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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b, c \mid a^{2}=b^{2}=c^{8}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$C_2^2\times C_8$ 1A $1$ $1$ $C_2^2\times C_8$ 1A $1$
$C_2^2\times C_8$ 2A $2$ $1$ $C_2^2\times C_8$ 1A $b$
$C_2^2\times C_8$ 2B $2$ $1$ $C_2^2\times C_8$ 1A $a$
$C_2^2\times C_8$ 2C $2$ $1$ $C_2^2\times C_8$ 1A $bc^{4}$
$C_2^2\times C_8$ 2D $2$ $1$ $C_2^2\times C_8$ 1A $ac^{4}$
$C_2^2\times C_8$ 2E $2$ $1$ $C_2^2\times C_8$ 1A $ab$
$C_2^2\times C_8$ 2F $2$ $1$ $C_2^2\times C_8$ 1A $abc^{4}$
$C_2^2\times C_8$ 2G $2$ $1$ $C_2^2\times C_8$ 1A $c^{4}$
$C_2^2\times C_8$ 4A1 $4$ $1$ $C_2^2\times C_8$ 2G $bc^{2}$
$C_2^2\times C_8$ 4A-1 $4$ $1$ $C_2^2\times C_8$ 2G $bc^{6}$
$C_2^2\times C_8$ 4B1 $4$ $1$ $C_2^2\times C_8$ 2G $ac^{2}$
$C_2^2\times C_8$ 4B-1 $4$ $1$ $C_2^2\times C_8$ 2G $ac^{6}$
$C_2^2\times C_8$ 4C1 $4$ $1$ $C_2^2\times C_8$ 2G $abc^{2}$
$C_2^2\times C_8$ 4C-1 $4$ $1$ $C_2^2\times C_8$ 2G $abc^{6}$
$C_2^2\times C_8$ 4D1 $4$ $1$ $C_2^2\times C_8$ 2G $c^{2}$
$C_2^2\times C_8$ 4D-1 $4$ $1$ $C_2^2\times C_8$ 2G $c^{6}$
$C_2^2\times C_8$ 8A1 $8$ $1$ $C_2^2\times C_8$ 4D1 $c$
$C_2^2\times C_8$ 8A-1 $8$ $1$ $C_2^2\times C_8$ 4D-1 $c^{7}$
$C_2^2\times C_8$ 8A3 $8$ $1$ $C_2^2\times C_8$ 4D-1 $c^{3}$
$C_2^2\times C_8$ 8A-3 $8$ $1$ $C_2^2\times C_8$ 4D1 $c^{5}$
$C_2^2\times C_8$ 8B1 $8$ $1$ $C_2^2\times C_8$ 4D1 $bc$
$C_2^2\times C_8$ 8B-1 $8$ $1$ $C_2^2\times C_8$ 4D-1 $bc^{7}$
$C_2^2\times C_8$ 8B3 $8$ $1$ $C_2^2\times C_8$ 4D-1 $bc^{3}$
$C_2^2\times C_8$ 8B-3 $8$ $1$ $C_2^2\times C_8$ 4D1 $bc^{5}$
$C_2^2\times C_8$ 8C1 $8$ $1$ $C_2^2\times C_8$ 4D1 $ac$
$C_2^2\times C_8$ 8C-1 $8$ $1$ $C_2^2\times C_8$ 4D-1 $ac^{7}$
$C_2^2\times C_8$ 8C3 $8$ $1$ $C_2^2\times C_8$ 4D-1 $ac^{3}$
$C_2^2\times C_8$ 8C-3 $8$ $1$ $C_2^2\times C_8$ 4D1 $ac^{5}$
$C_2^2\times C_8$ 8D1 $8$ $1$ $C_2^2\times C_8$ 4D1 $abc$
$C_2^2\times C_8$ 8D-1 $8$ $1$ $C_2^2\times C_8$ 4D-1 $abc^{7}$
$C_2^2\times C_8$ 8D3 $8$ $1$ $C_2^2\times C_8$ 4D-1 $abc^{3}$
$C_2^2\times C_8$ 8D-3 $8$ $1$ $C_2^2\times C_8$ 4D1 $abc^{5}$
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