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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{2}=c^{84}=[a,b]=1, c^{a}=c^{13}, c^{b}=c^{71} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 7P
$D_7\times D_{12}$ 1A $1$ $1$ $D_7\times D_{12}$ 1A 1A 1A $1$
$D_7\times D_{12}$ 2A $2$ $1$ $D_7\times D_{12}$ 1A 2A 2A $c^{42}$
$D_7\times D_{12}$ 2B $2$ $6$ $C_2\times D_{14}$ 1A 2B 2B $b$
$D_7\times D_{12}$ 2C $2$ $6$ $C_2\times D_{14}$ 1A 2C 2C $bc^{49}$
$D_7\times D_{12}$ 2D $2$ $7$ $C_2\times D_{12}$ 1A 2D 2D $ac^{60}$
$D_7\times D_{12}$ 2E $2$ $7$ $C_2\times D_{12}$ 1A 2E 2E $ac^{30}$
$D_7\times D_{12}$ 2F $2$ $42$ $C_2^3$ 1A 2F 2F $abc^{76}$
$D_7\times D_{12}$ 2G $2$ $42$ $C_2^3$ 1A 2G 2G $abc^{57}$
$D_7\times D_{12}$ 3A $3$ $2$ $C_{12}\times D_7$ 3A 1A 3A $c^{56}$
$D_7\times D_{12}$ 4A $4$ $2$ $C_{12}\times D_7$ 2A 4A 4A $c^{21}$
$D_7\times D_{12}$ 4B $4$ $14$ $C_2\times C_{12}$ 2A 4B 4B $ac^{15}$
$D_7\times D_{12}$ 6A $6$ $2$ $C_{12}\times D_7$ 3A 2A 6A $c^{14}$
$D_7\times D_{12}$ 6B $6$ $14$ $C_2\times C_{12}$ 3A 2D 6B $ac^{4}$
$D_7\times D_{12}$ 6C $6$ $14$ $C_2\times C_{12}$ 3A 2E 6C $ac^{2}$
$D_7\times D_{12}$ 7A1 $7$ $2$ $C_7\times D_{12}$ 7A2 7A3 1A $c^{24}$
$D_7\times D_{12}$ 7A2 $7$ $2$ $C_7\times D_{12}$ 7A3 7A1 1A $c^{48}$
$D_7\times D_{12}$ 7A3 $7$ $2$ $C_7\times D_{12}$ 7A1 7A2 1A $c^{72}$
$D_7\times D_{12}$ 12A1 $12$ $2$ $C_{12}\times D_7$ 6A 4A 12A5 $c^{7}$
$D_7\times D_{12}$ 12A5 $12$ $2$ $C_{12}\times D_7$ 6A 4A 12A1 $c^{35}$
$D_7\times D_{12}$ 12B1 $12$ $14$ $C_2\times C_{12}$ 6A 4B 12B5 $ac$
$D_7\times D_{12}$ 12B5 $12$ $14$ $C_2\times C_{12}$ 6A 4B 12B1 $ac^{5}$
$D_7\times D_{12}$ 14A1 $14$ $2$ $C_7\times D_{12}$ 7A3 14A3 2A $c^{6}$
$D_7\times D_{12}$ 14A3 $14$ $2$ $C_7\times D_{12}$ 7A2 14A5 2A $c^{18}$
$D_7\times D_{12}$ 14A5 $14$ $2$ $C_7\times D_{12}$ 7A1 14A1 2A $c^{30}$
$D_7\times D_{12}$ 14B1 $14$ $12$ $C_2\times C_{14}$ 7A1 14B3 2B $bc^{12}$
$D_7\times D_{12}$ 14B3 $14$ $12$ $C_2\times C_{14}$ 7A3 14B5 2B $bc^{8}$
$D_7\times D_{12}$ 14B5 $14$ $12$ $C_2\times C_{14}$ 7A2 14B1 2B $bc^{4}$
$D_7\times D_{12}$ 14C1 $14$ $12$ $C_2\times C_{14}$ 7A3 14C3 2C $bc$
$D_7\times D_{12}$ 14C3 $14$ $12$ $C_2\times C_{14}$ 7A2 14C5 2C $bc^{3}$
$D_7\times D_{12}$ 14C5 $14$ $12$ $C_2\times C_{14}$ 7A1 14C1 2C $bc^{5}$
$D_7\times D_{12}$ 21A1 $21$ $4$ $C_{84}$ 21A2 7A3 3A $c^{4}$
$D_7\times D_{12}$ 21A2 $21$ $4$ $C_{84}$ 21A4 7A1 3A $c^{8}$
$D_7\times D_{12}$ 21A4 $21$ $4$ $C_{84}$ 21A1 7A2 3A $c^{16}$
$D_7\times D_{12}$ 28A1 $28$ $4$ $C_{84}$ 14A1 28A3 4A $c^{3}$
$D_7\times D_{12}$ 28A3 $28$ $4$ $C_{84}$ 14A3 28A5 4A $c^{9}$
$D_7\times D_{12}$ 28A5 $28$ $4$ $C_{84}$ 14A5 28A1 4A $c^{15}$
$D_7\times D_{12}$ 42A1 $42$ $4$ $C_{84}$ 21A1 14A1 6A $c^{2}$
$D_7\times D_{12}$ 42A5 $42$ $4$ $C_{84}$ 21A2 14A5 6A $c^{10}$
$D_7\times D_{12}$ 42A11 $42$ $4$ $C_{84}$ 21A4 14A3 6A $c^{22}$
$D_7\times D_{12}$ 84A1 $84$ $4$ $C_{84}$ 42A1 28A1 12A1 $c$
$D_7\times D_{12}$ 84A5 $84$ $4$ $C_{84}$ 42A5 28A5 12A5 $c^{5}$
$D_7\times D_{12}$ 84A11 $84$ $4$ $C_{84}$ 42A11 28A3 12A1 $c^{25}$
$D_7\times D_{12}$ 84A17 $84$ $4$ $C_{84}$ 42A11 28A3 12A5 $c^{17}$
$D_7\times D_{12}$ 84A23 $84$ $4$ $C_{84}$ 42A5 28A5 12A1 $c^{37}$
$D_7\times D_{12}$ 84A29 $84$ $4$ $C_{84}$ 42A1 28A1 12A5 $c^{29}$
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