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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{10}=b^{11}=c^{11}=d^{22}=[b,d]=[c,d]=1, b^{a}=b^{9}c^{4}, c^{a}=c^{7}d^{14}, d^{a}=d^{19}, c^{b}=cd^{10} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 11P
$C_2\times C_{11}^2:F_{11}$ 1A $1$ $1$ $C_2\times C_{11}^2:F_{11}$ 1A 1A 1A $1$
$C_2\times C_{11}^2:F_{11}$ 2A $2$ $1$ $C_2\times C_{11}^2:F_{11}$ 1A 2A 2A $d^{11}$
$C_2\times C_{11}^2:F_{11}$ 2B $2$ $121$ $C_{22}:C_{10}$ 1A 2B 2B $a^{5}c^{2}d$
$C_2\times C_{11}^2:F_{11}$ 2C $2$ $121$ $C_{22}:C_{10}$ 1A 2C 2C $a^{5}c^{7}d^{16}$
$C_2\times C_{11}^2:F_{11}$ 5A1 $5$ $1331$ $C_2\times C_{10}$ 5A2 1A 5A1 $a^{6}c^{8}d^{2}$
$C_2\times C_{11}^2:F_{11}$ 5A-1 $5$ $1331$ $C_2\times C_{10}$ 5A-2 1A 5A-1 $a^{4}c^{9}d^{12}$
$C_2\times C_{11}^2:F_{11}$ 5A2 $5$ $1331$ $C_2\times C_{10}$ 5A-1 1A 5A2 $a^{2}c^{7}d^{6}$
$C_2\times C_{11}^2:F_{11}$ 5A-2 $5$ $1331$ $C_2\times C_{10}$ 5A1 1A 5A-2 $a^{8}c^{3}d^{10}$
$C_2\times C_{11}^2:F_{11}$ 10A1 $10$ $1331$ $C_2\times C_{10}$ 5A1 2B 10A1 $a^{3}c^{10}d^{13}$
$C_2\times C_{11}^2:F_{11}$ 10A-1 $10$ $1331$ $C_2\times C_{10}$ 5A-1 2B 10A-1 $a^{7}c^{6}d^{17}$
$C_2\times C_{11}^2:F_{11}$ 10A3 $10$ $1331$ $C_2\times C_{10}$ 5A-2 2B 10A3 $a^{9}c^{4}d^{11}$
$C_2\times C_{11}^2:F_{11}$ 10A-3 $10$ $1331$ $C_2\times C_{10}$ 5A2 2B 10A-3 $ac^{5}d^{21}$
$C_2\times C_{11}^2:F_{11}$ 10B1 $10$ $1331$ $C_2\times C_{10}$ 5A-1 2A 10B1 $a^{2}b^{8}c^{10}d^{17}$
$C_2\times C_{11}^2:F_{11}$ 10B-1 $10$ $1331$ $C_2\times C_{10}$ 5A1 2A 10B-1 $a^{8}b^{9}c^{6}d^{11}$
$C_2\times C_{11}^2:F_{11}$ 10B3 $10$ $1331$ $C_2\times C_{10}$ 5A2 2A 10B3 $a^{6}b^{3}c^{7}d^{17}$
$C_2\times C_{11}^2:F_{11}$ 10B-3 $10$ $1331$ $C_2\times C_{10}$ 5A-2 2A 10B-3 $a^{4}b^{7}d^{13}$
$C_2\times C_{11}^2:F_{11}$ 10C1 $10$ $1331$ $C_2\times C_{10}$ 5A2 2C 10C1 $ab^{6}c^{2}d^{18}$
$C_2\times C_{11}^2:F_{11}$ 10C-1 $10$ $1331$ $C_2\times C_{10}$ 5A-2 2C 10C-1 $a^{9}b^{3}c^{9}d^{16}$
$C_2\times C_{11}^2:F_{11}$ 10C3 $10$ $1331$ $C_2\times C_{10}$ 5A1 2C 10C3 $a^{3}b^{7}c^{5}d^{20}$
$C_2\times C_{11}^2:F_{11}$ 10C-3 $10$ $1331$ $C_2\times C_{10}$ 5A-1 2C 10C-3 $a^{7}b^{5}c^{9}d^{14}$
$C_2\times C_{11}^2:F_{11}$ 11A $11$ $10$ $C_2\times \He_{11}$ 11A 11A 1A $d^{2}$
