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Results (48 matches)

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

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_{12}:C_8$ 1A $1$ $1$ $C_{12}:C_8$ 1A 1A $1$
$C_{12}:C_8$ 2A $2$ $1$ $C_{12}:C_8$ 1A 2A $a^{4}$
$C_{12}:C_8$ 2B $2$ $1$ $C_{12}:C_8$ 1A 2B $b^{6}$
$C_{12}:C_8$ 2C $2$ $1$ $C_{12}:C_8$ 1A 2C $a^{4}b^{6}$
$C_{12}:C_8$ 3A $3$ $2$ $C_4\times C_{12}$ 3A 1A $b^{4}$
$C_{12}:C_8$ 4A1 $4$ $1$ $C_{12}:C_8$ 2A 4A-1 $a^{2}$
$C_{12}:C_8$ 4A-1 $4$ $1$ $C_{12}:C_8$ 2A 4A1 $a^{6}$
$C_{12}:C_8$ 4B1 $4$ $1$ $C_{12}:C_8$ 2A 4B-1 $a^{2}b^{6}$
$C_{12}:C_8$ 4B-1 $4$ $1$ $C_{12}:C_8$ 2A 4B1 $a^{6}b^{6}$
$C_{12}:C_8$ 4C1 $4$ $1$ $C_{12}:C_8$ 2B 4C-1 $b^{3}$
$C_{12}:C_8$ 4C-1 $4$ $1$ $C_{12}:C_8$ 2B 4C1 $b^{9}$
$C_{12}:C_8$ 4D1 $4$ $1$ $C_{12}:C_8$ 2B 4D-1 $a^{4}b^{3}$
$C_{12}:C_8$ 4D-1 $4$ $1$ $C_{12}:C_8$ 2B 4D1 $a^{4}b^{9}$
$C_{12}:C_8$ 4E1 $4$ $1$ $C_{12}:C_8$ 2C 4E-1 $a^{6}b^{3}$
$C_{12}:C_8$ 4E-1 $4$ $1$ $C_{12}:C_8$ 2C 4E1 $a^{2}b^{9}$
$C_{12}:C_8$ 4F1 $4$ $1$ $C_{12}:C_8$ 2C 4F-1 $a^{2}b^{3}$
$C_{12}:C_8$ 4F-1 $4$ $1$ $C_{12}:C_8$ 2C 4F1 $a^{6}b^{9}$
$C_{12}:C_8$ 6A $6$ $2$ $C_4\times C_{12}$ 3A 2B $b^{2}$
$C_{12}:C_8$ 6B $6$ $2$ $C_4\times C_{12}$ 3A 2A $a^{4}b^{8}$
$C_{12}:C_8$ 6C $6$ $2$ $C_4\times C_{12}$ 3A 2C $a^{4}b^{2}$
$C_{12}:C_8$ 8A1 $8$ $3$ $C_4\times C_8$ 4A1 8A3 $a$
$C_{12}:C_8$ 8A-1 $8$ $3$ $C_4\times C_8$ 4A-1 8A-3 $a^{7}$
$C_{12}:C_8$ 8A3 $8$ $3$ $C_4\times C_8$ 4A-1 8A1 $a^{3}$
$C_{12}:C_8$ 8A-3 $8$ $3$ $C_4\times C_8$ 4A1 8A-1 $a^{5}$
$C_{12}:C_8$ 8B1 $8$ $3$ $C_4\times C_8$ 4A1 8B3 $ab^{2}$
$C_{12}:C_8$ 8B-1 $8$ $3$ $C_4\times C_8$ 4A-1 8B-3 $a^{7}b^{2}$
$C_{12}:C_8$ 8B3 $8$ $3$ $C_4\times C_8$ 4A-1 8B1 $a^{3}b^{2}$
$C_{12}:C_8$ 8B-3 $8$ $3$ $C_4\times C_8$ 4A1 8B-1 $a^{5}b^{2}$
$C_{12}:C_8$ 8C1 $8$ $3$ $C_4\times C_8$ 4B1 8C3 $ab$
$C_{12}:C_8$ 8C-1 $8$ $3$ $C_4\times C_8$ 4B-1 8C-3 $a^{7}b^{3}$
$C_{12}:C_8$ 8C3 $8$ $3$ $C_4\times C_8$ 4B-1 8C1 $a^{3}b^{3}$
$C_{12}:C_8$ 8C-3 $8$ $3$ $C_4\times C_8$ 4B1 8C-1 $a^{5}b$
$C_{12}:C_8$ 8D1 $8$ $3$ $C_4\times C_8$ 4B1 8D3 $ab^{3}$
$C_{12}:C_8$ 8D-1 $8$ $3$ $C_4\times C_8$ 4B-1 8D-3 $a^{7}b$
$C_{12}:C_8$ 8D3 $8$ $3$ $C_4\times C_8$ 4B-1 8D1 $a^{3}b$
$C_{12}:C_8$ 8D-3 $8$ $3$ $C_4\times C_8$ 4B1 8D-1 $a^{5}b^{3}$
$C_{12}:C_8$ 12A1 $12$ $2$ $C_4\times C_{12}$ 6A 4C1 $b$
$C_{12}:C_8$ 12A-1 $12$ $2$ $C_4\times C_{12}$ 6A 4C-1 $b^{7}$
$C_{12}:C_8$ 12B1 $12$ $2$ $C_4\times C_{12}$ 6A 4D1 $a^{4}b$
$C_{12}:C_8$ 12B-1 $12$ $2$ $C_4\times C_{12}$ 6A 4D-1 $a^{4}b^{7}$
$C_{12}:C_8$ 12C1 $12$ $2$ $C_4\times C_{12}$ 6B 4A-1 $a^{2}b^{4}$
$C_{12}:C_8$ 12C-1 $12$ $2$ $C_4\times C_{12}$ 6B 4A1 $a^{6}b^{4}$
$C_{12}:C_8$ 12D1 $12$ $2$ $C_4\times C_{12}$ 6B 4B-1 $a^{2}b^{2}$
$C_{12}:C_8$ 12D-1 $12$ $2$ $C_4\times C_{12}$ 6B 4B1 $a^{6}b^{2}$
$C_{12}:C_8$ 12E1 $12$ $2$ $C_4\times C_{12}$ 6C 4E1 $a^{2}b$
$C_{12}:C_8$ 12E-1 $12$ $2$ $C_4\times C_{12}$ 6C 4E-1 $a^{6}b^{7}$
$C_{12}:C_8$ 12F1 $12$ $2$ $C_4\times C_{12}$ 6C 4F1 $a^{6}b$
$C_{12}:C_8$ 12F-1 $12$ $2$ $C_4\times C_{12}$ 6C 4F-1 $a^{2}b^{7}$
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