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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{3}=b^{6}=c^{18}=[a,b]=[a,c]=1, c^{b}=c^{11} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_9:C_6^2$ 1A $1$ $1$ $C_9:C_6^2$ 1A 1A $1$
$C_9:C_6^2$ 2A $2$ $1$ $C_9:C_6^2$ 1A 2A $c^{9}$
$C_9:C_6^2$ 2B $2$ $9$ $C_6^2$ 1A 2B $b^{3}$
$C_9:C_6^2$ 2C $2$ $9$ $C_6^2$ 1A 2C $b^{3}c^{7}$
$C_9:C_6^2$ 3A1 $3$ $1$ $C_9:C_6^2$ 3A-1 1A $a^{2}$
$C_9:C_6^2$ 3A-1 $3$ $1$ $C_9:C_6^2$ 3A1 1A $a$
$C_9:C_6^2$ 3B $3$ $2$ $C_{18}:C_3^2$ 3B 1A $c^{6}$
$C_9:C_6^2$ 3C1 $3$ $2$ $C_{18}:C_3^2$ 3C-1 1A $a^{2}c^{6}$
$C_9:C_6^2$ 3C-1 $3$ $2$ $C_{18}:C_3^2$ 3C1 1A $ac^{12}$
$C_9:C_6^2$ 3D1 $3$ $3$ $C_3^2\times D_6$ 3D-1 1A $b^{4}c^{6}$
$C_9:C_6^2$ 3D-1 $3$ $3$ $C_3^2\times D_6$ 3D1 1A $b^{2}c^{12}$
$C_9:C_6^2$ 3E1 $3$ $3$ $C_3^2\times D_6$ 3E-1 1A $a^{2}b^{4}c^{6}$
$C_9:C_6^2$ 3E-1 $3$ $3$ $C_3^2\times D_6$ 3E1 1A $ab^{2}c^{12}$
$C_9:C_6^2$ 3F1 $3$ $3$ $C_3^2\times D_6$ 3F-1 1A $a^{2}b^{2}c^{6}$
$C_9:C_6^2$ 3F-1 $3$ $3$ $C_3^2\times D_6$ 3F1 1A $ab^{4}c^{12}$
$C_9:C_6^2$ 6A1 $6$ $1$ $C_9:C_6^2$ 3A1 2A $ac^{9}$
$C_9:C_6^2$ 6A-1 $6$ $1$ $C_9:C_6^2$ 3A-1 2A $a^{2}c^{9}$
$C_9:C_6^2$ 6B $6$ $2$ $C_{18}:C_3^2$ 3B 2A $c^{3}$
$C_9:C_6^2$ 6C1 $6$ $2$ $C_{18}:C_3^2$ 3C1 2A $ac^{3}$
$C_9:C_6^2$ 6C-1 $6$ $2$ $C_{18}:C_3^2$ 3C-1 2A $a^{2}c^{3}$
$C_9:C_6^2$ 6D1 $6$ $3$ $C_3^2\times D_6$ 3D1 2A $b^{2}c^{3}$
$C_9:C_6^2$ 6D-1 $6$ $3$ $C_3^2\times D_6$ 3D-1 2A $b^{4}c^{3}$
$C_9:C_6^2$ 6E1 $6$ $3$ $C_3^2\times D_6$ 3E1 2A $ab^{2}c^{3}$
$C_9:C_6^2$ 6E-1 $6$ $3$ $C_3^2\times D_6$ 3E-1 2A $a^{2}b^{4}c^{3}$
$C_9:C_6^2$ 6F1 $6$ $3$ $C_3^2\times D_6$ 3F1 2A $ab^{4}c^{3}$
$C_9:C_6^2$ 6F-1 $6$ $3$ $C_3^2\times D_6$ 3F-1 2A $a^{2}b^{2}c^{3}$
$C_9:C_6^2$ 6G1 $6$ $9$ $C_6^2$ 3D-1 2B $b$
$C_9:C_6^2$ 6G-1 $6$ $9$ $C_6^2$ 3D1 2B $b^{5}$
$C_9:C_6^2$ 6H1 $6$ $9$ $C_6^2$ 3D-1 2C $bc$
$C_9:C_6^2$ 6H-1 $6$ $9$ $C_6^2$ 3D1 2C $b^{5}c$
$C_9:C_6^2$ 6I1 $6$ $9$ $C_6^2$ 3F1 2B $ab$
$C_9:C_6^2$ 6I-1 $6$ $9$ $C_6^2$ 3F-1 2B $a^{2}b^{5}$
$C_9:C_6^2$ 6J1 $6$ $9$ $C_6^2$ 3E-1 2B $a^{2}b$
$C_9:C_6^2$ 6J-1 $6$ $9$ $C_6^2$ 3E1 2B $ab^{5}$
$C_9:C_6^2$ 6K1 $6$ $9$ $C_6^2$ 3F1 2C $abc$
$C_9:C_6^2$ 6K-1 $6$ $9$ $C_6^2$ 3F-1 2C $a^{2}b^{5}c$
$C_9:C_6^2$ 6L1 $6$ $9$ $C_6^2$ 3A1 2B $ab^{3}$
$C_9:C_6^2$ 6L-1 $6$ $9$ $C_6^2$ 3A-1 2B $a^{2}b^{3}$
$C_9:C_6^2$ 6M1 $6$ $9$ $C_6^2$ 3E-1 2C $a^{2}bc$
$C_9:C_6^2$ 6M-1 $6$ $9$ $C_6^2$ 3E1 2C $ab^{5}c$
$C_9:C_6^2$ 6N1 $6$ $9$ $C_6^2$ 3A1 2C $ab^{3}c$
$C_9:C_6^2$ 6N-1 $6$ $9$ $C_6^2$ 3A-1 2C $a^{2}b^{3}c$
$C_9:C_6^2$ 9A $9$ $6$ $C_3\times C_{18}$ 9A 3B $c^{2}$
$C_9:C_6^2$ 9B1 $9$ $6$ $C_3\times C_{18}$ 9B-1 3B $b^{4}c^{14}$
$C_9:C_6^2$ 9B-1 $9$ $6$ $C_3\times C_{18}$ 9B1 3B $b^{2}c^{16}$
$C_9:C_6^2$ 9C1 $9$ $6$ $C_3\times C_{18}$ 9C-1 3B $a^{2}c^{2}$
$C_9:C_6^2$ 9C-1 $9$ $6$ $C_3\times C_{18}$ 9C1 3B $ac^{16}$
$C_9:C_6^2$ 9D1 $9$ $6$ $C_3\times C_{18}$ 9D-1 3B $a^{2}b^{4}c^{14}$
$C_9:C_6^2$ 9D-1 $9$ $6$ $C_3\times C_{18}$ 9D1 3B $ab^{2}c^{16}$
$C_9:C_6^2$ 9E1 $9$ $6$ $C_3\times C_{18}$ 9E-1 3B $a^{2}b^{2}c^{8}$
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