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Elements of the group are displayed as words in the presentation $\langle a, b, c, d, e \mid b^{2}=c^{6}=d^{6}=e^{12}=[a,b]=[a,c]=[a,d]=[b,d]=[c,e]=[d,e]=1, a^{2}=e^{6}, e^{a}=e^{11}, c^{b}=c^{5}, e^{b}=e^{5}, d^{c}=d^{5}e^{6} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_{12}.D_6^2$ 1A $1$ $1$ $C_{12}.D_6^2$ 1A 1A $1$
$C_{12}.D_6^2$ 2A $2$ $1$ $C_{12}.D_6^2$ 1A 2A $e^{6}$
$C_{12}.D_6^2$ 2B $2$ $2$ $C_6.D_6^2$ 1A 2B $d^{3}$
$C_{12}.D_6^2$ 2C $2$ $6$ $C_2.D_6^2$ 1A 2C $c^{3}$
$C_{12}.D_6^2$ 2D $2$ $6$ $C_2.D_6^2$ 1A 2D $c^{3}de^{3}$
$C_{12}.D_6^2$ 2E $2$ $9$ $C_{12}.C_2^4$ 1A 2E $b$
$C_{12}.D_6^2$ 2F $2$ $9$ $C_{12}.C_2^4$ 1A 2F $be^{2}$
$C_{12}.D_6^2$ 2G $2$ $18$ $C_6.C_2^4$ 1A 2G $bd^{3}$
$C_{12}.D_6^2$ 2H $2$ $18$ $Q_8\times D_6$ 1A 2H $ac^{3}d$
$C_{12}.D_6^2$ 2I $2$ $18$ $Q_8\times D_6$ 1A 2I $ac^{3}de$
$C_{12}.D_6^2$ 2J $2$ $18$ $Q_8\times D_6$ 1A 2J $abcd$
$C_{12}.D_6^2$ 2K $2$ $18$ $Q_8\times D_6$ 1A 2K $abcde^{9}$
$C_{12}.D_6^2$ 2L $2$ $54$ $C_2^2\times Q_8$ 1A 2L $bc^{5}de$
$C_{12}.D_6^2$ 2M $2$ $54$ $C_2^2\times Q_8$ 1A 2M $bcd^{2}e^{6}$
$C_{12}.D_6^2$ 3A $3$ $2$ $C_6.D_6^2$ 3A 1A $d^{2}$
$C_{12}.D_6^2$ 3B $3$ $2$ $C_6.D_6^2$ 3B 1A $e^{8}$
$C_{12}.D_6^2$ 3C $3$ $2$ $C_6.D_6^2$ 3C 1A $c^{4}$
$C_{12}.D_6^2$ 3D $3$ $4$ $C_{12}.C_6^2$ 3D 1A $d^{2}e^{8}$
$C_{12}.D_6^2$ 3E $3$ $4$ $C_{12}.C_6^2$ 3E 1A $c^{4}d^{2}$
$C_{12}.D_6^2$ 3F $3$ $4$ $C_{12}.C_6^2$ 3F 1A $c^{4}e^{8}$
$C_{12}.D_6^2$ 3G $3$ $8$ $C_3\times C_6\times C_{12}$ 3G 1A $c^{4}d^{2}e^{8}$
$C_{12}.D_6^2$ 4A $4$ $2$ $C_6.D_6^2$ 2A 4A $e^{3}$
$C_{12}.D_6^2$ 4B $4$ $2$ $C_6.D_6^2$ 2A 4B $d^{3}e^{9}$
$C_{12}.D_6^2$ 4C $4$ $6$ $D_{12}:D_6$ 2A 4C $c^{3}de^{6}$
$C_{12}.D_6^2$ 4D $4$ $6$ $D_{12}:D_6$ 2A 4D $ae^{6}$
$C_{12}.D_6^2$ 4E $4$ $6$ $D_{12}:D_6$ 2A 4E $ad^{3}e^{6}$
$C_{12}.D_6^2$ 4F $4$ $6$ $D_{12}:D_6$ 2A 4F $c^{3}e^{9}$
$C_{12}.D_6^2$ 4G $4$ $6$ $D_{12}:D_6$ 2A 4G $ae^{7}$
$C_{12}.D_6^2$ 4H $4$ $6$ $D_{12}:D_6$ 2A 4H $ad^{3}e^{7}$
$C_{12}.D_6^2$ 4I $4$ $6$ $D_{12}:D_6$ 2A 4I $abe^{6}$
$C_{12}.D_6^2$ 4J $4$ $6$ $D_{12}:D_6$ 2A 4J $abe^{3}$
$C_{12}.D_6^2$ 4K $4$ $6$ $D_{12}:D_6$ 2A 4K $abd^{3}e^{6}$
$C_{12}.D_6^2$ 4L $4$ $6$ $D_{12}:D_6$ 2A 4L $abd^{3}e^{9}$
$C_{12}.D_6^2$ 4M $4$ $18$ $D_4:D_6$ 2A 4M $ac^{3}e^{6}$
$C_{12}.D_6^2$ 4N $4$ $18$ $D_{12}:C_2^2$ 2A 4N $be^{7}$
$C_{12}.D_6^2$ 4O $4$ $18$ $D_{12}:C_2^2$ 2A 4O $bd^{3}e^{7}$
$C_{12}.D_6^2$ 4P $4$ $18$ $D_4:D_6$ 2A 4P $ac^{3}e^{7}$
$C_{12}.D_6^2$ 4Q $4$ $18$ $D_4:D_6$ 2A 4Q $abce^{6}$
$C_{12}.D_6^2$ 4R $4$ $18$ $D_4:D_6$ 2A 4R $abce^{3}$
$C_{12}.D_6^2$ 4S $4$ $54$ $D_4:C_2^2$ 2A 4S $bc^{5}d^{3}$
$C_{12}.D_6^2$ 4T $4$ $54$ $D_4:C_2^2$ 2A 4T $bc^{3}d^{4}e^{9}$
$C_{12}.D_6^2$ 6A $6$ $2$ $C_6.D_6^2$ 3B 2A $e^{2}$
$C_{12}.D_6^2$ 6B $6$ $2$ $C_6.D_6^2$ 3A 2A $d^{4}e^{6}$
$C_{12}.D_6^2$ 6C $6$ $2$ $C_6.D_6^2$ 3C 2A $c^{4}e^{6}$
$C_{12}.D_6^2$ 6D1 $6$ $2$ $C_6.D_6^2$ 3A 2B $d$
$C_{12}.D_6^2$ 6D-1 $6$ $2$ $C_6.D_6^2$ 3A 2B $d^{5}$
$C_{12}.D_6^2$ 6E $6$ $4$ $C_{12}.C_6^2$ 3B 2B $d^{3}e^{4}$
$C_{12}.D_6^2$ 6F $6$ $4$ $C_{12}.C_6^2$ 3C 2B $c^{2}d^{3}$
$C_{12}.D_6^2$ 6G $6$ $4$ $C_{12}.C_6^2$ 3F 2A $c^{4}e^{2}$
$C_{12}.D_6^2$ 6H $6$ $4$ $C_{12}.C_6^2$ 3D 2A $d^{4}e^{2}$
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