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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{2}=c^{4}=d^{24}=[a,b]=[a,c]=1, d^{a}=bc^{2}d^{13}, c^{b}=c^{3}d^{12}, d^{b}=c^{2}d^{13}, d^{c}=d^{19} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_3\times C_2^4.D_4$ 1A $1$ $1$ $C_3\times C_2^4.D_4$ 1A 1A $1$
$C_3\times C_2^4.D_4$ 2A $2$ $1$ $C_3\times C_2^4.D_4$ 1A 2A $c^{2}$
$C_3\times C_2^4.D_4$ 2B $2$ $1$ $C_3\times C_2^4.D_4$ 1A 2B $d^{12}$
$C_3\times C_2^4.D_4$ 2C $2$ $1$ $C_3\times C_2^4.D_4$ 1A 2C $c^{2}d^{12}$
$C_3\times C_2^4.D_4$ 2D $2$ $2$ $C_3\times C_2^3.D_4$ 1A 2D $bd^{12}$
$C_3\times C_2^4.D_4$ 2E $2$ $2$ $C_3\times C_2^3.D_4$ 1A 2E $bc^{2}d^{12}$
$C_3\times C_2^4.D_4$ 2F $2$ $4$ $C_2^3:C_{12}$ 1A 2F $a$
$C_3\times C_2^4.D_4$ 2G $2$ $4$ $C_2^3:C_{12}$ 1A 2G $ad^{12}$
$C_3\times C_2^4.D_4$ 3A1 $3$ $1$ $C_3\times C_2^4.D_4$ 3A-1 1A $d^{8}$
$C_3\times C_2^4.D_4$ 3A-1 $3$ $1$ $C_3\times C_2^4.D_4$ 3A1 1A $d^{16}$
$C_3\times C_2^4.D_4$ 4A $4$ $4$ $C_2^2:C_{24}$ 2B 4A $d^{6}$
$C_3\times C_2^4.D_4$ 4B $4$ $4$ $C_2^2:C_{24}$ 2B 4B $bc^{2}d^{18}$
$C_3\times C_2^4.D_4$ 4C $4$ $8$ $C_2^2\times C_{12}$ 2A 4C $c^{3}$
$C_3\times C_2^4.D_4$ 4D $4$ $8$ $C_2^2\times C_{12}$ 2A 4D $ac^{2}d^{18}$
$C_3\times C_2^4.D_4$ 4E $4$ $8$ $C_2^2\times C_{12}$ 2B 4E $bcd^{12}$
$C_3\times C_2^4.D_4$ 4F $4$ $8$ $C_2^2\times C_{12}$ 2A 4F $ac^{3}$
$C_3\times C_2^4.D_4$ 4G $4$ $8$ $C_2^2\times C_{12}$ 2B 4G $acd^{6}$
$C_3\times C_2^4.D_4$ 4H1 $4$ $8$ $C_2^2\times C_{12}$ 2C 4H-1 $c^{3}d^{21}$
$C_3\times C_2^4.D_4$ 4H-1 $4$ $8$ $C_2^2\times C_{12}$ 2C 4H1 $cd^{9}$
$C_3\times C_2^4.D_4$ 4I1 $4$ $8$ $C_2^2\times C_{12}$ 2E 4I-1 $abc^{3}d^{21}$
$C_3\times C_2^4.D_4$ 4I-1 $4$ $8$ $C_2^2\times C_{12}$ 2E 4I1 $acd^{9}$
$C_3\times C_2^4.D_4$ 6A1 $6$ $1$ $C_3\times C_2^4.D_4$ 3A1 2A $c^{2}d^{16}$
$C_3\times C_2^4.D_4$ 6A-1 $6$ $1$ $C_3\times C_2^4.D_4$ 3A-1 2A $c^{2}d^{8}$
$C_3\times C_2^4.D_4$ 6B1 $6$ $1$ $C_3\times C_2^4.D_4$ 3A1 2B $d^{4}$
