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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{4}=b^{8}=1 \rangle$ .

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