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Results (28 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{8}=b^{8}=1, b^{a}=b^{3} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$C_8:C_8$ 1A $1$ $1$ $C_8:C_8$ 1A $1$
$C_8:C_8$ 2A $2$ $1$ $C_8:C_8$ 1A $a^{4}b^{4}$
$C_8:C_8$ 2B $2$ $1$ $C_8:C_8$ 1A $b^{4}$
$C_8:C_8$ 2C $2$ $1$ $C_8:C_8$ 1A $a^{4}$
$C_8:C_8$ 4A1 $4$ $1$ $C_8:C_8$ 2C $a^{2}$
$C_8:C_8$ 4A-1 $4$ $1$ $C_8:C_8$ 2C $a^{6}$
$C_8:C_8$ 4B1 $4$ $1$ $C_8:C_8$ 2C $a^{2}b^{4}$
$C_8:C_8$ 4B-1 $4$ $1$ $C_8:C_8$ 2C $a^{6}b^{4}$
$C_8:C_8$ 4C $4$ $2$ $C_4\times C_8$ 2B $b^{2}$
$C_8:C_8$ 4D $4$ $2$ $C_4\times C_8$ 2B $a^{4}b^{2}$
$C_8:C_8$ 4E1 $4$ $2$ $C_4\times C_8$ 2A $a^{2}b^{2}$
$C_8:C_8$ 4E-1 $4$ $2$ $C_4\times C_8$ 2A $a^{6}b^{2}$
$C_8:C_8$ 8A1 $8$ $2$ $C_4\times C_8$ 4C $b$
$C_8:C_8$ 8A-1 $8$ $2$ $C_4\times C_8$ 4C $b^{5}$
$C_8:C_8$ 8B1 $8$ $2$ $C_4\times C_8$ 4C $a^{4}b$
$C_8:C_8$ 8B-1 $8$ $2$ $C_4\times C_8$ 4C $a^{4}b^{5}$
$C_8:C_8$ 8C1 $8$ $2$ $C_4\times C_8$ 4D $a^{2}b$
$C_8:C_8$ 8C-1 $8$ $2$ $C_4\times C_8$ 4D $a^{6}b^{5}$
$C_8:C_8$ 8C3 $8$ $2$ $C_4\times C_8$ 4D $a^{6}b$
$C_8:C_8$ 8C-3 $8$ $2$ $C_4\times C_8$ 4D $a^{2}b^{5}$
$C_8:C_8$ 8D1 $8$ $4$ $C_2\times C_8$ 4A1 $a$
$C_8:C_8$ 8D-1 $8$ $4$ $C_2\times C_8$ 4A-1 $a^{7}$
$C_8:C_8$ 8D3 $8$ $4$ $C_2\times C_8$ 4A-1 $a^{3}$
$C_8:C_8$ 8D-3 $8$ $4$ $C_2\times C_8$ 4A1 $a^{5}$
$C_8:C_8$ 8E1 $8$ $4$ $C_2\times C_8$ 4B1 $ab$
$C_8:C_8$ 8E-1 $8$ $4$ $C_2\times C_8$ 4B-1 $a^{7}b$
$C_8:C_8$ 8E3 $8$ $4$ $C_2\times C_8$ 4B-1 $a^{3}b$
$C_8:C_8$ 8E-3 $8$ $4$ $C_2\times C_8$ 4B1 $a^{5}b$
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