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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{2}=c^{6}=d^{8}=[a,b]=[a,c]=[a,d]=[b,d]=1, c^{b}=c^{5}d^{4}, d^{c}=d^{7} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$D_8:D_6$ 1A $1$ $1$ $D_8:D_6$ 1A 1A $1$
$D_8:D_6$ 2A $2$ $1$ $D_8:D_6$ 1A 2A $d^{4}$
$D_8:D_6$ 2B $2$ $1$ $D_8:D_6$ 1A 2B $a$
$D_8:D_6$ 2C $2$ $1$ $D_8:D_6$ 1A 2C $ad^{4}$
$D_8:D_6$ 2D $2$ $4$ $C_6.C_2^3$ 1A 2D $c^{3}$
$D_8:D_6$ 2E $2$ $4$ $C_6.C_2^3$ 1A 2E $c^{3}d$
$D_8:D_6$ 2F $2$ $4$ $C_6.C_2^3$ 1A 2F $ac^{3}$
$D_8:D_6$ 2G $2$ $4$ $C_6.C_2^3$ 1A 2G $ac^{3}d$
$D_8:D_6$ 2H $2$ $6$ $C_2^2\times C_8$ 1A 2H $b$
$D_8:D_6$ 2I $2$ $6$ $C_2^2\times C_8$ 1A 2I $ab$
$D_8:D_6$ 3A $3$ $2$ $C_6\times D_8$ 3A 1A $c^{4}$
$D_8:D_6$ 4A $4$ $2$ $C_8\times D_6$ 2A 4A $d^{2}$
$D_8:D_6$ 4B $4$ $2$ $C_8\times D_6$ 2A 4B $ad^{6}$
$D_8:D_6$ 4C1 $4$ $3$ $D_8:C_2^2$ 2A 4C-1 $bd^{2}$
$D_8:D_6$ 4C-1 $4$ $3$ $D_8:C_2^2$ 2A 4C1 $bd^{6}$
$D_8:D_6$ 4D1 $4$ $3$ $D_8:C_2^2$ 2A 4D-1 $abd^{2}$
$D_8:D_6$ 4D-1 $4$ $3$ $D_8:C_2^2$ 2A 4D1 $abd^{6}$
$D_8:D_6$ 4E $4$ $12$ $C_2^2\times C_4$ 2A 4E $bc$
$D_8:D_6$ 4F $4$ $12$ $C_2^2\times C_4$ 2A 4F $bcd$
$D_8:D_6$ 4G $4$ $12$ $C_2^2\times C_4$ 2A 4G $abc$
$D_8:D_6$ 4H $4$ $12$ $C_2^2\times C_4$ 2A 4H $abcd$
$D_8:D_6$ 6A $6$ $2$ $C_6\times D_8$ 3A 2B $ac^{2}$
$D_8:D_6$ 6B $6$ $2$ $C_6\times D_8$ 3A 2C $ac^{2}d^{4}$
$D_8:D_6$ 6C $6$ $2$ $C_6\times D_8$ 3A 2A $c^{4}d^{4}$
$D_8:D_6$ 6D $6$ $8$ $C_2^2\times C_6$ 3A 2D $c$
$D_8:D_6$ 6E $6$ $8$ $C_2^2\times C_6$ 3A 2E $cd$
$D_8:D_6$ 6F $6$ $8$ $C_2^2\times C_6$ 3A 2F $ac$
$D_8:D_6$ 6G $6$ $8$ $C_2^2\times C_6$ 3A 2G $acd$
$D_8:D_6$ 8A1 $8$ $2$ $C_8\times D_6$ 4A 8A3 $d^{3}$
$D_8:D_6$ 8A3 $8$ $2$ $C_8\times D_6$ 4A 8A1 $d$
$D_8:D_6$ 8B1 $8$ $2$ $C_8\times D_6$ 4A 8B3 $ad^{3}$
$D_8:D_6$ 8B3 $8$ $2$ $C_8\times D_6$ 4A 8B1 $ad$
$D_8:D_6$ 8C1 $8$ $6$ $C_2^2\times C_8$ 4A 8C1 $bd$
$D_8:D_6$ 8C-1 $8$ $6$ $C_2^2\times C_8$ 4A 8C-1 $bd^{5}$
$D_8:D_6$ 8D1 $8$ $6$ $C_2^2\times C_8$ 4A 8D1 $abd$
$D_8:D_6$ 8D-1 $8$ $6$ $C_2^2\times C_8$ 4A 8D-1 $abd^{5}$
$D_8:D_6$ 12A $12$ $4$ $C_2\times C_{24}$ 6C 4B $ac^{2}d^{2}$
$D_8:D_6$ 12B $12$ $4$ $C_2\times C_{24}$ 6C 4A $c^{4}d^{2}$
$D_8:D_6$ 24A1 $24$ $4$ $C_2\times C_{24}$ 12B 8A1 $c^{2}d$
$D_8:D_6$ 24A5 $24$ $4$ $C_2\times C_{24}$ 12B 8A3 $c^{2}d^{5}$
$D_8:D_6$ 24B1 $24$ $4$ $C_2\times C_{24}$ 12B 8B1 $ac^{2}d$
$D_8:D_6$ 24B5 $24$ $4$ $C_2\times C_{24}$ 12B 8B3 $ac^{2}d^{5}$
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