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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{20}=c^{14}=[a,c]=1, b^{a}=b^{19}, c^{b}=c^{13} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 7P
$C_{14}:D_{20}$ 1A $1$ $1$ $C_{14}:D_{20}$ 1A 1A 1A $1$
$C_{14}:D_{20}$ 2A $2$ $1$ $C_{14}:D_{20}$ 1A 2A 2A $b^{10}$
$C_{14}:D_{20}$ 2B $2$ $1$ $C_{14}:D_{20}$ 1A 2B 2B $c^{7}$
$C_{14}:D_{20}$ 2C $2$ $1$ $C_{14}:D_{20}$ 1A 2C 2C $b^{10}c^{7}$
$C_{14}:D_{20}$ 2D $2$ $10$ $C_2^2\times C_{14}$ 1A 2D 2D $a$
$C_{14}:D_{20}$ 2E $2$ $10$ $C_2^2\times C_{14}$ 1A 2E 2E $ac^{7}$
$C_{14}:D_{20}$ 2F $2$ $70$ $C_2^3$ 1A 2F 2F $ab^{9}c$
$C_{14}:D_{20}$ 2G $2$ $70$ $C_2^3$ 1A 2G 2G $ab^{5}c^{2}$
$C_{14}:D_{20}$ 4A $4$ $14$ $C_2\times C_{20}$ 2A 4A 4A $b^{5}$
$C_{14}:D_{20}$ 4B $4$ $14$ $C_2\times C_{20}$ 2A 4B 4B $b^{5}c$
$C_{14}:D_{20}$ 5A1 $5$ $2$ $C_{14}:C_{20}$ 5A2 5A2 1A $b^{4}$
$C_{14}:D_{20}$ 5A2 $5$ $2$ $C_{14}:C_{20}$ 5A1 5A1 1A $b^{8}$
$C_{14}:D_{20}$ 7A1 $7$ $2$ $C_{14}\times D_{10}$ 7A2 7A3 7A2 $c^{4}$
$C_{14}:D_{20}$ 7A2 $7$ $2$ $C_{14}\times D_{10}$ 7A3 7A1 7A3 $c^{8}$
$C_{14}:D_{20}$ 7A3 $7$ $2$ $C_{14}\times D_{10}$ 7A1 7A2 7A1 $c^{12}$
$C_{14}:D_{20}$ 10A1 $10$ $2$ $C_{14}:C_{20}$ 5A1 10A3 2A $b^{2}$
$C_{14}:D_{20}$ 10A3 $10$ $2$ $C_{14}:C_{20}$ 5A2 10A1 2A $b^{6}$
$C_{14}:D_{20}$ 10B1 $10$ $2$ $C_{14}:C_{20}$ 5A1 10B3 2B $b^{8}c^{7}$
$C_{14}:D_{20}$ 10B3 $10$ $2$ $C_{14}:C_{20}$ 5A2 10B1 2B $b^{4}c^{7}$
$C_{14}:D_{20}$ 10C1 $10$ $2$ $C_{14}:C_{20}$ 5A2 10C3 2C $b^{14}c^{7}$
$C_{14}:D_{20}$ 10C3 $10$ $2$ $C_{14}:C_{20}$ 5A1 10C1 2C $b^{2}c^{7}$
$C_{14}:D_{20}$ 14A1 $14$ $2$ $C_{14}\times D_{10}$ 7A1 14A3 14A5 $c^{5}$
$C_{14}:D_{20}$ 14A3 $14$ $2$ $C_{14}\times D_{10}$ 7A3 14A5 14A1 $c$
$C_{14}:D_{20}$ 14A5 $14$ $2$ $C_{14}\times D_{10}$ 7A2 14A1 14A3 $c^{11}$
$C_{14}:D_{20}$ 14B1 $14$ $2$ $C_{14}\times D_{10}$ 7A2 14B3 14B5 $b^{10}c^{10}$
