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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid b^{2}=c^{4}=d^{84}=[a,b]=[b,c]=[b,d]=1, a^{2}=d^{42}, c^{a}=c^{3}, d^{a}=d^{55}, d^{c}=d^{29} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 7P
$C_2\times C_{12}.D_{28}$ 1A $1$ $1$ $C_2\times C_{12}.D_{28}$ 1A 1A 1A $1$
$C_2\times C_{12}.D_{28}$ 2A $2$ $1$ $C_2\times C_{12}.D_{28}$ 1A 2A 2A $d^{42}$
$C_2\times C_{12}.D_{28}$ 2B $2$ $1$ $C_2\times C_{12}.D_{28}$ 1A 2B 2B $c^{2}$
$C_2\times C_{12}.D_{28}$ 2C $2$ $1$ $C_2\times C_{12}.D_{28}$ 1A 2C 2C $c^{2}d^{42}$
$C_2\times C_{12}.D_{28}$ 2D $2$ $1$ $C_2\times C_{12}.D_{28}$ 1A 2D 2D $b$
$C_2\times C_{12}.D_{28}$ 2E $2$ $1$ $C_2\times C_{12}.D_{28}$ 1A 2E 2E $bd^{42}$
$C_2\times C_{12}.D_{28}$ 2F $2$ $1$ $C_2\times C_{12}.D_{28}$ 1A 2F 2F $bc^{2}$
$C_2\times C_{12}.D_{28}$ 2G $2$ $1$ $C_2\times C_{12}.D_{28}$ 1A 2G 2G $bc^{2}d^{42}$
$C_2\times C_{12}.D_{28}$ 3A $3$ $2$ $C_{84}.C_2^3$ 3A 1A 3A $d^{28}$
$C_2\times C_{12}.D_{28}$ 4A $4$ $2$ $C_{42}:C_4^2$ 2A 4A 4A $d^{21}$
$C_2\times C_{12}.D_{28}$ 4B $4$ $2$ $C_{42}:C_4^2$ 2A 4B 4B $c^{2}d^{21}$
$C_2\times C_{12}.D_{28}$ 4C $4$ $2$ $C_{42}:C_4^2$ 2A 4C 4C $bd^{21}$
$C_2\times C_{12}.D_{28}$ 4D $4$ $2$ $C_{42}:C_4^2$ 2A 4D 4D $bc^{2}d^{21}$
$C_2\times C_{12}.D_{28}$ 4E $4$ $6$ $C_2\times C_4\times C_{28}$ 2B 4E 4E $c^{3}$
$C_2\times C_{12}.D_{28}$ 4F $4$ $6$ $C_2\times C_4\times C_{28}$ 2B 4F 4F $c^{3}d^{14}$
$C_2\times C_{12}.D_{28}$ 4G $4$ $6$ $C_2\times C_4\times C_{28}$ 2C 4G 4G $c^{3}d^{7}$
$C_2\times C_{12}.D_{28}$ 4H $4$ $6$ $C_2\times C_4\times C_{28}$ 2C 4H 4H $c^{3}d^{21}$
$C_2\times C_{12}.D_{28}$ 4I $4$ $6$ $C_2\times C_4\times C_{28}$ 2B 4I 4I $bc^{3}$
$C_2\times C_{12}.D_{28}$ 4J $4$ $6$ $C_2\times C_4\times C_{28}$ 2B 4J 4J $bc^{3}d^{14}$
$C_2\times C_{12}.D_{28}$ 4K $4$ $6$ $C_2\times C_4\times C_{28}$ 2C 4K 4K $bc^{3}d^{7}$
$C_2\times C_{12}.D_{28}$ 4L $4$ $6$ $C_2\times C_4\times C_{28}$ 2C 4L 4L $bc^{3}d^{21}$
$C_2\times C_{12}.D_{28}$ 4M $4$ $28$ $C_2^2\times C_{12}$ 2A 4M 4M $ad^{18}$
$C_2\times C_{12}.D_{28}$ 4N $4$ $28$ $C_2^2\times C_{12}$ 2A 4N 4N $ad^{15}$
