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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{12}=c^{12}=1, a^{12}=b^{6}, b^{a}=b^{11}c^{9}, c^{a}=b^{10}c^{11}, c^{b}=c^{7} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_{12}^2.D_6$ 1A $1$ $1$ $C_{12}^2.D_6$ 1A 1A $1$
$C_{12}^2.D_6$ 2A $2$ $1$ $C_{12}^2.D_6$ 1A 2A $b^{6}$
$C_{12}^2.D_6$ 2B $2$ $1$ $C_{12}^2.D_6$ 1A 2B $b^{6}c^{6}$
$C_{12}^2.D_6$ 2C $2$ $1$ $C_{12}^2.D_6$ 1A 2C $c^{6}$
$C_{12}^2.D_6$ 3A $3$ $2$ $C_{12}^2.C_6$ 3A 1A $b^{4}$
$C_{12}^2.D_6$ 3B1 $3$ $3$ $C_{12}^2.C_2^2$ 3B-1 1A $a^{8}$
$C_{12}^2.D_6$ 3B-1 $3$ $3$ $C_{12}^2.C_2^2$ 3B1 1A $a^{4}b^{6}$
$C_{12}^2.D_6$ 3C $3$ $6$ $C_{12}^2.C_2$ 3C 1A $c^{4}$
$C_{12}^2.D_6$ 3D1 $3$ $6$ $C_{12}^2.C_2$ 3D-1 1A $a^{4}b^{6}c^{4}$
$C_{12}^2.D_6$ 3D-1 $3$ $6$ $C_{12}^2.C_2$ 3D1 1A $a^{8}b^{8}c^{8}$
$C_{12}^2.D_6$ 4A $4$ $2$ $C_{12}^2.C_6$ 2A 4A $a^{6}b^{6}$
$C_{12}^2.D_6$ 4B $4$ $2$ $C_{12}^2.C_6$ 2A 4B $a^{6}b^{6}c^{6}$
$C_{12}^2.D_6$ 4C $4$ $2$ $C_{12}^2.C_6$ 2B 4C $a^{6}b^{6}c^{9}$
$C_{12}^2.D_6$ 4D $4$ $2$ $C_{12}^2.C_6$ 2B 4D $a^{6}c^{9}$
$C_{12}^2.D_6$ 4E $4$ $4$ $C_4^2\times \He_3$ 2C 4E $c^{9}$
$C_{12}^2.D_6$ 4F $4$ $8$ $C_6.C_6^2$ 2A 4F $b^{3}$
$C_{12}^2.D_6$ 4G $4$ $8$ $C_6.C_6^2$ 2A 4G $a^{6}b^{3}$
$C_{12}^2.D_6$ 6A $6$ $2$ $C_{12}^2.C_6$ 3A 2A $b^{2}$
$C_{12}^2.D_6$ 6B $6$ $2$ $C_{12}^2.C_6$ 3A 2B $b^{2}c^{6}$
$C_{12}^2.D_6$ 6C $6$ $2$ $C_{12}^2.C_6$ 3A 2C $b^{8}c^{6}$
$C_{12}^2.D_6$ 6D1 $6$ $3$ $C_{12}^2.C_2^2$ 3B1 2A $a^{4}$
$C_{12}^2.D_6$ 6D-1 $6$ $3$ $C_{12}^2.C_2^2$ 3B-1 2A $a^{8}b^{6}$
$C_{12}^2.D_6$ 6E1 $6$ $3$ $C_{12}^2.C_2^2$ 3B1 2B $a^{4}c^{6}$
$C_{12}^2.D_6$ 6E-1 $6$ $3$ $C_{12}^2.C_2^2$ 3B-1 2B $a^{8}b^{6}c^{6}$
$C_{12}^2.D_6$ 6F1 $6$ $3$ $C_{12}^2.C_2^2$ 3B-1 2C $a^{8}c^{6}$
