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Results (28 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid b^{12}=c^{13}=d^{13}=[c,d]=1, a^{2}=b^{6}c^{4}d^{11}, b^{a}=b^{5}c^{10}d^{8}, c^{a}=c^{2}d^{12}, d^{a}=c^{5}d^{11}, c^{b}=c^{6}d, d^{b}=d^{2} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 13P
$C_{13}^2:(C_4\times S_3)$ 1A $1$ $1$ $C_{13}^2:(C_4\times S_3)$ 1A 1A 1A $1$
$C_{13}^2:(C_4\times S_3)$ 2A $2$ $39$ $C_{26}:C_4$ 1A 2A 2A $ab^{9}c^{10}d^{7}$
$C_{13}^2:(C_4\times S_3)$ 2B $2$ $39$ $C_{26}:C_4$ 1A 2B 2B $ab^{3}c^{2}d^{8}$
$C_{13}^2:(C_4\times S_3)$ 2C $2$ $169$ $C_4\times S_3$ 1A 2C 2C $b^{6}c^{11}d^{11}$
$C_{13}^2:(C_4\times S_3)$ 3A $3$ $338$ $C_{12}$ 3A 1A 3A $b^{8}c^{2}$
$C_{13}^2:(C_4\times S_3)$ 4A1 $4$ $169$ $C_4\times S_3$ 2C 4A-1 4A1 $b^{9}c^{4}d^{4}$
$C_{13}^2:(C_4\times S_3)$ 4A-1 $4$ $169$ $C_4\times S_3$ 2C 4A1 4A-1 $b^{3}c^{7}d^{7}$
$C_{13}^2:(C_4\times S_3)$ 4B1 $4$ $507$ $C_2\times C_4$ 2C 4B-1 4B1 $ab^{2}c^{4}d^{11}$
$C_{13}^2:(C_4\times S_3)$ 4B-1 $4$ $507$ $C_2\times C_4$ 2C 4B1 4B-1 $ab^{8}c^{11}d^{3}$
$C_{13}^2:(C_4\times S_3)$ 6A $6$ $338$ $C_{12}$ 3A 2C 6A $b^{10}c^{3}d$
$C_{13}^2:(C_4\times S_3)$ 12A1 $12$ $338$ $C_{12}$ 6A 4A1 12A1 $b^{11}c^{10}d^{7}$
$C_{13}^2:(C_4\times S_3)$ 12A-1 $12$ $338$ $C_{12}$ 6A 4A-1 12A-1 $bc^{5}d^{2}$
$C_{13}^2:(C_4\times S_3)$ 13A1 $13$ $12$ $C_{13}\times D_{13}$ 13A2 13A2 1A $c^{10}d^{12}$
$C_{13}^2:(C_4\times S_3)$ 13A2 $13$ $12$ $C_{13}\times D_{13}$ 13A4 13A4 1A $c^{7}d^{11}$
$C_{13}^2:(C_4\times S_3)$ 13A4 $13$ $12$ $C_{13}\times D_{13}$ 13A1 13A1 1A $cd^{9}$
$C_{13}^2:(C_4\times S_3)$ 13B1 $13$ $12$ $C_{13}\times D_{13}$ 13B2 13B2 1A $c^{8}d^{10}$
$C_{13}^2:(C_4\times S_3)$ 13B2 $13$ $12$ $C_{13}\times D_{13}$ 13B4 13B4 1A $c^{3}d^{7}$
$C_{13}^2:(C_4\times S_3)$ 13B4 $13$ $12$ $C_{13}\times D_{13}$ 13B1 13B1 1A $c^{6}d$
$C_{13}^2:(C_4\times S_3)$ 13C $13$ $24$ $C_{13}^2$ 13C 13C 1A $d$
$C_{13}^2:(C_4\times S_3)$ 13D1 $13$ $24$ $C_{13}^2$ 13D2 13D2 1A $cd^{2}$
$C_{13}^2:(C_4\times S_3)$ 13D2 $13$ $24$ $C_{13}^2$ 13D4 13D4 1A $cd^{3}$
$C_{13}^2:(C_4\times S_3)$ 13D4 $13$ $24$ $C_{13}^2$ 13D1 13D1 1A $c^{5}d$
$C_{13}^2:(C_4\times S_3)$ 26A1 $26$ $156$ $C_{26}$ 13A1 26A3 2A $ab^{9}c^{2}$
$C_{13}^2:(C_4\times S_3)$ 26A3 $26$ $156$ $C_{26}$ 13A2 26A7 2A $ab^{9}c^{12}d^{12}$
$C_{13}^2:(C_4\times S_3)$ 26A7 $26$ $156$ $C_{26}$ 13A4 26A1 2A $ab^{9}c^{6}d^{10}$
$C_{13}^2:(C_4\times S_3)$ 26B1 $26$ $156$ $C_{26}$ 13B1 26B3 2B $ab^{3}c^{6}$
$C_{13}^2:(C_4\times S_3)$ 26B3 $26$ $156$ $C_{26}$ 13B2 26B7 2B $ab^{3}cd^{10}$
$C_{13}^2:(C_4\times S_3)$ 26B7 $26$ $156$ $C_{26}$ 13B4 26B1 2B $ab^{3}c^{4}d^{4}$
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