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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{4}=c^{24}=[a,b]=1, a^{2}=b^{2}c^{12}, c^{a}=c^{13}, c^{b}=c^{11} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_4^2.D_6$ 1A $1$ $1$ $C_4^2.D_6$ 1A 1A $1$
$C_4^2.D_6$ 2A $2$ $1$ $C_4^2.D_6$ 1A 2A $c^{12}$
$C_4^2.D_6$ 2B $2$ $1$ $C_4^2.D_6$ 1A 2B $b^{2}$
$C_4^2.D_6$ 2C $2$ $1$ $C_4^2.D_6$ 1A 2C $b^{2}c^{12}$
$C_4^2.D_6$ 3A $3$ $2$ $C_8:C_{12}$ 3A 1A $c^{8}$
$C_4^2.D_6$ 4A $4$ $2$ $C_8:C_{12}$ 2A 4A $c^{6}$
$C_4^2.D_6$ 4B $4$ $2$ $C_8:C_{12}$ 2A 4B $b^{2}c^{6}$
$C_4^2.D_6$ 4C1 $4$ $2$ $C_{12}:Q_8$ 2C 4C-1 $ab^{2}c^{12}$
$C_4^2.D_6$ 4C-1 $4$ $2$ $C_{12}:Q_8$ 2C 4C1 $a$
$C_4^2.D_6$ 4D1 $4$ $2$ $C_{12}:Q_8$ 2B 4D-1 $ab^{2}c^{18}$
$C_4^2.D_6$ 4D-1 $4$ $2$ $C_{12}:Q_8$ 2B 4D1 $ac^{18}$
$C_4^2.D_6$ 4E $4$ $12$ $C_4^2$ 2A 4E $ab$
$C_4^2.D_6$ 4F $4$ $12$ $C_4^2$ 2A 4F $abc$
$C_4^2.D_6$ 4G $4$ $12$ $C_4^2$ 2A 4G $ab^{3}$
$C_4^2.D_6$ 4H $4$ $12$ $C_4^2$ 2A 4H $ab^{3}c$
$C_4^2.D_6$ 4I1 $4$ $12$ $C_4^2$ 2B 4I-1 $b$
$C_4^2.D_6$ 4I-1 $4$ $12$ $C_4^2$ 2B 4I1 $b^{3}$
$C_4^2.D_6$ 4J1 $4$ $12$ $C_4^2$ 2C 4J-1 $bc$
$C_4^2.D_6$ 4J-1 $4$ $12$ $C_4^2$ 2C 4J1 $b^{3}c$
$C_4^2.D_6$ 6A $6$ $2$ $C_8:C_{12}$ 3A 2C $b^{2}c^{4}$
$C_4^2.D_6$ 6B $6$ $2$ $C_8:C_{12}$ 3A 2B $b^{2}c^{16}$
$C_4^2.D_6$ 6C $6$ $2$ $C_8:C_{12}$ 3A 2A $c^{4}$
$C_4^2.D_6$ 8A $8$ $4$ $C_2\times C_{24}$ 4A 8A $c^{3}$
$C_4^2.D_6$ 8B $8$ $4$ $C_2\times C_{24}$ 4A 8B $b^{2}c^{3}$
$C_4^2.D_6$ 8C1 $8$ $4$ $C_2\times C_{24}$ 4B 8C-1 $ab^{2}c^{3}$
$C_4^2.D_6$ 8C-1 $8$ $4$ $C_2\times C_{24}$ 4B 8C1 $ac^{21}$
$C_4^2.D_6$ 12A1 $12$ $2$ $C_8:C_{12}$ 6C 4A $c^{2}$
$C_4^2.D_6$ 12A5 $12$ $2$ $C_8:C_{12}$ 6C 4A $c^{10}$
$C_4^2.D_6$ 12B1 $12$ $2$ $C_8:C_{12}$ 6C 4B $b^{2}c^{2}$
$C_4^2.D_6$ 12B5 $12$ $2$ $C_8:C_{12}$ 6C 4B $b^{2}c^{10}$
$C_4^2.D_6$ 12C1 $12$ $4$ $C_4\times C_{12}$ 6A 4C1 $ac^{8}$
$C_4^2.D_6$ 12C-1 $12$ $4$ $C_4\times C_{12}$ 6A 4C-1 $ab^{2}c^{8}$
$C_4^2.D_6$ 12D1 $12$ $4$ $C_4\times C_{12}$ 6B 4D1 $ac^{2}$
$C_4^2.D_6$ 12D-1 $12$ $4$ $C_4\times C_{12}$ 6B 4D-1 $ab^{2}c^{2}$
$C_4^2.D_6$ 24A1 $24$ $4$ $C_2\times C_{24}$ 12A1 8A $c$
$C_4^2.D_6$ 24A5 $24$ $4$ $C_2\times C_{24}$ 12A5 8A $c^{5}$
$C_4^2.D_6$ 24B1 $24$ $4$ $C_2\times C_{24}$ 12A1 8B $b^{2}c$
$C_4^2.D_6$ 24B5 $24$ $4$ $C_2\times C_{24}$ 12A5 8B $b^{2}c^{5}$
$C_4^2.D_6$ 24C1 $24$ $4$ $C_2\times C_{24}$ 12B1 8C1 $ac$
$C_4^2.D_6$ 24C-1 $24$ $4$ $C_2\times C_{24}$ 12B1 8C-1 $ab^{2}c$
$C_4^2.D_6$ 24C5 $24$ $4$ $C_2\times C_{24}$ 12B5 8C1 $ac^{5}$
$C_4^2.D_6$ 24C-5 $24$ $4$ $C_2\times C_{24}$ 12B5 8C-1 $ab^{2}c^{5}$
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