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

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_6.C_2^4$ 1A $1$ $1$ $C_6.C_2^4$ 1A 1A $1$
$C_6.C_2^4$ 2A $2$ $1$ $C_6.C_2^4$ 1A 2A $c^{2}$
$C_6.C_2^4$ 2B $2$ $2$ $C_6\times D_4$ 1A 2B $d^{3}$
$C_6.C_2^4$ 2C $2$ $2$ $C_6\times D_4$ 1A 2C $b$
$C_6.C_2^4$ 2D $2$ $2$ $C_6\times D_4$ 1A 2D $bd^{3}$
$C_6.C_2^4$ 2E $2$ $2$ $C_6\times D_4$ 1A 2E $a$
$C_6.C_2^4$ 2F $2$ $2$ $C_6\times D_4$ 1A 2F $bc$
$C_6.C_2^4$ 2G $2$ $2$ $C_6\times D_4$ 1A 2G $bcd^{3}$
$C_6.C_2^4$ 2H $2$ $2$ $C_6\times D_4$ 1A 2H $acd^{3}$
$C_6.C_2^4$ 2I $2$ $2$ $C_6\times D_4$ 1A 2I $ab$
$C_6.C_2^4$ 2J $2$ $2$ $C_6\times D_4$ 1A 2J $abc$
$C_6.C_2^4$ 3A1 $3$ $1$ $C_6.C_2^4$ 3A-1 1A $d^{2}$
$C_6.C_2^4$ 3A-1 $3$ $1$ $C_6.C_2^4$ 3A1 1A $d^{4}$
$C_6.C_2^4$ 4A $4$ $2$ $D_4:C_6$ 2A 4A $c^{3}$
$C_6.C_2^4$ 4B $4$ $2$ $D_4:C_6$ 2A 4B $c^{3}d^{3}$
$C_6.C_2^4$ 4C $4$ $2$ $D_4:C_6$ 2A 4C $ac^{2}d^{3}$
$C_6.C_2^4$ 4D $4$ $2$ $D_4:C_6$ 2A 4D $ac^{3}$
$C_6.C_2^4$ 4E $4$ $2$ $D_4:C_6$ 2A 4E $abc^{2}d^{3}$
$C_6.C_2^4$ 4F $4$ $2$ $D_4:C_6$ 2A 4F $abc^{3}d^{3}$
$C_6.C_2^4$ 6A1 $6$ $1$ $C_6.C_2^4$ 3A1 2A $c^{2}d^{4}$
$C_6.C_2^4$ 6A-1 $6$ $1$ $C_6.C_2^4$ 3A-1 2A $c^{2}d^{2}$
$C_6.C_2^4$ 6B1 $6$ $2$ $C_6\times D_4$ 3A1 2B $d$
$C_6.C_2^4$ 6B-1 $6$ $2$ $C_6\times D_4$ 3A-1 2B $d^{5}$
$C_6.C_2^4$ 6C1 $6$ $2$ $C_6\times D_4$ 3A-1 2C $bd^{2}$
$C_6.C_2^4$ 6C-1 $6$ $2$ $C_6\times D_4$ 3A1 2C $bd^{4}$
$C_6.C_2^4$ 6D1 $6$ $2$ $C_6\times D_4$ 3A1 2D $bd$
$C_6.C_2^4$ 6D-1 $6$ $2$ $C_6\times D_4$ 3A-1 2D $bd^{5}$
$C_6.C_2^4$ 6E1 $6$ $2$ $C_6\times D_4$ 3A-1 2E $ad^{2}$
$C_6.C_2^4$ 6E-1 $6$ $2$ $C_6\times D_4$ 3A1 2E $ad^{4}$
$C_6.C_2^4$ 6F1 $6$ $2$ $C_6\times D_4$ 3A-1 2F $bcd^{2}$
$C_6.C_2^4$ 6F-1 $6$ $2$ $C_6\times D_4$ 3A1 2F $bcd^{4}$
$C_6.C_2^4$ 6G1 $6$ $2$ $C_6\times D_4$ 3A1 2G $bcd$
$C_6.C_2^4$ 6G-1 $6$ $2$ $C_6\times D_4$ 3A-1 2G $bcd^{5}$
$C_6.C_2^4$ 6H1 $6$ $2$ $C_6\times D_4$ 3A1 2H $acd$
$C_6.C_2^4$ 6H-1 $6$ $2$ $C_6\times D_4$ 3A-1 2H $acd^{5}$
$C_6.C_2^4$ 6I1 $6$ $2$ $C_6\times D_4$ 3A-1 2I $abd^{2}$
$C_6.C_2^4$ 6I-1 $6$ $2$ $C_6\times D_4$ 3A1 2I $abd^{4}$
$C_6.C_2^4$ 6J1 $6$ $2$ $C_6\times D_4$ 3A-1 2J $abcd^{2}$
$C_6.C_2^4$ 6J-1 $6$ $2$ $C_6\times D_4$ 3A1 2J $abcd^{4}$
$C_6.C_2^4$ 12A1 $12$ $2$ $D_4:C_6$ 6A1 4A $cd^{2}$
$C_6.C_2^4$ 12A-1 $12$ $2$ $D_4:C_6$ 6A-1 4A $cd^{4}$
$C_6.C_2^4$ 12B1 $12$ $2$ $D_4:C_6$ 6A-1 4B $cd$
$C_6.C_2^4$ 12B-1 $12$ $2$ $D_4:C_6$ 6A1 4B $cd^{5}$
$C_6.C_2^4$ 12C1 $12$ $2$ $D_4:C_6$ 6A-1 4C $ad$
$C_6.C_2^4$ 12C-1 $12$ $2$ $D_4:C_6$ 6A1 4C $ad^{5}$
$C_6.C_2^4$ 12D1 $12$ $2$ $D_4:C_6$ 6A1 4D $acd^{2}$
$C_6.C_2^4$ 12D-1 $12$ $2$ $D_4:C_6$ 6A-1 4D $acd^{4}$
$C_6.C_2^4$ 12E1 $12$ $2$ $D_4:C_6$ 6A-1 4E $abd$
$C_6.C_2^4$ 12E-1 $12$ $2$ $D_4:C_6$ 6A1 4E $abd^{5}$
$C_6.C_2^4$ 12F1 $12$ $2$ $D_4:C_6$ 6A-1 4F $abcd$
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