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Results (24 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{4}=b^{12}=1, b^{a}=b^{5} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_{12}:C_4$ 1A $1$ $1$ $C_{12}:C_4$ 1A 1A $1$
$C_{12}:C_4$ 2A $2$ $1$ $C_{12}:C_4$ 1A 2A $a^{2}$
$C_{12}:C_4$ 2B $2$ $1$ $C_{12}:C_4$ 1A 2B $a^{2}b^{6}$
$C_{12}:C_4$ 2C $2$ $1$ $C_{12}:C_4$ 1A 2C $b^{6}$
$C_{12}:C_4$ 3A $3$ $2$ $C_2\times C_{12}$ 3A 1A $b^{8}$
$C_{12}:C_4$ 4A1 $4$ $1$ $C_{12}:C_4$ 2C 4A-1 $b^{3}$
$C_{12}:C_4$ 4A-1 $4$ $1$ $C_{12}:C_4$ 2C 4A1 $b^{9}$
$C_{12}:C_4$ 4B1 $4$ $1$ $C_{12}:C_4$ 2C 4B-1 $a^{2}b^{3}$
$C_{12}:C_4$ 4B-1 $4$ $1$ $C_{12}:C_4$ 2C 4B1 $a^{2}b^{9}$
$C_{12}:C_4$ 4C1 $4$ $3$ $C_4^2$ 2A 4C-1 $a$
$C_{12}:C_4$ 4C-1 $4$ $3$ $C_4^2$ 2A 4C1 $a^{3}$
$C_{12}:C_4$ 4D1 $4$ $3$ $C_4^2$ 2A 4D-1 $ab^{2}$
$C_{12}:C_4$ 4D-1 $4$ $3$ $C_4^2$ 2A 4D1 $a^{3}b^{2}$
$C_{12}:C_4$ 4E1 $4$ $3$ $C_4^2$ 2B 4E-1 $ab$
$C_{12}:C_4$ 4E-1 $4$ $3$ $C_4^2$ 2B 4E1 $a^{3}b^{3}$
$C_{12}:C_4$ 4F1 $4$ $3$ $C_4^2$ 2B 4F-1 $ab^{3}$
$C_{12}:C_4$ 4F-1 $4$ $3$ $C_4^2$ 2B 4F1 $a^{3}b$
$C_{12}:C_4$ 6A $6$ $2$ $C_2\times C_{12}$ 3A 2A $a^{2}b^{4}$
$C_{12}:C_4$ 6B $6$ $2$ $C_2\times C_{12}$ 3A 2B $a^{2}b^{2}$
$C_{12}:C_4$ 6C $6$ $2$ $C_2\times C_{12}$ 3A 2C $b^{2}$
$C_{12}:C_4$ 12A1 $12$ $2$ $C_2\times C_{12}$ 6C 4A1 $b$
$C_{12}:C_4$ 12A-1 $12$ $2$ $C_2\times C_{12}$ 6C 4A-1 $b^{7}$
$C_{12}:C_4$ 12B1 $12$ $2$ $C_2\times C_{12}$ 6C 4B1 $a^{2}b$
$C_{12}:C_4$ 12B-1 $12$ $2$ $C_2\times C_{12}$ 6C 4B-1 $a^{2}b^{7}$
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