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Results (34 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{28}=c^{2}=[a,c]=[b,c]=1, a^{2}=b^{14}, b^{a}=b^{27} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 7P
$C_{14}:Q_8$ 1A $1$ $1$ $C_{14}:Q_8$ 1A 1A $1$
$C_{14}:Q_8$ 2A $2$ $1$ $C_{14}:Q_8$ 1A 2A $c$
$C_{14}:Q_8$ 2B $2$ $1$ $C_{14}:Q_8$ 1A 2B $b^{14}c$
$C_{14}:Q_8$ 2C $2$ $1$ $C_{14}:Q_8$ 1A 2C $b^{14}$
$C_{14}:Q_8$ 4A $4$ $2$ $C_2\times C_{28}$ 2C 4A $b^{7}$
$C_{14}:Q_8$ 4B $4$ $2$ $C_2\times C_{28}$ 2C 4B $b^{7}c$
$C_{14}:Q_8$ 4C $4$ $14$ $C_2\times C_4$ 2C 4C $ab^{11}c$
$C_{14}:Q_8$ 4D $4$ $14$ $C_2\times C_4$ 2C 4D $ab^{14}c$
$C_{14}:Q_8$ 4E $4$ $14$ $C_2\times C_4$ 2C 4E $ab^{6}$
$C_{14}:Q_8$ 4F $4$ $14$ $C_2\times C_4$ 2C 4F $ab^{21}$
$C_{14}:Q_8$ 7A1 $7$ $2$ $C_2\times C_{28}$ 7A2 7A3 $b^{8}$
$C_{14}:Q_8$ 7A2 $7$ $2$ $C_2\times C_{28}$ 7A3 7A1 $b^{16}$
$C_{14}:Q_8$ 7A3 $7$ $2$ $C_2\times C_{28}$ 7A1 7A2 $b^{24}$
$C_{14}:Q_8$ 14A1 $14$ $2$ $C_2\times C_{28}$ 7A1 14A3 $b^{4}c$
$C_{14}:Q_8$ 14A3 $14$ $2$ $C_2\times C_{28}$ 7A3 14A5 $b^{12}c$
$C_{14}:Q_8$ 14A5 $14$ $2$ $C_2\times C_{28}$ 7A2 14A1 $b^{8}c$
$C_{14}:Q_8$ 14B1 $14$ $2$ $C_2\times C_{28}$ 7A3 14B3 $b^{2}c$
$C_{14}:Q_8$ 14B3 $14$ $2$ $C_2\times C_{28}$ 7A2 14B5 $b^{6}c$
$C_{14}:Q_8$ 14B5 $14$ $2$ $C_2\times C_{28}$ 7A1 14B1 $b^{10}c$
$C_{14}:Q_8$ 14C1 $14$ $2$ $C_2\times C_{28}$ 7A3 14C3 $b^{2}$
$C_{14}:Q_8$ 14C3 $14$ $2$ $C_2\times C_{28}$ 7A2 14C5 $b^{6}$
$C_{14}:Q_8$ 14C5 $14$ $2$ $C_2\times C_{28}$ 7A1 14C1 $b^{10}$
$C_{14}:Q_8$ 28A1 $28$ $2$ $C_2\times C_{28}$ 14C1 28A3 $b$
$C_{14}:Q_8$ 28A3 $28$ $2$ $C_2\times C_{28}$ 14C3 28A9 $b^{3}$
$C_{14}:Q_8$ 28A5 $28$ $2$ $C_2\times C_{28}$ 14C5 28A13 $b^{5}$
$C_{14}:Q_8$ 28A9 $28$ $2$ $C_2\times C_{28}$ 14C5 28A1 $b^{9}$
$C_{14}:Q_8$ 28A11 $28$ $2$ $C_2\times C_{28}$ 14C3 28A5 $b^{17}$
$C_{14}:Q_8$ 28A13 $28$ $2$ $C_2\times C_{28}$ 14C1 28A11 $b^{13}$
$C_{14}:Q_8$ 28B1 $28$ $2$ $C_2\times C_{28}$ 14C1 28B3 $bc$
$C_{14}:Q_8$ 28B3 $28$ $2$ $C_2\times C_{28}$ 14C3 28B9 $b^{3}c$
$C_{14}:Q_8$ 28B5 $28$ $2$ $C_2\times C_{28}$ 14C5 28B13 $b^{5}c$
$C_{14}:Q_8$ 28B9 $28$ $2$ $C_2\times C_{28}$ 14C5 28B1 $b^{9}c$
$C_{14}:Q_8$ 28B11 $28$ $2$ $C_2\times C_{28}$ 14C3 28B5 $b^{17}c$
$C_{14}:Q_8$ 28B13 $28$ $2$ $C_2\times C_{28}$ 14C1 28B11 $b^{13}c$
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