$C_{12}^2.D_6$ 6F-1 $6$ $3$ $C_{12}^2.C_2^2$ 3B1 2C $a^{4}b^{6}c^{6}$
$C_{12}^2.D_6$ 6G $6$ $6$ $C_{12}^2.C_2$ 3C 2A $b^{6}c^{8}$
$C_{12}^2.D_6$ 6H $6$ $6$ $C_{12}^2.C_2$ 3C 2B $b^{6}c^{2}$
$C_{12}^2.D_6$ 6I $6$ $6$ $C_{12}^2.C_2$ 3C 2C $c^{2}$
$C_{12}^2.D_6$ 6J1 $6$ $6$ $C_{12}^2.C_2$ 3D1 2C $a^{8}b^{8}c^{2}$
$C_{12}^2.D_6$ 6J-1 $6$ $6$ $C_{12}^2.C_2$ 3D-1 2C $a^{4}b^{6}c^{10}$
$C_{12}^2.D_6$ 6K1 $6$ $6$ $C_{12}^2.C_2$ 3D-1 2A $a^{4}b^{4}c^{8}$
$C_{12}^2.D_6$ 6K-1 $6$ $6$ $C_{12}^2.C_2$ 3D1 2A $a^{8}b^{6}c^{4}$
$C_{12}^2.D_6$ 6L1 $6$ $6$ $C_{12}^2.C_2$ 3D-1 2B $a^{4}b^{4}c^{2}$
$C_{12}^2.D_6$ 6L-1 $6$ $6$ $C_{12}^2.C_2$ 3D1 2B $a^{8}b^{6}c^{10}$
$C_{12}^2.D_6$ 8A1 $8$ $36$ $C_2\times C_{24}$ 4A 8A3 $a^{3}$
$C_{12}^2.D_6$ 8A-1 $8$ $36$ $C_2\times C_{24}$ 4A 8A-3 $a^{9}b^{6}$
$C_{12}^2.D_6$ 8A3 $8$ $36$ $C_2\times C_{24}$ 4A 8A1 $a^{9}$
$C_{12}^2.D_6$ 8A-3 $8$ $36$ $C_2\times C_{24}$ 4A 8A-1 $a^{3}b^{6}$
$C_{12}^2.D_6$ 8B1 $8$ $36$ $C_2\times C_{24}$ 4D 8B3 $a^{3}b^{7}c^{3}$
$C_{12}^2.D_6$ 8B-1 $8$ $36$ $C_2\times C_{24}$ 4D 8B-3 $a^{9}b^{7}c^{6}$
$C_{12}^2.D_6$ 8B3 $8$ $36$ $C_2\times C_{24}$ 4D 8B1 $a^{9}b$
$C_{12}^2.D_6$ 8B-3 $8$ $36$ $C_2\times C_{24}$ 4D 8B-1 $a^{3}bc^{9}$
$C_{12}^2.D_6$ 12A $12$ $4$ $C_4^2\times \He_3$ 6A 4A $a^{6}b^{4}$
$C_{12}^2.D_6$ 12B $12$ $4$ $C_4^2\times \He_3$ 6A 4B $a^{6}b^{4}c^{6}$
$C_{12}^2.D_6$ 12C $12$ $4$ $C_4^2\times \He_3$ 6B 4C $a^{6}b^{4}c^{3}$
$C_{12}^2.D_6$ 12D $12$ $4$ $C_4^2\times \He_3$ 6B 4D $a^{6}b^{2}c^{3}$
$C_{12}^2.D_6$ 12E1 $12$ $4$ $C_4^2\times \He_3$ 6C 4E $b^{4}c^{3}$
$C_{12}^2.D_6$ 12E-1 $12$ $4$ $C_4^2\times \He_3$ 6C 4E $b^{8}c^{3}$
$C_{12}^2.D_6$ 12F1 $12$ $6$ $C_{12}:C_{24}$ 6D1 4B $a^{2}c^{6}$
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