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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{8}=c^{21}=[a,c]=1, a^{2}=b^{4}, b^{a}=b^{7}, c^{b}=c^{20} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 7P
$C_{21}:Q_{16}$ 1A $1$ $1$ $C_{21}:Q_{16}$ 1A 1A 1A $1$
$C_{21}:Q_{16}$ 2A $2$ $1$ $C_{21}:Q_{16}$ 1A 2A 2A $b^{4}$
$C_{21}:Q_{16}$ 3A $3$ $2$ $Q_8\times C_{21}$ 3A 1A 3A $c^{7}$
$C_{21}:Q_{16}$ 4A $4$ $2$ $C_{21}:C_8$ 2A 4A 4A $b^{2}$
$C_{21}:Q_{16}$ 4B $4$ $4$ $C_{84}$ 2A 4B 4B $a$
$C_{21}:Q_{16}$ 4C $4$ $84$ $C_4$ 2A 4C 4C $abc^{2}$
$C_{21}:Q_{16}$ 6A $6$ $2$ $Q_8\times C_{21}$ 3A 2A 6A $b^{4}c^{14}$
$C_{21}:Q_{16}$ 7A1 $7$ $2$ $Q_8\times C_{21}$ 7A2 7A3 1A $c^{12}$
$C_{21}:Q_{16}$ 7A2 $7$ $2$ $Q_8\times C_{21}$ 7A3 7A1 1A $c^{3}$
$C_{21}:Q_{16}$ 7A3 $7$ $2$ $Q_8\times C_{21}$ 7A1 7A2 1A $c^{15}$
$C_{21}:Q_{16}$ 8A1 $8$ $42$ $C_8$ 4A 8A3 8A1 $b^{3}c^{20}$
$C_{21}:Q_{16}$ 8A3 $8$ $42$ $C_8$ 4A 8A1 8A3 $bc^{20}$
$C_{21}:Q_{16}$ 12A $12$ $4$ $C_{84}$ 6A 4A 12A $b^{6}c^{7}$
$C_{21}:Q_{16}$ 12B1 $12$ $4$ $C_{84}$ 6A 4B 12B1 $ab^{4}c^{7}$
$C_{21}:Q_{16}$ 12B-1 $12$ $4$ $C_{84}$ 6A 4B 12B-1 $ac^{14}$
$C_{21}:Q_{16}$ 14A1 $14$ $2$ $Q_8\times C_{21}$ 7A1 14A3 2A $b^{4}c^{6}$
$C_{21}:Q_{16}$ 14A3 $14$ $2$ $Q_8\times C_{21}$ 7A3 14A5 2A $b^{4}c^{18}$
$C_{21}:Q_{16}$ 14A5 $14$ $2$ $Q_8\times C_{21}$ 7A2 14A1 2A $b^{4}c^{9}$
$C_{21}:Q_{16}$ 21A1 $21$ $2$ $Q_8\times C_{21}$ 21A2 7A1 3A $c^{4}$
$C_{21}:Q_{16}$ 21A2 $21$ $2$ $Q_8\times C_{21}$ 21A4 7A2 3A $c^{8}$
$C_{21}:Q_{16}$ 21A4 $21$ $2$ $Q_8\times C_{21}$ 21A8 7A3 3A $c^{16}$
$C_{21}:Q_{16}$ 21A5 $21$ $2$ $Q_8\times C_{21}$ 21A10 7A2 3A $c^{20}$
$C_{21}:Q_{16}$ 21A8 $21$ $2$ $Q_8\times C_{21}$ 21A5 7A1 3A $c^{11}$
$C_{21}:Q_{16}$ 21A10 $21$ $2$ $Q_8\times C_{21}$ 21A1 7A3 3A $c^{19}$
$C_{21}:Q_{16}$ 28A1 $28$ $4$ $C_{84}$ 14A1 28A3 4A $b^{6}c^{3}$
$C_{21}:Q_{16}$ 28A3 $28$ $4$ $C_{84}$ 14A3 28A5 4A $b^{2}c^{9}$
$C_{21}:Q_{16}$ 28A5 $28$ $4$ $C_{84}$ 14A5 28A1 4A $b^{6}c^{15}$
$C_{21}:Q_{16}$ 28B1 $28$ $4$ $C_{84}$ 14A1 28B3 4B $ab^{4}c^{3}$
$C_{21}:Q_{16}$ 28B-1 $28$ $4$ $C_{84}$ 14A1 28B-3 4B $ac^{18}$
$C_{21}:Q_{16}$ 28B3 $28$ $4$ $C_{84}$ 14A3 28B-5 4B $ac^{9}$
$C_{21}:Q_{16}$ 28B-3 $28$ $4$ $C_{84}$ 14A3 28B5 4B $ab^{4}c^{12}$
$C_{21}:Q_{16}$ 28B5 $28$ $4$ $C_{84}$ 14A5 28B1 4B $ab^{4}c^{15}$
$C_{21}:Q_{16}$ 28B-5 $28$ $4$ $C_{84}$ 14A5 28B-1 4B $ac^{6}$
$C_{21}:Q_{16}$ 42A1 $42$ $2$ $Q_8\times C_{21}$ 21A1 14A1 6A $b^{4}c^{2}$
$C_{21}:Q_{16}$ 42A5 $42$ $2$ $Q_8\times C_{21}$ 21A5 14A5 6A $b^{4}c^{10}$
$C_{21}:Q_{16}$ 42A11 $42$ $2$ $Q_8\times C_{21}$ 21A10 14A3 6A $b^{4}c$
$C_{21}:Q_{16}$ 42A13 $42$ $2$ $Q_8\times C_{21}$ 21A8 14A1 6A $b^{4}c^{5}$
$C_{21}:Q_{16}$ 42A17 $42$ $2$ $Q_8\times C_{21}$ 21A4 14A3 6A $b^{4}c^{13}$
$C_{21}:Q_{16}$ 42A19 $42$ $2$ $Q_8\times C_{21}$ 21A2 14A5 6A $b^{4}c^{17}$
$C_{21}:Q_{16}$ 84A1 $84$ $4$ $C_{84}$ 42A1 28A1 12A $b^{2}c$
$C_{21}:Q_{16}$ 84A5 $84$ $4$ $C_{84}$ 42A5 28A5 12A $b^{2}c^{5}$
$C_{21}:Q_{16}$ 84A11 $84$ $4$ $C_{84}$ 42A11 28A3 12A $b^{2}c^{10}$
$C_{21}:Q_{16}$ 84A13 $84$ $4$ $C_{84}$ 42A13 28A1 12A $b^{2}c^{8}$
$C_{21}:Q_{16}$ 84A17 $84$ $4$ $C_{84}$ 42A17 28A3 12A $b^{2}c^{4}$
$C_{21}:Q_{16}$ 84A19 $84$ $4$ $C_{84}$ 42A19 28A5 12A $b^{2}c^{2}$
$C_{21}:Q_{16}$ 84B1 $84$ $4$ $C_{84}$ 42A1 28B1 12B1 $ac$
$C_{21}:Q_{16}$ 84B-1 $84$ $4$ $C_{84}$ 42A1 28B-1 12B-1 $ab^{2}c$
$C_{21}:Q_{16}$ 84B5 $84$ $4$ $C_{84}$ 42A5 28B5 12B-1 $ac^{5}$
$C_{21}:Q_{16}$ 84B-5 $84$ $4$ $C_{84}$ 42A5 28B-5 12B1 $ac^{16}$
$C_{21}:Q_{16}$ 84B11 $84$ $4$ $C_{84}$ 42A11 28B-3 12B-1 $ac^{11}$
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