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Elements of the group are displayed as words in the presentation $\langle a, b, c, d, e \mid b^{6}=c^{12}=d^{3}=e^{3}=[b,d]=[d,e]=1, a^{2}=c^{9}, b^{a}=b^{5}c^{3}, c^{a}=c^{5}, d^{a}=de, e^{a}=d^{2}e, c^{b}=c^{7}, e^{b}=e^{2}, d^{c}=e^{2}, e^{c}=d \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_3^4:\SD_{16}$ 1A $1$ $1$ $C_3^4:\SD_{16}$ 1A 1A $1$
$C_3^4:\SD_{16}$ 2A $2$ $9$ $C_{12}.D_6$ 1A 2A $c^{6}$
$C_3^4:\SD_{16}$ 2B $2$ $12$ $C_3^2\times D_6$ 1A 2B $b^{3}$
$C_3^4:\SD_{16}$ 3A $3$ $2$ $C_3^4:D_4$ 3A 1A $b^{2}$
$C_3^4:\SD_{16}$ 3B $3$ $2$ $C_3^4:D_4$ 3B 1A $b^{2}c^{8}$
$C_3^4:\SD_{16}$ 3C $3$ $2$ $C_3^4:D_4$ 3C 1A $b^{2}c^{4}$
$C_3^4:\SD_{16}$ 3D $3$ $2$ $C_3^4:D_4$ 3D 1A $c^{8}$
$C_3^4:\SD_{16}$ 3E $3$ $8$ $S_3\times C_3^3$ 3E 1A $d^{2}$
$C_3^4:\SD_{16}$ 3F1 $3$ $8$ $S_3\times C_3^3$ 3F-1 1A $b^{2}d^{2}$
$C_3^4:\SD_{16}$ 3F-1 $3$ $8$ $S_3\times C_3^3$ 3F1 1A $b^{4}d$
$C_3^4:\SD_{16}$ 3G1 $3$ $8$ $S_3\times C_3^3$ 3G-1 1A $b^{2}c^{8}d^{2}$
$C_3^4:\SD_{16}$ 3G-1 $3$ $8$ $S_3\times C_3^3$ 3G1 1A $b^{4}c^{4}d$
$C_3^4:\SD_{16}$ 3H1 $3$ $8$ $S_3\times C_3^3$ 3H-1 1A $b^{2}c^{4}e^{2}$
$C_3^4:\SD_{16}$ 3H-1 $3$ $8$ $S_3\times C_3^3$ 3H1 1A $b^{4}c^{8}e$
$C_3^4:\SD_{16}$ 3I1 $3$ $8$ $S_3\times C_3^3$ 3I-1 1A $c^{8}d^{2}$
$C_3^4:\SD_{16}$ 3I-1 $3$ $8$ $S_3\times C_3^3$ 3I1 1A $c^{4}d$
$C_3^4:\SD_{16}$ 4A $4$ $18$ $C_3^2:C_8$ 2A 4A $c^{3}$
$C_3^4:\SD_{16}$ 4B $4$ $324$ $C_4$ 2A 4B $ab^{3}c^{4}$
$C_3^4:\SD_{16}$ 6A1 $6$ $12$ $C_3^2\times D_6$ 3A 2B $b$
$C_3^4:\SD_{16}$ 6A-1 $6$ $12$ $C_3^2\times D_6$ 3A 2B $b^{5}$
$C_3^4:\SD_{16}$ 6B1 $6$ $12$ $C_3^2\times D_6$ 3B 2B $bc^{4}$
$C_3^4:\SD_{16}$ 6B-1 $6$ $12$ $C_3^2\times D_6$ 3B 2B $bc$
$C_3^4:\SD_{16}$ 6C1 $6$ $12$ $C_3^2\times D_6$ 3C 2B $bc^{2}$
$C_3^4:\SD_{16}$ 6C-1 $6$ $12$ $C_3^2\times D_6$ 3C 2B $bc^{5}$
$C_3^4:\SD_{16}$ 6D1 $6$ $12$ $C_3^2\times D_6$ 3D 2B $b^{3}c^{4}$
$C_3^4:\SD_{16}$ 6D-1 $6$ $12$ $C_3^2\times D_6$ 3D 2B $b^{3}c^{2}$
$C_3^4:\SD_{16}$ 6E $6$ $18$ $D_4\times C_3^2$ 3D 2A $c^{2}$
$C_3^4:\SD_{16}$ 6F $6$ $18$ $D_4\times C_3^2$ 3C 2A $b^{4}c^{2}$
$C_3^4:\SD_{16}$ 6G $6$ $18$ $D_4\times C_3^2$ 3B 2A $b^{2}c^{2}$
$C_3^4:\SD_{16}$ 6H $6$ $18$ $D_4\times C_3^2$ 3A 2A $b^{4}c^{6}$
$C_3^4:\SD_{16}$ 6I $6$ $24$ $C_3^2\times C_6$ 3E 2B $b^{3}d$
$C_3^4:\SD_{16}$ 6J1 $6$ $24$ $C_3^2\times C_6$ 3F1 2B $bd$
$C_3^4:\SD_{16}$ 6J-1 $6$ $24$ $C_3^2\times C_6$ 3F-1 2B $b^{5}d$
$C_3^4:\SD_{16}$ 6K1 $6$ $24$ $C_3^2\times C_6$ 3G1 2B $bc^{4}d$
$C_3^4:\SD_{16}$ 6K-1 $6$ $24$ $C_3^2\times C_6$ 3G-1 2B $bce$
$C_3^4:\SD_{16}$ 6L1 $6$ $24$ $C_3^2\times C_6$ 3H1 2B $bc^{2}e$
$C_3^4:\SD_{16}$ 6L-1 $6$ $24$ $C_3^2\times C_6$ 3H-1 2B $bc^{5}e$
$C_3^4:\SD_{16}$ 6M1 $6$ $24$ $C_3^2\times C_6$ 3I1 2B $b^{3}c^{4}d$
$C_3^4:\SD_{16}$ 6M-1 $6$ $24$ $C_3^2\times C_6$ 3I-1 2B $b^{3}c^{2}e$
$C_3^4:\SD_{16}$ 8A1 $8$ $162$ $C_8$ 4A 8A1 $ac^{10}$
$C_3^4:\SD_{16}$ 8A-1 $8$ $162$ $C_8$ 4A 8A-1 $ac$
$C_3^4:\SD_{16}$ 12A $12$ $36$ $C_3\times C_{12}$ 6E 4A $c$
$C_3^4:\SD_{16}$ 12B $12$ $36$ $C_3\times C_{12}$ 6F 4A $b^{2}c$
$C_3^4:\SD_{16}$ 12C $12$ $36$ $C_3\times C_{12}$ 6G 4A $b^{4}c$
$C_3^4:\SD_{16}$ 12D $12$ $36$ $C_3\times C_{12}$ 6H 4A $b^{2}c^{3}$
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