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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{4}=c^{12}=[b,c]=1, b^{a}=bc^{6}, c^{a}=b^{2}c^{7} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_4^2:C_{12}$ 1A $1$ $1$ $C_4^2:C_{12}$ 1A 1A $1$
$C_4^2:C_{12}$ 2A $2$ $1$ $C_4^2:C_{12}$ 1A 2A $c^{6}$
$C_4^2:C_{12}$ 2B $2$ $1$ $C_4^2:C_{12}$ 1A 2B $b^{2}$
$C_4^2:C_{12}$ 2C $2$ $1$ $C_4^2:C_{12}$ 1A 2C $b^{2}c^{6}$
$C_4^2:C_{12}$ 2D $2$ $1$ $C_4^2:C_{12}$ 1A 2D $a^{2}$
$C_4^2:C_{12}$ 2E $2$ $1$ $C_4^2:C_{12}$ 1A 2E $a^{2}b^{2}$
$C_4^2:C_{12}$ 2F $2$ $1$ $C_4^2:C_{12}$ 1A 2F $a^{2}b^{2}c^{6}$
$C_4^2:C_{12}$ 2G $2$ $1$ $C_4^2:C_{12}$ 1A 2G $a^{2}c^{6}$
$C_4^2:C_{12}$ 3A1 $3$ $1$ $C_4^2:C_{12}$ 3A-1 1A $c^{4}$
$C_4^2:C_{12}$ 3A-1 $3$ $1$ $C_4^2:C_{12}$ 3A1 1A $c^{8}$
$C_4^2:C_{12}$ 4A1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2A 4A-1 $c^{3}$
$C_4^2:C_{12}$ 4A-1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2A 4A1 $c^{9}$
$C_4^2:C_{12}$ 4B1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2B 4B-1 $b^{3}$
$C_4^2:C_{12}$ 4B-1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2B 4B1 $b$
$C_4^2:C_{12}$ 4C1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2C 4C-1 $b^{3}c^{3}$
$C_4^2:C_{12}$ 4C-1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2C 4C1 $bc^{9}$
$C_4^2:C_{12}$ 4D1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2A 4D-1 $a^{2}c^{3}$
$C_4^2:C_{12}$ 4D-1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2A 4D1 $a^{2}c^{9}$
$C_4^2:C_{12}$ 4E1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2B 4E-1 $a^{2}b^{3}$
$C_4^2:C_{12}$ 4E-1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2B 4E1 $a^{2}b$
$C_4^2:C_{12}$ 4F1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2C 4F-1 $a^{2}b^{3}c^{3}$
$C_4^2:C_{12}$ 4F-1 $4$ $2$ $C_2\times C_4\times C_{12}$ 2C 4F1 $a^{2}bc^{9}$
$C_4^2:C_{12}$ 4G1 $4$ $4$ $C_2^2\times C_{12}$ 2D 4G-1 $a^{3}$
$C_4^2:C_{12}$ 4G-1 $4$ $4$ $C_2^2\times C_{12}$ 2D 4G1 $a$
$C_4^2:C_{12}$ 4H1 $4$ $4$ $C_2^2\times C_{12}$ 2E 4H-1 $a^{3}b^{2}c^{9}$
$C_4^2:C_{12}$ 4H-1 $4$ $4$ $C_2^2\times C_{12}$ 2E 4H1 $ac^{9}$
$C_4^2:C_{12}$ 4I1 $4$ $4$ $C_2^2\times C_{12}$ 2F 4I-1 $a^{3}b^{3}c^{6}$
$C_4^2:C_{12}$ 4I-1 $4$ $4$ $C_2^2\times C_{12}$ 2F 4I1 $ab$
$C_4^2:C_{12}$ 4J1 $4$ $4$ $C_2^2\times C_{12}$ 2G 4J-1 $a^{3}bc^{3}$
$C_4^2:C_{12}$ 4J-1 $4$ $4$ $C_2^2\times C_{12}$ 2G 4J1 $abc^{9}$
$C_4^2:C_{12}$ 6A1 $6$ $1$ $C_4^2:C_{12}$ 3A1 2A $c^{2}$
$C_4^2:C_{12}$ 6A-1 $6$ $1$ $C_4^2:C_{12}$ 3A-1 2A $c^{10}$
$C_4^2:C_{12}$ 6B1 $6$ $1$ $C_4^2:C_{12}$ 3A1 2B $b^{2}c^{8}$
$C_4^2:C_{12}$ 6B-1 $6$ $1$ $C_4^2:C_{12}$ 3A-1 2B $b^{2}c^{4}$
$C_4^2:C_{12}$ 6C1 $6$ $1$ $C_4^2:C_{12}$ 3A1 2C $b^{2}c^{2}$
$C_4^2:C_{12}$ 6C-1 $6$ $1$ $C_4^2:C_{12}$ 3A-1 2C $b^{2}c^{10}$
$C_4^2:C_{12}$ 6D1 $6$ $1$ $C_4^2:C_{12}$ 3A1 2D $a^{2}c^{8}$
$C_4^2:C_{12}$ 6D-1 $6$ $1$ $C_4^2:C_{12}$ 3A-1 2D $a^{2}c^{4}$
$C_4^2:C_{12}$ 6E1 $6$ $1$ $C_4^2:C_{12}$ 3A1 2E $a^{2}b^{2}c^{8}$
$C_4^2:C_{12}$ 6E-1 $6$ $1$ $C_4^2:C_{12}$ 3A-1 2E $a^{2}b^{2}c^{4}$
$C_4^2:C_{12}$ 6F1 $6$ $1$ $C_4^2:C_{12}$ 3A1 2F $a^{2}b^{2}c^{2}$
$C_4^2:C_{12}$ 6F-1 $6$ $1$ $C_4^2:C_{12}$ 3A-1 2F $a^{2}b^{2}c^{10}$
$C_4^2:C_{12}$ 6G1 $6$ $1$ $C_4^2:C_{12}$ 3A1 2G $a^{2}c^{2}$
$C_4^2:C_{12}$ 6G-1 $6$ $1$ $C_4^2:C_{12}$ 3A-1 2G $a^{2}c^{10}$
$C_4^2:C_{12}$ 12A1 $12$ $2$ $C_2\times C_4\times C_{12}$ 6A1 4A1 $c$
$C_4^2:C_{12}$ 12A-1 $12$ $2$ $C_2\times C_4\times C_{12}$ 6A-1 4A-1 $b^{2}c^{5}$
$C_4^2:C_{12}$ 12A5 $12$ $2$ $C_2\times C_4\times C_{12}$ 6A-1 4A1 $c^{5}$
$C_4^2:C_{12}$ 12A-5 $12$ $2$ $C_2\times C_4\times C_{12}$ 6A1 4A-1 $b^{2}c$
$C_4^2:C_{12}$ 12B1 $12$ $2$ $C_2\times C_4\times C_{12}$ 6B1 4B1 $bc^{4}$
$C_4^2:C_{12}$ 12B-1 $12$ $2$ $C_2\times C_4\times C_{12}$ 6B-1 4B-1 $b^{3}c^{2}$
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