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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{4}=c^{6}=d^{6}=[a,c]=[a,d]=[c,d]=1, b^{a}=b^{3}, c^{b}=c^{5}, d^{b}=d^{5} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_6^2:D_4$ 1A $1$ $1$ $C_6^2:D_4$ 1A 1A $1$
$C_6^2:D_4$ 2A $2$ $1$ $C_6^2:D_4$ 1A 2A $d^{3}$
$C_6^2:D_4$ 2B $2$ $1$ $C_6^2:D_4$ 1A 2B $c^{3}$
$C_6^2:D_4$ 2C $2$ $1$ $C_6^2:D_4$ 1A 2C $c^{3}d^{3}$
$C_6^2:D_4$ 2D $2$ $1$ $C_6^2:D_4$ 1A 2D $b^{2}$
$C_6^2:D_4$ 2E $2$ $1$ $C_6^2:D_4$ 1A 2E $b^{2}d^{3}$
$C_6^2:D_4$ 2F $2$ $1$ $C_6^2:D_4$ 1A 2F $b^{2}c^{3}$
$C_6^2:D_4$ 2G $2$ $1$ $C_6^2:D_4$ 1A 2G $b^{2}c^{3}d^{3}$
$C_6^2:D_4$ 2H $2$ $2$ $C_2^2\times C_6^2$ 1A 2H $a$
$C_6^2:D_4$ 2I $2$ $2$ $C_2^2\times C_6^2$ 1A 2I $ad^{3}$
$C_6^2:D_4$ 2J $2$ $2$ $C_2^2\times C_6^2$ 1A 2J $ac^{3}$
$C_6^2:D_4$ 2K $2$ $2$ $C_2^2\times C_6^2$ 1A 2K $ac^{3}d^{3}$
$C_6^2:D_4$ 2L $2$ $18$ $C_2^4$ 1A 2L $ab^{3}d^{3}$
$C_6^2:D_4$ 2M $2$ $18$ $C_2^4$ 1A 2M $ab^{3}c^{2}$
$C_6^2:D_4$ 2N $2$ $18$ $C_2^4$ 1A 2N $abc^{3}d^{5}$
$C_6^2:D_4$ 2O $2$ $18$ $C_2^4$ 1A 2O $abc^{5}$
$C_6^2:D_4$ 3A $3$ $2$ $C_2^2\times C_6^2$ 3A 1A $d^{2}$
$C_6^2:D_4$ 3B $3$ $2$ $C_2^2\times C_6^2$ 3B 1A $c^{2}$
$C_6^2:D_4$ 3C $3$ $2$ $C_2^2\times C_6^2$ 3C 1A $c^{4}d^{2}$
$C_6^2:D_4$ 3D $3$ $2$ $C_2^2\times C_6^2$ 3D 1A $c^{2}d^{2}$
$C_6^2:D_4$ 4A $4$ $18$ $C_2^2\times C_4$ 2D 4A $bc^{4}d$
$C_6^2:D_4$ 4B $4$ $18$ $C_2^2\times C_4$ 2D 4B $b^{3}c^{3}$
$C_6^2:D_4$ 4C $4$ $18$ $C_2^2\times C_4$ 2D 4C $b^{3}c^{5}d^{3}$
$C_6^2:D_4$ 4D $4$ $18$ $C_2^2\times C_4$ 2D 4D $bd^{4}$
$C_6^2:D_4$ 6A $6$ $2$ $C_2^2\times C_6^2$ 3A 2A $d$
$C_6^2:D_4$ 6B $6$ $2$ $C_2^2\times C_6^2$ 3B 2B $c$
$C_6^2:D_4$ 6C $6$ $2$ $C_2^2\times C_6^2$ 3C 2A $c^{2}d$
$C_6^2:D_4$ 6D $6$ $2$ $C_2^2\times C_6^2$ 3C 2B $cd^{2}$
$C_6^2:D_4$ 6E $6$ $2$ $C_2^2\times C_6^2$ 3D 2C $cd$
$C_6^2:D_4$ 6F $6$ $2$ $C_2^2\times C_6^2$ 3A 2D $b^{2}d^{2}$
$C_6^2:D_4$ 6G $6$ $2$ $C_2^2\times C_6^2$ 3A 2E $b^{2}d$
$C_6^2:D_4$ 6H $6$ $2$ $C_2^2\times C_6^2$ 3B 2D $b^{2}c^{2}$
$C_6^2:D_4$ 6I $6$ $2$ $C_2^2\times C_6^2$ 3B 2F $b^{2}c$
$C_6^2:D_4$ 6J $6$ $2$ $C_2^2\times C_6^2$ 3D 2A $c^{4}d$
$C_6^2:D_4$ 6K $6$ $2$ $C_2^2\times C_6^2$ 3D 2B $cd^{4}$
$C_6^2:D_4$ 6L $6$ $2$ $C_2^2\times C_6^2$ 3B 2A $c^{2}d^{3}$
$C_6^2:D_4$ 6M $6$ $2$ $C_2^2\times C_6^2$ 3B 2C $cd^{3}$
$C_6^2:D_4$ 6N $6$ $2$ $C_2^2\times C_6^2$ 3A 2B $c^{3}d^{2}$
$C_6^2:D_4$ 6O $6$ $2$ $C_2^2\times C_6^2$ 3A 2C $c^{3}d$
$C_6^2:D_4$ 6P $6$ $2$ $C_2^2\times C_6^2$ 3D 2D $b^{2}c^{2}d^{2}$
$C_6^2:D_4$ 6Q $6$ $2$ $C_2^2\times C_6^2$ 3C 2E $b^{2}c^{2}d$
$C_6^2:D_4$ 6R $6$ $2$ $C_2^2\times C_6^2$ 3C 2F $b^{2}cd^{2}$
$C_6^2:D_4$ 6S $6$ $2$ $C_2^2\times C_6^2$ 3D 2G $b^{2}cd$
$C_6^2:D_4$ 6T $6$ $2$ $C_2^2\times C_6^2$ 3C 2C $cd^{5}$
$C_6^2:D_4$ 6U $6$ $2$ $C_2^2\times C_6^2$ 3C 2D $b^{2}c^{2}d^{4}$
$C_6^2:D_4$ 6V $6$ $2$ $C_2^2\times C_6^2$ 3D 2E $b^{2}c^{4}d$
$C_6^2:D_4$ 6W $6$ $2$ $C_2^2\times C_6^2$ 3D 2F $b^{2}cd^{4}$
$C_6^2:D_4$ 6X $6$ $2$ $C_2^2\times C_6^2$ 3B 2E $b^{2}c^{2}d^{3}$
$C_6^2:D_4$ 6Y $6$ $2$ $C_2^2\times C_6^2$ 3B 2G $b^{2}cd^{3}$
$C_6^2:D_4$ 6Z $6$ $2$ $C_2^2\times C_6^2$ 3A 2F $b^{2}c^{3}d^{2}$
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