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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{2}=c^{12}=d^{14}=[a,b]=[a,c]=[a,d]=[b,c]=[b,d]=1, d^{c}=d^{5} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 7P
$C_2^4.F_7$ 1A $1$ $1$ $C_2^4.F_7$ 1A 1A 1A $1$
$C_2^4.F_7$ 2A $2$ $1$ $C_2^4.F_7$ 1A 2A 2A $d^{7}$
$C_2^4.F_7$ 2B $2$ $1$ $C_2^4.F_7$ 1A 2B 2B $c^{6}d^{7}$
$C_2^4.F_7$ 2C $2$ $1$ $C_2^4.F_7$ 1A 2C 2C $b$
$C_2^4.F_7$ 2D $2$ $1$ $C_2^4.F_7$ 1A 2D 2D $bc^{6}$
$C_2^4.F_7$ 2E $2$ $1$ $C_2^4.F_7$ 1A 2E 2E $a$
$C_2^4.F_7$ 2F $2$ $1$ $C_2^4.F_7$ 1A 2F 2F $ac^{6}$
$C_2^4.F_7$ 2G $2$ $1$ $C_2^4.F_7$ 1A 2G 2G $bd^{7}$
$C_2^4.F_7$ 2H $2$ $1$ $C_2^4.F_7$ 1A 2H 2H $bc^{6}d^{7}$
$C_2^4.F_7$ 2I $2$ $1$ $C_2^4.F_7$ 1A 2I 2I $ad^{7}$
$C_2^4.F_7$ 2J $2$ $1$ $C_2^4.F_7$ 1A 2J 2J $ac^{6}d^{7}$
$C_2^4.F_7$ 2K $2$ $1$ $C_2^4.F_7$ 1A 2K 2K $ab$
$C_2^4.F_7$ 2L $2$ $1$ $C_2^4.F_7$ 1A 2L 2L $abc^{6}$
$C_2^4.F_7$ 2M $2$ $1$ $C_2^4.F_7$ 1A 2M 2M $abd^{7}$
$C_2^4.F_7$ 2N $2$ $1$ $C_2^4.F_7$ 1A 2N 2N $abc^{6}d^{7}$
$C_2^4.F_7$ 2O $2$ $1$ $C_2^4.F_7$ 1A 2O 2O $c^{6}$
$C_2^4.F_7$ 3A1 $3$ $7$ $C_2^3\times C_{12}$ 3A-1 1A 3A1 $c^{8}d^{10}$
$C_2^4.F_7$ 3A-1 $3$ $7$ $C_2^3\times C_{12}$ 3A1 1A 3A-1 $c^{4}d^{8}$
$C_2^4.F_7$ 4A1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4A-1 4A-1 $c^{3}$
$C_2^4.F_7$ 4A-1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4A1 4A1 $c^{9}$
$C_2^4.F_7$ 4B1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4B-1 4B-1 $c^{3}d^{3}$
$C_2^4.F_7$ 4B-1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4B1 4B1 $c^{9}d^{3}$
$C_2^4.F_7$ 4C1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4C-1 4C-1 $bc^{3}$
$C_2^4.F_7$ 4C-1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4C1 4C1 $bc^{9}$
$C_2^4.F_7$ 4D1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4D-1 4D-1 $ac^{3}$
$C_2^4.F_7$ 4D-1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4D1 4D1 $ac^{9}$
$C_2^4.F_7$ 4E1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4E-1 4E-1 $bc^{3}d^{3}$
$C_2^4.F_7$ 4E-1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4E1 4E1 $bc^{9}d^{3}$
$C_2^4.F_7$ 4F1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4F-1 4F-1 $ac^{3}d^{3}$
$C_2^4.F_7$ 4F-1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4F1 4F1 $ac^{9}d^{3}$
$C_2^4.F_7$ 4G1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4G-1 4G-1 $abc^{3}$
$C_2^4.F_7$ 4G-1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4G1 4G1 $abc^{9}$
$C_2^4.F_7$ 4H1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4H-1 4H-1 $abc^{3}d^{3}$
$C_2^4.F_7$ 4H-1 $4$ $7$ $C_2^3\times C_{12}$ 2O 4H1 4H1 $abc^{9}d^{3}$
$C_2^4.F_7$ 6A1 $6$ $7$ $C_2^3\times C_{12}$ 3A1 2A 6A1 $c^{4}d$
$C_2^4.F_7$ 6A-1 $6$ $7$ $C_2^3\times C_{12}$ 3A-1 2A 6A-1 $c^{8}d$
$C_2^4.F_7$ 6B1 $6$ $7$ $C_2^3\times C_{12}$ 3A-1 2B 6B1 $c^{2}d$
$C_2^4.F_7$ 6B-1 $6$ $7$ $C_2^3\times C_{12}$ 3A1 2B 6B-1 $c^{10}d$
$C_2^4.F_7$ 6C1 $6$ $7$ $C_2^3\times C_{12}$ 3A1 2C 6C1 $bc^{4}$
$C_2^4.F_7$ 6C-1 $6$ $7$ $C_2^3\times C_{12}$ 3A-1 2C 6C-1 $bc^{8}$
$C_2^4.F_7$ 6D1 $6$ $7$ $C_2^3\times C_{12}$ 3A-1 2D 6D1 $bc^{2}$
$C_2^4.F_7$ 6D-1 $6$ $7$ $C_2^3\times C_{12}$ 3A1 2D 6D-1 $bc^{10}$
$C_2^4.F_7$ 6E1 $6$ $7$ $C_2^3\times C_{12}$ 3A1 2E 6E1 $ac^{4}$
$C_2^4.F_7$ 6E-1 $6$ $7$ $C_2^3\times C_{12}$ 3A-1 2E 6E-1 $ac^{8}$
$C_2^4.F_7$ 6F1 $6$ $7$ $C_2^3\times C_{12}$ 3A-1 2F 6F1 $ac^{2}$
$C_2^4.F_7$ 6F-1 $6$ $7$ $C_2^3\times C_{12}$ 3A1 2F 6F-1 $ac^{10}$
$C_2^4.F_7$ 6G1 $6$ $7$ $C_2^3\times C_{12}$ 3A1 2G 6G1 $bc^{4}d$
$C_2^4.F_7$ 6G-1 $6$ $7$ $C_2^3\times C_{12}$ 3A-1 2G 6G-1 $bc^{8}d$
$C_2^4.F_7$ 6H1 $6$ $7$ $C_2^3\times C_{12}$ 3A-1 2H 6H1 $bc^{2}d$
$C_2^4.F_7$ 6H-1 $6$ $7$ $C_2^3\times C_{12}$ 3A1 2H 6H-1 $bc^{10}d$
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