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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{8}=b^{6}=c^{12}=[a,c]=1, b^{a}=b^{5}, c^{b}=c^{11} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_4^2.S_3^2$ 1A $1$ $1$ $C_4^2.S_3^2$ 1A 1A $1$
$C_4^2.S_3^2$ 2A $2$ $1$ $C_4^2.S_3^2$ 1A 2A $a^{4}$
$C_4^2.S_3^2$ 2B $2$ $1$ $C_4^2.S_3^2$ 1A 2B $c^{6}$
$C_4^2.S_3^2$ 2C $2$ $1$ $C_4^2.S_3^2$ 1A 2C $a^{4}c^{6}$
$C_4^2.S_3^2$ 2D $2$ $6$ $C_{12}.C_2^3$ 1A 2D $b^{3}$
$C_4^2.S_3^2$ 2E $2$ $6$ $C_{12}.C_2^3$ 1A 2E $b^{3}c$
$C_4^2.S_3^2$ 2F $2$ $6$ $C_{12}.C_2^3$ 1A 2F $a^{4}b^{3}$
$C_4^2.S_3^2$ 2G $2$ $6$ $C_{12}.C_2^3$ 1A 2G $a^{4}b^{3}c$
$C_4^2.S_3^2$ 3A $3$ $2$ $C_{12}\times D_{12}$ 3A 1A $b^{2}$
$C_4^2.S_3^2$ 3B $3$ $2$ $C_{12}:C_{24}$ 3B 1A $c^{4}$
$C_4^2.S_3^2$ 3C $3$ $4$ $C_{12}^2$ 3C 1A $b^{2}c^{4}$
$C_4^2.S_3^2$ 4A1 $4$ $1$ $C_4^2.S_3^2$ 2A 4A-1 $a^{2}$
$C_4^2.S_3^2$ 4A-1 $4$ $1$ $C_4^2.S_3^2$ 2A 4A1 $a^{6}$
$C_4^2.S_3^2$ 4B1 $4$ $1$ $C_4^2.S_3^2$ 2A 4B-1 $a^{6}c^{6}$
$C_4^2.S_3^2$ 4B-1 $4$ $1$ $C_4^2.S_3^2$ 2A 4B1 $a^{2}c^{6}$
$C_4^2.S_3^2$ 4C $4$ $2$ $C_{12}:C_{24}$ 2B 4C $c^{3}$
$C_4^2.S_3^2$ 4D $4$ $2$ $C_{12}:C_{24}$ 2B 4D $a^{4}c^{3}$
$C_4^2.S_3^2$ 4E1 $4$ $2$ $C_{12}:C_{24}$ 2C 4E-1 $a^{6}c^{3}$
$C_4^2.S_3^2$ 4E-1 $4$ $2$ $C_{12}:C_{24}$ 2C 4E1 $a^{2}c^{9}$
$C_4^2.S_3^2$ 4F1 $4$ $6$ $C_{12}.C_2^3$ 2A 4F-1 $a^{6}b^{3}$
$C_4^2.S_3^2$ 4F-1 $4$ $6$ $C_{12}.C_2^3$ 2A 4F1 $a^{2}b^{3}$
$C_4^2.S_3^2$ 4G1 $4$ $6$ $C_{12}.C_2^3$ 2A 4G-1 $a^{6}b^{3}c$
$C_4^2.S_3^2$ 4G-1 $4$ $6$ $C_{12}.C_2^3$ 2A 4G1 $a^{2}b^{3}c$
$C_4^2.S_3^2$ 6A $6$ $2$ $C_{12}:C_{24}$ 3B 2B $c^{2}$
$C_4^2.S_3^2$ 6B $6$ $2$ $C_{12}\times D_{12}$ 3A 2A $a^{4}b^{4}$
$C_4^2.S_3^2$ 6C $6$ $2$ $C_{12}:C_{24}$ 3B 2C $a^{4}c^{2}$
$C_4^2.S_3^2$ 6D $6$ $2$ $C_{12}\times D_{12}$ 3A 2B $b^{4}c^{6}$
$C_4^2.S_3^2$ 6E $6$ $2$ $C_{12}\times D_{12}$ 3A 2C $a^{4}b^{4}c^{6}$
$C_4^2.S_3^2$ 6F $6$ $2$ $C_{12}:C_{24}$ 3B 2A $a^{4}c^{4}$
$C_4^2.S_3^2$ 6G $6$ $4$ $C_{12}^2$ 3C 2B $b^{4}c^{2}$
$C_4^2.S_3^2$ 6H $6$ $4$ $C_{12}^2$ 3C 2A $a^{4}b^{4}c^{8}$
$C_4^2.S_3^2$ 6I $6$ $4$ $C_{12}^2$ 3C 2C $a^{4}b^{4}c^{2}$
$C_4^2.S_3^2$ 6J $6$ $12$ $C_2^2\times C_{12}$ 3A 2D $b$
$C_4^2.S_3^2$ 6K $6$ $12$ $C_2^2\times C_{12}$ 3A 2E $bc$
$C_4^2.S_3^2$ 6L $6$ $12$ $C_2^2\times C_{12}$ 3A 2F $a^{4}b$
$C_4^2.S_3^2$ 6M $6$ $12$ $C_2^2\times C_{12}$ 3A 2G $a^{4}bc$
$C_4^2.S_3^2$ 8A1 $8$ $3$ $C_8\times D_{12}$ 4A-1 8A3 $a^{3}$
$C_4^2.S_3^2$ 8A-1 $8$ $3$ $C_8\times D_{12}$ 4A1 8A-3 $a^{5}$
$C_4^2.S_3^2$ 8A3 $8$ $3$ $C_8\times D_{12}$ 4A1 8A1 $a$
$C_4^2.S_3^2$ 8A-3 $8$ $3$ $C_8\times D_{12}$ 4A-1 8A-1 $a^{7}$
$C_4^2.S_3^2$ 8B1 $8$ $3$ $C_8\times D_{12}$ 4A-1 8B3 $a^{3}c^{6}$
$C_4^2.S_3^2$ 8B-1 $8$ $3$ $C_8\times D_{12}$ 4A1 8B-3 $a^{5}c^{6}$
$C_4^2.S_3^2$ 8B3 $8$ $3$ $C_8\times D_{12}$ 4A1 8B1 $ac^{6}$
$C_4^2.S_3^2$ 8B-3 $8$ $3$ $C_8\times D_{12}$ 4A-1 8B-1 $a^{7}c^{6}$
$C_4^2.S_3^2$ 8C1 $8$ $6$ $C_4\times C_{24}$ 4B1 8C3 $a^{3}c^{3}$
$C_4^2.S_3^2$ 8C-1 $8$ $6$ $C_4\times C_{24}$ 4B-1 8C-3 $a^{5}c^{9}$
$C_4^2.S_3^2$ 8C3 $8$ $6$ $C_4\times C_{24}$ 4B-1 8C1 $ac^{9}$
$C_4^2.S_3^2$ 8C-3 $8$ $6$ $C_4\times C_{24}$ 4B1 8C-1 $a^{7}c^{3}$
$C_4^2.S_3^2$ 8D1 $8$ $18$ $C_2^2\times C_8$ 4A1 8D3 $ab$
$C_4^2.S_3^2$ 8D-1 $8$ $18$ $C_2^2\times C_8$ 4A-1 8D-3 $a^{7}b$
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