$C_3\times C_2^4.D_4$ 6B-1 $6$ $1$ $C_3\times C_2^4.D_4$ 3A-1 2B $d^{20}$
$C_3\times C_2^4.D_4$ 6C1 $6$ $1$ $C_3\times C_2^4.D_4$ 3A-1 2C $c^{2}d^{20}$
$C_3\times C_2^4.D_4$ 6C-1 $6$ $1$ $C_3\times C_2^4.D_4$ 3A1 2C $c^{2}d^{4}$
$C_3\times C_2^4.D_4$ 6D1 $6$ $2$ $C_3\times C_2^3.D_4$ 3A1 2D $bd^{4}$
$C_3\times C_2^4.D_4$ 6D-1 $6$ $2$ $C_3\times C_2^3.D_4$ 3A-1 2D $bc^{2}d^{8}$
$C_3\times C_2^4.D_4$ 6E1 $6$ $2$ $C_3\times C_2^3.D_4$ 3A-1 2E $bc^{2}d^{20}$
$C_3\times C_2^4.D_4$ 6E-1 $6$ $2$ $C_3\times C_2^3.D_4$ 3A1 2E $bc^{2}d^{4}$
$C_3\times C_2^4.D_4$ 6F1 $6$ $4$ $C_2^3:C_{12}$ 3A-1 2F $ad^{8}$
$C_3\times C_2^4.D_4$ 6F-1 $6$ $4$ $C_2^3:C_{12}$ 3A1 2F $ad^{16}$
$C_3\times C_2^4.D_4$ 6G1 $6$ $4$ $C_2^3:C_{12}$ 3A1 2G $ad^{4}$
$C_3\times C_2^4.D_4$ 6G-1 $6$ $4$ $C_2^3:C_{12}$ 3A-1 2G $ac^{2}d^{8}$
$C_3\times C_2^4.D_4$ 8A1 $8$ $8$ $C_2\times C_{24}$ 4A 8A1 $d^{3}$
$C_3\times C_2^4.D_4$ 8A-1 $8$ $8$ $C_2\times C_{24}$ 4A 8A-1 $d^{21}$
$C_3\times C_2^4.D_4$ 8B1 $8$ $8$ $C_2\times C_{24}$ 4B 8B1 $abd^{3}$
$C_3\times C_2^4.D_4$ 8B-1 $8$ $8$ $C_2\times C_{24}$ 4B 8B-1 $ad^{21}$
$C_3\times C_2^4.D_4$ 12A1 $12$ $4$ $C_2^2:C_{24}$ 6B1 4A $d^{2}$
$C_3\times C_2^4.D_4$ 12A-1 $12$ $4$ $C_2^2:C_{24}$ 6B-1 4A $d^{22}$
$C_3\times C_2^4.D_4$ 12B1 $12$ $4$ $C_2^2:C_{24}$ 6B1 4B $bc^{2}d^{14}$
$C_3\times C_2^4.D_4$ 12B-1 $12$ $4$ $C_2^2:C_{24}$ 6B-1 4B $bc^{2}d^{10}$
$C_3\times C_2^4.D_4$ 12C1 $12$ $8$ $C_2^2\times C_{12}$ 6A1 4C $cd^{8}$
$C_3\times C_2^4.D_4$ 12C-1 $12$ $8$ $C_2^2\times C_{12}$ 6A-1 4C $cd^{4}$
$C_3\times C_2^4.D_4$ 12D1 $12$ $8$ $C_2^2\times C_{12}$ 6A1 4D $ad^{2}$
$C_3\times C_2^4.D_4$ 12D-1 $12$ $8$ $C_2^2\times C_{12}$ 6A-1 4D $ad^{10}$
$C_3\times C_2^4.D_4$ 12E1 $12$ $8$ $C_2^2\times C_{12}$ 6B1 4E $bcd^{8}$
$C_3\times C_2^4.D_4$ 12E-1 $12$ $8$ $C_2^2\times C_{12}$ 6B-1 4E $bcd^{4}$
$C_3\times C_2^4.D_4$ 12F1 $12$ $8$ $C_2^2\times C_{12}$ 6A1 4F $acd^{8}$
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