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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{2}=b^{14}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 7P
$C_2\times C_{14}$ 1A $1$ $1$ $C_2\times C_{14}$ 1A 1A $1$
$C_2\times C_{14}$ 2A $2$ $1$ $C_2\times C_{14}$ 1A 2A $b^{7}$
$C_2\times C_{14}$ 2B $2$ $1$ $C_2\times C_{14}$ 1A 2B $a$
$C_2\times C_{14}$ 2C $2$ $1$ $C_2\times C_{14}$ 1A 2C $ab^{7}$
$C_2\times C_{14}$ 7A1 $7$ $1$ $C_2\times C_{14}$ 7A2 7A3 $b^{2}$
$C_2\times C_{14}$ 7A-1 $7$ $1$ $C_2\times C_{14}$ 7A-2 7A-3 $b^{12}$
$C_2\times C_{14}$ 7A2 $7$ $1$ $C_2\times C_{14}$ 7A-3 7A-1 $b^{4}$
$C_2\times C_{14}$ 7A-2 $7$ $1$ $C_2\times C_{14}$ 7A3 7A1 $b^{10}$
$C_2\times C_{14}$ 7A3 $7$ $1$ $C_2\times C_{14}$ 7A-1 7A2 $b^{6}$
$C_2\times C_{14}$ 7A-3 $7$ $1$ $C_2\times C_{14}$ 7A1 7A-2 $b^{8}$
$C_2\times C_{14}$ 14A1 $14$ $1$ $C_2\times C_{14}$ 7A1 14A3 $b$
$C_2\times C_{14}$ 14A-1 $14$ $1$ $C_2\times C_{14}$ 7A-1 14A-3 $b^{13}$
$C_2\times C_{14}$ 14A3 $14$ $1$ $C_2\times C_{14}$ 7A3 14A-5 $b^{3}$
$C_2\times C_{14}$ 14A-3 $14$ $1$ $C_2\times C_{14}$ 7A-3 14A5 $b^{11}$
$C_2\times C_{14}$ 14A5 $14$ $1$ $C_2\times C_{14}$ 7A-2 14A1 $b^{5}$
$C_2\times C_{14}$ 14A-5 $14$ $1$ $C_2\times C_{14}$ 7A2 14A-1 $b^{9}$
$C_2\times C_{14}$ 14B1 $14$ $1$ $C_2\times C_{14}$ 7A2 14B3 $ab^{2}$
$C_2\times C_{14}$ 14B-1 $14$ $1$ $C_2\times C_{14}$ 7A-2 14B-3 $ab^{12}$
$C_2\times C_{14}$ 14B3 $14$ $1$ $C_2\times C_{14}$ 7A-1 14B-5 $ab^{6}$
$C_2\times C_{14}$ 14B-3 $14$ $1$ $C_2\times C_{14}$ 7A1 14B5 $ab^{8}$
$C_2\times C_{14}$ 14B5 $14$ $1$ $C_2\times C_{14}$ 7A3 14B1 $ab^{10}$
$C_2\times C_{14}$ 14B-5 $14$ $1$ $C_2\times C_{14}$ 7A-3 14B-1 $ab^{4}$
$C_2\times C_{14}$ 14C1 $14$ $1$ $C_2\times C_{14}$ 7A1 14C3 $ab$
$C_2\times C_{14}$ 14C-1 $14$ $1$ $C_2\times C_{14}$ 7A-1 14C-3 $ab^{13}$
$C_2\times C_{14}$ 14C3 $14$ $1$ $C_2\times C_{14}$ 7A3 14C-5 $ab^{3}$
$C_2\times C_{14}$ 14C-3 $14$ $1$ $C_2\times C_{14}$ 7A-3 14C5 $ab^{11}$
$C_2\times C_{14}$ 14C5 $14$ $1$ $C_2\times C_{14}$ 7A-2 14C1 $ab^{5}$
$C_2\times C_{14}$ 14C-5 $14$ $1$ $C_2\times C_{14}$ 7A2 14C-1 $ab^{9}$
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