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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{18}=b^{12}=c^{6}=[a,c]=1, b^{a}=b^{11}, c^{b}=c^{5} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_3:D_{12}\times C_{18}$ 1A $1$ $1$ $C_3:D_{12}\times C_{18}$ 1A 1A $1$
$C_3:D_{12}\times C_{18}$ 2A $2$ $1$ $C_3:D_{12}\times C_{18}$ 1A 2A $c^{3}$
$C_3:D_{12}\times C_{18}$ 2B $2$ $1$ $C_3:D_{12}\times C_{18}$ 1A 2B $b^{6}c^{3}$
$C_3:D_{12}\times C_{18}$ 2C $2$ $1$ $C_3:D_{12}\times C_{18}$ 1A 2C $b^{6}$
$C_3:D_{12}\times C_{18}$ 2D $2$ $6$ $C_2\times C_6\times C_{18}$ 1A 2D $a^{9}$
$C_3:D_{12}\times C_{18}$ 2E $2$ $6$ $C_2\times C_6\times C_{18}$ 1A 2E $a^{9}c^{3}$
$C_3:D_{12}\times C_{18}$ 2F $2$ $18$ $C_2^2\times C_{18}$ 1A 2F $a^{9}b$
$C_3:D_{12}\times C_{18}$ 2G $2$ $18$ $C_2^2\times C_{18}$ 1A 2G $a^{9}bc$
$C_3:D_{12}\times C_{18}$ 3A1 $3$ $1$ $C_3:D_{12}\times C_{18}$ 3A-1 1A $a^{12}$
$C_3:D_{12}\times C_{18}$ 3A-1 $3$ $1$ $C_3:D_{12}\times C_{18}$ 3A1 1A $a^{6}$
$C_3:D_{12}\times C_{18}$ 3B $3$ $2$ $C_6^2:C_{18}$ 3B 1A $c^{2}$
$C_3:D_{12}\times C_{18}$ 3C $3$ $2$ $C_6^2.C_{18}$ 3C 1A $b^{8}$
$C_3:D_{12}\times C_{18}$ 3D1 $3$ $2$ $C_6^2:C_{18}$ 3D-1 1A $a^{12}c^{2}$
$C_3:D_{12}\times C_{18}$ 3D-1 $3$ $2$ $C_6^2:C_{18}$ 3D1 1A $a^{6}c^{4}$
$C_3:D_{12}\times C_{18}$ 3E1 $3$ $2$ $C_6^2.C_{18}$ 3E-1 1A $a^{12}b^{8}$
$C_3:D_{12}\times C_{18}$ 3E-1 $3$ $2$ $C_6^2.C_{18}$ 3E1 1A $a^{6}b^{4}$
$C_3:D_{12}\times C_{18}$ 3F $3$ $4$ $C_3\times C_6\times C_{18}$ 3F 1A $b^{8}c^{2}$
$C_3:D_{12}\times C_{18}$ 3G1 $3$ $4$ $C_3\times C_6\times C_{18}$ 3G-1 1A $a^{12}b^{8}c^{2}$
$C_3:D_{12}\times C_{18}$ 3G-1 $3$ $4$ $C_3\times C_6\times C_{18}$ 3G1 1A $a^{6}b^{4}c^{4}$
$C_3:D_{12}\times C_{18}$ 4A $4$ $6$ $C_6\times C_{36}$ 2C 4A $b^{3}$
$C_3:D_{12}\times C_{18}$ 4B $4$ $6$ $C_6\times C_{36}$ 2C 4B $b^{3}c$
$C_3:D_{12}\times C_{18}$ 6A1 $6$ $1$ $C_3:D_{12}\times C_{18}$ 3A1 2A $a^{6}c^{3}$
$C_3:D_{12}\times C_{18}$ 6A-1 $6$ $1$ $C_3:D_{12}\times C_{18}$ 3A-1 2A $a^{12}c^{3}$
$C_3:D_{12}\times C_{18}$ 6B1 $6$ $1$ $C_3:D_{12}\times C_{18}$ 3A1 2B $a^{6}b^{6}c^{3}$
