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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid b^{6}=c^{11}=d^{22}=[a,d]=[c,d]=1, a^{10}=d^{20}, b^{a}=b^{5}cd^{18}, c^{a}=c^{10}d^{4}, c^{b}=cd^{18}, d^{b}=c^{3}d^{11} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P 11P
$C_{10}\times C_{11}^2:D_6$ 1A $1$ $1$ $C_{10}\times C_{11}^2:D_6$ 1A 1A 1A 1A $1$
$C_{10}\times C_{11}^2:D_6$ 2A $2$ $1$ $C_{10}\times C_{11}^2:D_6$ 1A 2A 2A 2A $d^{11}$
$C_{10}\times C_{11}^2:D_6$ 2B $2$ $33$ $C_{10}\times D_{22}$ 1A 2B 2B 2B $a^{5}d^{12}$
$C_{10}\times C_{11}^2:D_6$ 2C $2$ $33$ $C_{10}\times D_{22}$ 1A 2C 2C 2C $a^{5}d$
$C_{10}\times C_{11}^2:D_6$ 2D $2$ $33$ $C_{10}\times D_{22}$ 1A 2D 2D 2D $a^{5}bc^{6}d^{12}$
$C_{10}\times C_{11}^2:D_6$ 2E $2$ $33$ $C_{10}\times D_{22}$ 1A 2E 2E 2E $a^{5}bc^{2}d^{17}$
$C_{10}\times C_{11}^2:D_6$ 2F $2$ $121$ $C_{10}\times D_6$ 1A 2F 2F 2F $b^{3}c^{4}d^{15}$
$C_{10}\times C_{11}^2:D_6$ 2G $2$ $121$ $C_{10}\times D_6$ 1A 2G 2G 2G $b^{3}c^{7}d^{4}$
$C_{10}\times C_{11}^2:D_6$ 3A $3$ $242$ $C_2\times C_{30}$ 3A 1A 3A 3A $b^{2}c^{7}d^{12}$
$C_{10}\times C_{11}^2:D_6$ 5A1 $5$ $1$ $C_{10}\times C_{11}^2:D_6$ 5A2 5A-2 1A 5A1 $a^{4}d^{14}$
$C_{10}\times C_{11}^2:D_6$ 5A-1 $5$ $1$ $C_{10}\times C_{11}^2:D_6$ 5A-2 5A2 1A 5A-1 $a^{6}d^{10}$
$C_{10}\times C_{11}^2:D_6$ 5A2 $5$ $1$ $C_{10}\times C_{11}^2:D_6$ 5A-1 5A1 1A 5A2 $a^{8}d^{6}$
$C_{10}\times C_{11}^2:D_6$ 5A-2 $5$ $1$ $C_{10}\times C_{11}^2:D_6$ 5A1 5A-1 1A 5A-2 $a^{2}d^{18}$
$C_{10}\times C_{11}^2:D_6$ 6A $6$ $242$ $C_2\times C_{30}$ 3A 2F 6A 6A $bc^{5}d^{21}$
$C_{10}\times C_{11}^2:D_6$ 6B $6$ $242$ $C_2\times C_{30}$ 3A 2A 6B 6B $b^{4}cd^{9}$
$C_{10}\times C_{11}^2:D_6$ 6C $6$ $242$ $C_2\times C_{30}$ 3A 2G 6C 6C $bc^{5}d^{16}$
$C_{10}\times C_{11}^2:D_6$ 10A1 $10$ $1$ $C_{10}\times C_{11}^2:D_6$ 5A1 10A3 2A 10A1 $a^{2}d^{7}$
$C_{10}\times C_{11}^2:D_6$ 10A-1 $10$ $1$ $C_{10}\times C_{11}^2:D_6$ 5A-1 10A-3 2A 10A-1 $a^{8}d^{17}$
$C_{10}\times C_{11}^2:D_6$ 10A3 $10$ $1$ $C_{10}\times C_{11}^2:D_6$ 5A-2 10A-1 2A 10A3 $a^{6}d^{21}$
$C_{10}\times C_{11}^2:D_6$ 10A-3 $10$ $1$ $C_{10}\times C_{11}^2:D_6$ 5A2 10A1 2A 10A-3 $a^{4}d^{3}$
$C_{10}\times C_{11}^2:D_6$ 10B1 $10$ $33$ $C_{10}\times D_{22}$ 5A-2 10B3 2B 10B1 $ad^{20}$
$C_{10}\times C_{11}^2:D_6$ 10B-1 $10$ $33$ $C_{10}\times D_{22}$ 5A2 10B-3 2B 10B-1 $a^{9}d^{4}$
$C_{10}\times C_{11}^2:D_6$ 10B3 $10$ $33$ $C_{10}\times D_{22}$ 5A-1 10B-1 2B 10B3 $a^{3}d^{16}$
$C_{10}\times C_{11}^2:D_6$ 10B-3 $10$ $33$ $C_{10}\times D_{22}$ 5A1 10B1 2B 10B-3 $a^{7}d^{8}$
$C_{10}\times C_{11}^2:D_6$ 10C1 $10$ $33$ $C_{10}\times D_{22}$ 5A-2 10C3 2C 10C1 $ad^{9}$