$C_{14}:D_{20}$ 14B3 $14$ $2$ $C_{14}\times D_{10}$ 7A1 14B5 14B1 $b^{10}c^{2}$
$C_{14}:D_{20}$ 14B5 $14$ $2$ $C_{14}\times D_{10}$ 7A3 14B1 14B3 $b^{10}c^{8}$
$C_{14}:D_{20}$ 14C1 $14$ $2$ $C_{14}\times D_{10}$ 7A1 14C3 14C5 $b^{10}c^{5}$
$C_{14}:D_{20}$ 14C3 $14$ $2$ $C_{14}\times D_{10}$ 7A3 14C5 14C1 $b^{10}c$
$C_{14}:D_{20}$ 14C5 $14$ $2$ $C_{14}\times D_{10}$ 7A2 14C1 14C3 $b^{10}c^{11}$
$C_{14}:D_{20}$ 14D1 $14$ $10$ $C_2^2\times C_{14}$ 7A1 14D3 14D5 $ac^{2}$
$C_{14}:D_{20}$ 14D-1 $14$ $10$ $C_2^2\times C_{14}$ 7A1 14D-3 14D-5 $ac^{12}$
$C_{14}:D_{20}$ 14D3 $14$ $10$ $C_2^2\times C_{14}$ 7A3 14D-5 14D1 $ac^{6}$
$C_{14}:D_{20}$ 14D-3 $14$ $10$ $C_2^2\times C_{14}$ 7A3 14D5 14D-1 $ac^{8}$
$C_{14}:D_{20}$ 14D5 $14$ $10$ $C_2^2\times C_{14}$ 7A2 14D1 14D-3 $ac^{10}$
$C_{14}:D_{20}$ 14D-5 $14$ $10$ $C_2^2\times C_{14}$ 7A2 14D-1 14D3 $ac^{4}$
$C_{14}:D_{20}$ 14E1 $14$ $10$ $C_2^2\times C_{14}$ 7A3 14E3 14E5 $ac$
$C_{14}:D_{20}$ 14E-1 $14$ $10$ $C_2^2\times C_{14}$ 7A3 14E-3 14E-5 $ab^{2}c$
$C_{14}:D_{20}$ 14E3 $14$ $10$ $C_2^2\times C_{14}$ 7A2 14E-5 14E1 $ac^{3}$
$C_{14}:D_{20}$ 14E-3 $14$ $10$ $C_2^2\times C_{14}$ 7A2 14E5 14E-1 $ac^{11}$
$C_{14}:D_{20}$ 14E5 $14$ $10$ $C_2^2\times C_{14}$ 7A1 14E1 14E-3 $ac^{5}$
$C_{14}:D_{20}$ 14E-5 $14$ $10$ $C_2^2\times C_{14}$ 7A1 14E-1 14E3 $ac^{9}$
$C_{14}:D_{20}$ 20A1 $20$ $14$ $C_2\times C_{20}$ 10A1 20A3 4A $b$
$C_{14}:D_{20}$ 20A3 $20$ $14$ $C_2\times C_{20}$ 10A3 20A9 4A $b^{3}$
$C_{14}:D_{20}$ 20A7 $20$ $14$ $C_2\times C_{20}$ 10A3 20A1 4A $b^{13}$
$C_{14}:D_{20}$ 20A9 $20$ $14$ $C_2\times C_{20}$ 10A1 20A7 4A $b^{9}$
$C_{14}:D_{20}$ 20B1 $20$ $14$ $C_2\times C_{20}$ 10A1 20B3 4B $bc$
$C_{14}:D_{20}$ 20B3 $20$ $14$ $C_2\times C_{20}$ 10A3 20B9 4B $b^{3}c$
$C_{14}:D_{20}$ 20B7 $20$ $14$ $C_2\times C_{20}$ 10A3 20B1 4B $b^{13}c$
$C_{14}:D_{20}$ 20B9 $20$ $14$ $C_2\times C_{20}$ 10A1 20B7 4B $b^{9}c$
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