$C_2\times C_{12}.D_{28}$ 4O $4$ $28$ $C_2^2\times C_{12}$ 2A 4O 4O $abd^{18}$
$C_2\times C_{12}.D_{28}$ 4P $4$ $28$ $C_2^2\times C_{12}$ 2A 4P 4P $abd^{15}$
$C_2\times C_{12}.D_{28}$ 4Q $4$ $84$ $C_2^2\times C_4$ 2A 4Q 4Q $abcd^{39}$
$C_2\times C_{12}.D_{28}$ 4R $4$ $84$ $C_2^2\times C_4$ 2A 4R 4R $abc^{3}d^{38}$
$C_2\times C_{12}.D_{28}$ 4S $4$ $84$ $C_2^2\times C_4$ 2A 4S 4S $ac^{3}d^{30}$
$C_2\times C_{12}.D_{28}$ 4T $4$ $84$ $C_2^2\times C_4$ 2A 4T 4T $ac^{3}d^{5}$
$C_2\times C_{12}.D_{28}$ 6A $6$ $2$ $C_{84}.C_2^3$ 3A 2A 6A $d^{14}$
$C_2\times C_{12}.D_{28}$ 6B $6$ $2$ $C_{84}.C_2^3$ 3A 2B 6B $c^{2}d^{28}$
$C_2\times C_{12}.D_{28}$ 6C $6$ $2$ $C_{84}.C_2^3$ 3A 2C 6C $c^{2}d^{14}$
$C_2\times C_{12}.D_{28}$ 6D $6$ $2$ $C_{84}.C_2^3$ 3A 2D 6D $bd^{28}$
$C_2\times C_{12}.D_{28}$ 6E $6$ $2$ $C_{84}.C_2^3$ 3A 2E 6E $bd^{14}$
$C_2\times C_{12}.D_{28}$ 6F $6$ $2$ $C_{84}.C_2^3$ 3A 2F 6F $bc^{2}d^{28}$
$C_2\times C_{12}.D_{28}$ 6G $6$ $2$ $C_{84}.C_2^3$ 3A 2G 6G $bc^{2}d^{14}$
$C_2\times C_{12}.D_{28}$ 7A1 $7$ $2$ $C_{42}:C_4^2$ 7A2 7A3 1A $d^{48}$
$C_2\times C_{12}.D_{28}$ 7A2 $7$ $2$ $C_{42}:C_4^2$ 7A3 7A1 1A $d^{12}$
$C_2\times C_{12}.D_{28}$ 7A3 $7$ $2$ $C_{42}:C_4^2$ 7A1 7A2 1A $d^{60}$
$C_2\times C_{12}.D_{28}$ 12A $12$ $4$ $C_2^2\times C_{84}$ 6A 4A 12A $d^{7}$
$C_2\times C_{12}.D_{28}$ 12B $12$ $4$ $C_2^2\times C_{84}$ 6A 4B 12B $c^{2}d^{7}$
$C_2\times C_{12}.D_{28}$ 12C $12$ $4$ $C_2^2\times C_{84}$ 6A 4C 12C $bd^{7}$
$C_2\times C_{12}.D_{28}$ 12D $12$ $4$ $C_2^2\times C_{84}$ 6A 4D 12D $bc^{2}d^{7}$
$C_2\times C_{12}.D_{28}$ 12E1 $12$ $28$ $C_2^2\times C_{12}$ 6A 4M 12E1 $ad^{4}$
$C_2\times C_{12}.D_{28}$ 12E-1 $12$ $28$ $C_2^2\times C_{12}$ 6A 4M 12E-1 $ad^{2}$
$C_2\times C_{12}.D_{28}$ 12F1 $12$ $28$ $C_2^2\times C_{12}$ 6A 4N 12F1 $ad$
$C_2\times C_{12}.D_{28}$ 12F-1 $12$ $28$ $C_2^2\times C_{12}$ 6A 4N 12F-1 $ad^{5}$
$C_2\times C_{12}.D_{28}$ 12G1 $12$ $28$ $C_2^2\times C_{12}$ 6A 4O 12G1 $abd^{4}$
$C_2\times C_{12}.D_{28}$ 12G-1 $12$ $28$ $C_2^2\times C_{12}$ 6A 4O 12G-1 $abd^{2}$
$C_2\times C_{12}.D_{28}$ 12H1 $12$ $28$ $C_2^2\times C_{12}$ 6A 4P 12H1 $abd$
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