$C_{10}\times C_{11}^2:D_6$ 10C-1 $10$ $33$ $C_{10}\times D_{22}$ 5A2 10C-3 2C 10C-1 $a^{9}d^{15}$
$C_{10}\times C_{11}^2:D_6$ 10C3 $10$ $33$ $C_{10}\times D_{22}$ 5A-1 10C-1 2C 10C3 $a^{3}d^{5}$
$C_{10}\times C_{11}^2:D_6$ 10C-3 $10$ $33$ $C_{10}\times D_{22}$ 5A1 10C1 2C 10C-3 $a^{7}d^{19}$
$C_{10}\times C_{11}^2:D_6$ 10D1 $10$ $33$ $C_{10}\times D_{22}$ 5A-2 10D3 2D 10D1 $abc^{8}d^{12}$
$C_{10}\times C_{11}^2:D_6$ 10D-1 $10$ $33$ $C_{10}\times D_{22}$ 5A2 10D-3 2D 10D-1 $a^{9}bc^{4}d^{12}$
$C_{10}\times C_{11}^2:D_6$ 10D3 $10$ $33$ $C_{10}\times D_{22}$ 5A-1 10D-1 2D 10D3 $a^{3}bc^{7}d^{12}$
$C_{10}\times C_{11}^2:D_6$ 10D-3 $10$ $33$ $C_{10}\times D_{22}$ 5A1 10D1 2D 10D-3 $a^{7}bc^{5}d^{12}$
$C_{10}\times C_{11}^2:D_6$ 10E1 $10$ $33$ $C_{10}\times D_{22}$ 5A-2 10E3 2E 10E1 $abc^{4}d^{17}$
$C_{10}\times C_{11}^2:D_6$ 10E-1 $10$ $33$ $C_{10}\times D_{22}$ 5A2 10E-3 2E 10E-1 $a^{9}bd^{17}$
$C_{10}\times C_{11}^2:D_6$ 10E3 $10$ $33$ $C_{10}\times D_{22}$ 5A-1 10E-1 2E 10E3 $a^{3}bc^{3}d^{17}$
$C_{10}\times C_{11}^2:D_6$ 10E-3 $10$ $33$ $C_{10}\times D_{22}$ 5A1 10E1 2E 10E-3 $a^{7}bcd^{17}$
$C_{10}\times C_{11}^2:D_6$ 10F1 $10$ $121$ $C_{10}\times D_6$ 5A1 10F3 2F 10F1 $a^{2}b^{3}c^{4}d^{19}$
$C_{10}\times C_{11}^2:D_6$ 10F-1 $10$ $121$ $C_{10}\times D_6$ 5A-1 10F-3 2F 10F-1 $a^{8}b^{3}c^{4}d^{9}$
$C_{10}\times C_{11}^2:D_6$ 10F3 $10$ $121$ $C_{10}\times D_6$ 5A-2 10F-1 2F 10F3 $a^{6}b^{3}c^{4}d^{5}$
$C_{10}\times C_{11}^2:D_6$ 10F-3 $10$ $121$ $C_{10}\times D_6$ 5A2 10F1 2F 10F-3 $a^{4}b^{3}c^{4}d$
$C_{10}\times C_{11}^2:D_6$ 10G1 $10$ $121$ $C_{10}\times D_6$ 5A-1 10G3 2G 10G1 $a^{8}b^{3}c^{7}d^{20}$
$C_{10}\times C_{11}^2:D_6$ 10G-1 $10$ $121$ $C_{10}\times D_6$ 5A1 10G-3 2G 10G-1 $a^{2}b^{3}c^{7}d^{8}$
$C_{10}\times C_{11}^2:D_6$ 10G3 $10$ $121$ $C_{10}\times D_6$ 5A2 10G-1 2G 10G3 $a^{4}b^{3}c^{7}d^{12}$
$C_{10}\times C_{11}^2:D_6$ 10G-3 $10$ $121$ $C_{10}\times D_6$ 5A-2 10G1 2G 10G-3 $a^{6}b^{3}c^{7}d^{16}$
$C_{10}\times C_{11}^2:D_6$ 11A1 $11$ $6$ $C_{110}\times D_{11}$ 11A2 11A3 11A5 1A $d^{6}$
$C_{10}\times C_{11}^2:D_6$ 11A2 $11$ $6$ $C_{110}\times D_{11}$ 11A4 11A5 11A1 1A $d^{12}$
$C_{10}\times C_{11}^2:D_6$ 11A3 $11$ $6$ $C_{110}\times D_{11}$ 11A5 11A2 11A4 1A $d^{18}$
$C_{10}\times C_{11}^2:D_6$ 11A4 $11$ $6$ $C_{110}\times D_{11}$ 11A3 11A1 11A2 1A $d^{2}$
$C_{10}\times C_{11}^2:D_6$ 11A5 $11$ $6$ $C_{110}\times D_{11}$ 11A1 11A4 11A3 1A $d^{8}$
$C_{10}\times C_{11}^2:D_6$ 11B1 $11$ $6$ $C_{110}\times D_{11}$ 11B2 11B3 11B5 1A $c^{10}d^{2}$
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