d^{2}$
$C_{12}.(C_2\times D_4)$ 4A $4$ $2$ $C_6:\OD_{16}$ 2B 4A $c^{6}$
$C_{12}.(C_2\times D_4)$ 4B $4$ $2$ $C_6:\OD_{16}$ 2B 4B $c^{6}d^{3}$
$C_{12}.(C_2\times D_4)$ 4C $4$ $4$ $C_2^2\times C_{12}$ 2B 4C $bc^{6}$
$C_{12}.(C_2\times D_4)$ 4D $4$ $8$ $C_2\times C_{12}$ 2C 4D $abd^{3}$
$C_{12}.(C_2\times D_4)$ 4E $4$ $24$ $C_2\times C_4$ 2A 4E $ac^{5}d$
$C_{12}.(C_2\times D_4)$ 6A $6$ $2$ $C_{12}:D_4$ 3A 2A $c^{4}d$
$C_{12}.(C_2\times D_4)$ 6B $6$ $2$ $C_{12}:D_4$ 3A 2B $c^{4}d^{4}$
$C_{12}.(C_2\times D_4)$ 6C $6$ $2$ $C_{12}:D_4$ 3A 2C $d$
$C_{12}.(C_2\times D_4)$ 6D1 $6$ $4$ $C_2^2\times C_{12}$ 3A 2D $bd^{2}$
$C_{12}.(C_2\times D_4)$ 6D-1 $6$ $4$ $C_2^2\times C_{12}$ 3A 2D $bd$
$C_{12}.(C_2\times D_4)$ 6E1 $6$ $8$ $C_2^2\times C_6$ 3A 2E $ad^{2}$
$C_{12}.(C_2\times D_4)$ 6E-1 $6$ $8$ $C_2^2\times C_6$ 3A 2E $ad$
$C_{12}.(C_2\times D_4)$ 8A $8$ $12$ $C_2\times C_8$ 4A 8A $bc$
$C_{12}.(C_2\times D_4)$ 8B $8$ $12$ $C_2\times C_8$ 4A 8B $bcd$
$C_{12}.(C_2\times D_4)$ 8C1 $8$ $12$ $C_2\times C_8$ 4A 8C-1 $c$
$C_{12}.(C_2\times D_4)$ 8C-1 $8$ $12$ $C_2\times C_8$ 4A 8C1 $cd$
$C_{12}.(C_2\times D_4)$ 12A $12$ $4$ $C_2^2\times C_{12}$ 6B 4A $c^{2}d^{2}$
$C_{12}.(C_2\times D_4)$ 12B $12$ $4$ $C_2^2\times C_{12}$ 6B 4B $c^{2}d$
$C_{12}.(C_2\times D_4)$ 12C1 $12$ $4$ $C_2^2\times C_{12}$ 6B 4C $bc^{2}d^{2}$
$C_{12}.(C_2\times D_4)$ 12C5 $12$ $4$ $C_2^2\times C_{12}$ 6B 4C $bc^{2}d^{4}$
$C_{12}.(C_2\times D_4)$ 12D1 $12$ $8$ $C_2\times C_{12}$ 6C 4D $abd^{2}$
$C_{12}.(C_2\times D_4)$ 12D-1 $12$ $8$ $C_2\times C_{12}$ 6C 4D $abd$
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