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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{6}=c^{9}=d^{9}=[a,c]=[c,d]=1, b^{a}=b^{5}, d^{a}=d^{8}, c^{b}=c^{5}d^{8}, d^{b}=c^{3}d^{5} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_9^2:D_6$ 1A $1$ $1$ $C_9^2:D_6$ 1A 1A $1$
$C_9^2:D_6$ 2A $2$ $27$ $D_{18}$ 1A 2A $ab^{2}c^{3}d^{5}$
$C_9^2:D_6$ 2B $2$ $27$ $D_{18}$ 1A 2B $abc^{5}d$
$C_9^2:D_6$ 2C $2$ $81$ $D_6$ 1A 2C $b^{3}c^{6}d^{3}$
$C_9^2:D_6$ 3A $3$ $2$ $C_9^2:S_3$ 3A 1A $d^{6}$
$C_9^2:D_6$ 3B $3$ $6$ $C_9\times D_9$ 3B 1A $c^{3}$
$C_9^2:D_6$ 3C $3$ $54$ $C_3\times S_3$ 3C 1A $b^{4}d^{6}$
$C_9^2:D_6$ 3D $3$ $108$ $C_3^2$ 3D 1A $b^{2}c^{2}d$
$C_9^2:D_6$ 6A $6$ $54$ $C_{18}$ 3B 2A $ab^{2}d^{2}$
$C_9^2:D_6$ 6B $6$ $54$ $C_{18}$ 3A 2B $abc^{5}d^{4}$
$C_9^2:D_6$ 6C $6$ $162$ $C_6$ 3C 2C $b^{5}c^{6}$
$C_9^2:D_6$ 9A1 $9$ $6$ $C_9\times D_9$ 9A2 3B $cd^{7}$
$C_9^2:D_6$ 9A2 $9$ $6$ $C_9\times D_9$ 9A4 3B $c^{2}d^{5}$
$C_9^2:D_6$ 9A4 $9$ $6$ $C_9\times D_9$ 9A1 3B $c^{4}d$
$C_9^2:D_6$ 9B1 $9$ $6$ $C_9\times D_9$ 9B2 3A $c^{6}d^{5}$
$C_9^2:D_6$ 9B2 $9$ $6$ $C_9\times D_9$ 9B4 3A $c^{3}d$
$C_9^2:D_6$ 9B4 $9$ $6$ $C_9\times D_9$ 9B1 3A $c^{6}d^{2}$
$C_9^2:D_6$ 9C1 $9$ $12$ $C_9^2$ 9C2 3B $cd^{3}$
$C_9^2:D_6$ 9C2 $9$ $12$ $C_9^2$ 9C4 3B $cd$
$C_9^2:D_6$ 9C4 $9$ $12$ $C_9^2$ 9C1 3B $c^{2}d$
$C_9^2:D_6$ 18A1 $18$ $54$ $C_{18}$ 9A1 6A $ab^{2}c^{8}d^{4}$
$C_9^2:D_6$ 18A5 $18$ $54$ $C_{18}$ 9A4 6A $ab^{2}c$
$C_9^2:D_6$ 18A7 $18$ $54$ $C_{18}$ 9A2 6A $ab^{2}c^{2}d^{7}$
$C_9^2:D_6$ 18B1 $18$ $54$ $C_{18}$ 9B1 6B $abc^{8}d^{8}$
$C_9^2:D_6$ 18B5 $18$ $54$ $C_{18}$ 9B4 6B $abc^{2}$
$C_9^2:D_6$ 18B7 $18$ $54$ $C_{18}$ 9B2 6B $abc^{8}d^{5}$
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