$C_3:D_{12}\times C_{18}$ 6B-1 $6$ $1$ $C_3:D_{12}\times C_{18}$ 3A-1 2B $a^{12}b^{6}c^{3}$
$C_3:D_{12}\times C_{18}$ 6C1 $6$ $1$ $C_3:D_{12}\times C_{18}$ 3A1 2C $a^{6}b^{6}$
$C_3:D_{12}\times C_{18}$ 6C-1 $6$ $1$ $C_3:D_{12}\times C_{18}$ 3A-1 2C $a^{12}b^{6}$
$C_3:D_{12}\times C_{18}$ 6D $6$ $2$ $C_6^2:C_{18}$ 3B 2A $c$
$C_3:D_{12}\times C_{18}$ 6E $6$ $2$ $C_6^2.C_{18}$ 3C 2A $b^{4}c^{3}$
$C_3:D_{12}\times C_{18}$ 6F $6$ $2$ $C_6^2.C_{18}$ 3C 2B $b^{2}c^{3}$
$C_3:D_{12}\times C_{18}$ 6G $6$ $2$ $C_6^2:C_{18}$ 3B 2C $b^{6}c^{2}$
$C_3:D_{12}\times C_{18}$ 6H $6$ $2$ $C_6^2:C_{18}$ 3B 2B $b^{6}c$
$C_3:D_{12}\times C_{18}$ 6I $6$ $2$ $C_6^2.C_{18}$ 3C 2C $b^{2}$
$C_3:D_{12}\times C_{18}$ 6J1 $6$ $2$ $C_6^2:C_{18}$ 3D1 2A $a^{6}c$
$C_3:D_{12}\times C_{18}$ 6J-1 $6$ $2$ $C_6^2:C_{18}$ 3D-1 2A $a^{12}c$
$C_3:D_{12}\times C_{18}$ 6K1 $6$ $2$ $C_6^2.C_{18}$ 3E1 2A $a^{6}b^{4}c^{3}$
$C_3:D_{12}\times C_{18}$ 6K-1 $6$ $2$ $C_6^2.C_{18}$ 3E-1 2A $a^{12}b^{4}c^{3}$
$C_3:D_{12}\times C_{18}$ 6L1 $6$ $2$ $C_6^2.C_{18}$ 3E1 2B $a^{6}b^{2}c^{3}$
$C_3:D_{12}\times C_{18}$ 6L-1 $6$ $2$ $C_6^2.C_{18}$ 3E-1 2B $a^{12}b^{2}c^{3}$
$C_3:D_{12}\times C_{18}$ 6M1 $6$ $2$ $C_6^2:C_{18}$ 3D1 2C $a^{6}b^{6}c^{2}$
$C_3:D_{12}\times C_{18}$ 6M-1 $6$ $2$ $C_6^2:C_{18}$ 3D-1 2C $a^{12}b^{6}c^{2}$
$C_3:D_{12}\times C_{18}$ 6N1 $6$ $2$ $C_6^2:C_{18}$ 3D1 2B $a^{6}b^{6}c$
$C_3:D_{12}\times C_{18}$ 6N-1 $6$ $2$ $C_6^2:C_{18}$ 3D-1 2B $a^{12}b^{6}c$
$C_3:D_{12}\times C_{18}$ 6O1 $6$ $2$ $C_6^2.C_{18}$ 3E-1 2C $a^{12}b^{2}$
$C_3:D_{12}\times C_{18}$ 6O-1 $6$ $2$ $C_6^2.C_{18}$ 3E1 2C $a^{6}b^{10}$
$C_3:D_{12}\times C_{18}$ 6P $6$ $4$ $C_3\times C_6\times C_{18}$ 3F 2A $b^{4}c$
$C_3:D_{12}\times C_{18}$ 6Q $6$ $4$ $C_3\times C_6\times C_{18}$ 3F 2C $b^{2}c^{2}$
$C_3:D_{12}\times C_{18}$ 6R $6$ $4$ $C_3\times C_6\times C_{18}$ 3F 2B $b^{2}c$
$C_3:D_{12}\times C_{18}$ 6S1 $6$ $4$ $C_3\times C_6\times C_{18}$ 3G1 2A $a^{6}b^{4}c$
$C_3:D_{12}\times C_{18}$ 6S-1 $6$ $4$ $C_3\times C_6\times C_{18}$ 3G-1 2A $a^{12}b^{4}c$
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