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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{6}=c^{12}=[a,b]=[b,c]=1, a^{6}=c^{6}, c^{a}=b^{4}c^{7} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_{12}.C_6^2$ 1A $1$ $1$ $C_{12}.C_6^2$ 1A 1A $1$
$C_{12}.C_6^2$ 2A $2$ $1$ $C_{12}.C_6^2$ 1A 2A $b^{3}$
$C_{12}.C_6^2$ 2B $2$ $1$ $C_{12}.C_6^2$ 1A 2B $b^{3}c^{6}$
$C_{12}.C_6^2$ 2C $2$ $1$ $C_{12}.C_6^2$ 1A 2C $c^{6}$
$C_{12}.C_6^2$ 3A1 $3$ $1$ $C_{12}.C_6^2$ 3A-1 1A $b^{2}$
$C_{12}.C_6^2$ 3A-1 $3$ $1$ $C_{12}.C_6^2$ 3A1 1A $b^{4}$
$C_{12}.C_6^2$ 3B1 $3$ $3$ $C_4.C_6^2$ 3B-1 1A $b^{2}c^{8}$
$C_{12}.C_6^2$ 3B-1 $3$ $3$ $C_4.C_6^2$ 3B1 1A $b^{4}c^{4}$
$C_{12}.C_6^2$ 3C1 $3$ $3$ $C_4.C_6^2$ 3C-1 1A $a^{4}b^{2}$
$C_{12}.C_6^2$ 3C-1 $3$ $3$ $C_4.C_6^2$ 3C1 1A $a^{2}b^{4}c^{6}$
$C_{12}.C_6^2$ 3D1 $3$ $3$ $C_4.C_6^2$ 3D-1 1A $a^{4}b^{4}c^{8}$
$C_{12}.C_6^2$ 3D-1 $3$ $3$ $C_4.C_6^2$ 3D1 1A $a^{2}b^{4}c^{10}$
$C_{12}.C_6^2$ 3E1 $3$ $3$ $C_4.C_6^2$ 3E-1 1A $a^{4}c^{4}$
$C_{12}.C_6^2$ 3E-1 $3$ $3$ $C_4.C_6^2$ 3E1 1A $a^{2}b^{4}c^{2}$
$C_{12}.C_6^2$ 4A $4$ $2$ $C_6.C_6^2$ 2C 4A $c^{9}$
$C_{12}.C_6^2$ 4B $4$ $2$ $C_6.C_6^2$ 2C 4B $b^{3}c^{9}$
$C_{12}.C_6^2$ 4C $4$ $2$ $C_6.C_6^2$ 2C 4C $a^{3}c^{6}$
$C_{12}.C_6^2$ 4D $4$ $2$ $C_6.C_6^2$ 2C 4D $a^{3}b^{3}c^{6}$
$C_{12}.C_6^2$ 4E $4$ $2$ $C_6.C_6^2$ 2C 4E $a^{3}c^{9}$
$C_{12}.C_6^2$ 4F $4$ $2$ $C_6.C_6^2$ 2C 4F $a^{3}b^{3}c^{9}$
$C_{12}.C_6^2$ 6A1 $6$ $1$ $C_{12}.C_6^2$ 3A1 2A $b$
$C_{12}.C_6^2$ 6A-1 $6$ $1$ $C_{12}.C_6^2$ 3A-1 2A $b^{5}$
$C_{12}.C_6^2$ 6B1 $6$ $1$ $C_{12}.C_6^2$ 3A1 2B $bc^{6}$
$C_{12}.C_6^2$ 6B-1 $6$ $1$ $C_{12}.C_6^2$ 3A-1 2B $b^{5}c^{6}$
$C_{12}.C_6^2$ 6C1 $6$ $1$ $C_{12}.C_6^2$ 3A1 2C $b^{4}c^{6}$
$C_{12}.C_6^2$ 6C-1 $6$ $1$ $C_{12}.C_6^2$ 3A-1 2C $b^{2}c^{6}$
$C_{12}.C_6^2$ 6D1 $6$ $3$ $C_4.C_6^2$ 3B1 2A $bc^{4}$
$C_{12}.C_6^2$ 6D-1 $6$ $3$ $C_4.C_6^2$ 3B-1 2A $bc^{8}$
$C_{12}.C_6^2$ 6E1 $6$ $3$ $C_4.C_6^2$ 3B-1 2B $bc^{2}$
$C_{12}.C_6^2$ 6E-1 $6$ $3$ $C_4.C_6^2$ 3B1 2B $bc^{10}$
$C_{12}.C_6^2$ 6F1 $6$ $3$ $C_4.C_6^2$ 3C1 2B $a^{2}b$
$C_{12}.C_6^2$ 6F-1 $6$ $3$ $C_4.C_6^2$ 3C-1 2B $a^{4}bc^{6}$
$C_{12}.C_6^2$ 6G1 $6$ $3$ $C_4.C_6^2$ 3C-1 2A $a^{4}b$
$C_{12}.C_6^2$ 6G-1 $6$ $3$ $C_4.C_6^2$ 3C1 2A $a^{2}bc^{6}$
$C_{12}.C_6^2$ 6H1 $6$ $3$ $C_4.C_6^2$ 3D1 2B $a^{2}bc^{4}$
$C_{12}.C_6^2$ 6H-1 $6$ $3$ $C_4.C_6^2$ 3D-1 2B $a^{4}bc^{2}$
$C_{12}.C_6^2$ 6I1 $6$ $3$ $C_4.C_6^2$ 3E1 2A $a^{2}bc^{2}$
$C_{12}.C_6^2$ 6I-1 $6$ $3$ $C_4.C_6^2$ 3E-1 2A $a^{4}bc^{4}$
$C_{12}.C_6^2$ 6J1 $6$ $3$ $C_4.C_6^2$ 3E1 2B $a^{2}bc^{8}$
$C_{12}.C_6^2$ 6J-1 $6$ $3$ $C_4.C_6^2$ 3E-1 2B $a^{4}bc^{10}$
$C_{12}.C_6^2$ 6K1 $6$ $3$ $C_4.C_6^2$ 3D-1 2A $a^{4}bc^{8}$
$C_{12}.C_6^2$ 6K-1 $6$ $3$ $C_4.C_6^2$ 3D1 2A $a^{2}bc^{10}$
$C_{12}.C_6^2$ 6L1 $6$ $3$ $C_4.C_6^2$ 3B-1 2C $c^{2}$
$C_{12}.C_6^2$ 6L-1 $6$ $3$ $C_4.C_6^2$ 3B1 2C $c^{10}$
$C_{12}.C_6^2$ 6M1 $6$ $3$ $C_4.C_6^2$ 3C1 2C $a^{2}$
$C_{12}.C_6^2$ 6M-1 $6$ $3$ $C_4.C_6^2$ 3C-1 2C $a^{4}c^{6}$
$C_{12}.C_6^2$ 6N1 $6$ $3$ $C_4.C_6^2$ 3D-1 2C $a^{4}b^{2}c^{2}$
$C_{12}.C_6^2$ 6N-1 $6$ $3$ $C_4.C_6^2$ 3D1 2C $a^{2}c^{4}$
$C_{12}.C_6^2$ 6O1 $6$ $3$ $C_4.C_6^2$ 3E1 2C $a^{2}b^{4}c^{8}$
$C_{12}.C_6^2$ 6O-1 $6$ $3$ $C_4.C_6^2$ 3E-1 2C $a^{4}c^{10}$
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