$C_2\times C_{11}^2:F_{11}$ 11B1 $11$ $55$ $C_{11}\times D_{22}$ 11B-1 11B1 1A $b^{2}c^{4}$
$C_2\times C_{11}^2:F_{11}$ 11B-1 $11$ $55$ $C_{11}\times D_{22}$ 11B1 11B-1 1A $b^{9}c^{7}d^{14}$
$C_2\times C_{11}^2:F_{11}$ 11C $11$ $110$ $C_{11}\times C_{22}$ 11C 11C 1A $c^{2}d^{2}$
$C_2\times C_{11}^2:F_{11}$ 11D1 $11$ $110$ $C_{11}\times C_{22}$ 11D2 11D5 1A $b^{2}d^{2}$
$C_2\times C_{11}^2:F_{11}$ 11D-1 $11$ $110$ $C_{11}\times C_{22}$ 11D-2 11D-5 1A $b^{9}d^{20}$
$C_2\times C_{11}^2:F_{11}$ 11D2 $11$ $110$ $C_{11}\times C_{22}$ 11D4 11D-1 1A $b^{4}d^{4}$
$C_2\times C_{11}^2:F_{11}$ 11D-2 $11$ $110$ $C_{11}\times C_{22}$ 11D-4 11D1 1A $b^{7}d^{18}$
$C_2\times C_{11}^2:F_{11}$ 11D3 $11$ $110$ $C_{11}\times C_{22}$ 11D-5 11D4 1A $b^{6}d^{6}$
$C_2\times C_{11}^2:F_{11}$ 11D-3 $11$ $110$ $C_{11}\times C_{22}$ 11D5 11D-4 1A $b^{5}d^{16}$
$C_2\times C_{11}^2:F_{11}$ 11D4 $11$ $110$ $C_{11}\times C_{22}$ 11D-3 11D-2 1A $b^{8}d^{8}$
$C_2\times C_{11}^2:F_{11}$ 11D-4 $11$ $110$ $C_{11}\times C_{22}$ 11D3 11D2 1A $b^{3}d^{14}$
$C_2\times C_{11}^2:F_{11}$ 11D5 $11$ $110$ $C_{11}\times C_{22}$ 11D-1 11D3 1A $b^{10}d^{10}$
$C_2\times C_{11}^2:F_{11}$ 11D-5 $11$ $110$ $C_{11}\times C_{22}$ 11D1 11D-3 1A $bd^{12}$
$C_2\times C_{11}^2:F_{11}$ 22A $22$ $10$ $C_2\times \He_{11}$ 11A 22A 2A $d$
$C_2\times C_{11}^2:F_{11}$ 22B1 $22$ $55$ $C_{11}\times D_{22}$ 11B1 22B1 2A $bc^{2}d$
$C_2\times C_{11}^2:F_{11}$ 22B-1 $22$ $55$ $C_{11}\times D_{22}$ 11B-1 22B-1 2A $b^{2}c^{4}d$
$C_2\times C_{11}^2:F_{11}$ 22C $22$ $110$ $C_{11}\times C_{22}$ 11C 22C 2A $cd$
$C_2\times C_{11}^2:F_{11}$ 22D1 $22$ $110$ $C_{11}\times C_{22}$ 11D1 22D5 2A $bd$
$C_2\times C_{11}^2:F_{11}$ 22D-1 $22$ $110$ $C_{11}\times C_{22}$ 11D-1 22D-5 2A $b^{10}d$
$C_2\times C_{11}^2:F_{11}$ 22D3 $22$ $110$ $C_{11}\times C_{22}$ 11D3 22D-7 2A $b^{3}d$
$C_2\times C_{11}^2:F_{11}$ 22D-3 $22$ $110$ $C_{11}\times C_{22}$ 11D-3 22D7 2A $b^{8}d$
$C_2\times C_{11}^2:F_{11}$ 22D5 $22$ $110$ $C_{11}\times C_{22}$ 11D5 22D3 2A $b^{5}d$
$C_2\times C_{11}^2:F_{11}$ 22D-5 $22$ $110$ $C_{11}\times C_{22}$ 11D-5 22D-3 2A $b^{6}d$
$C_2\times C_{11}^2:F_{11}$ 22D7 $22$ $110$ $C_{11}\times C_{22}$ 11D-4 22D-9 2A $b^{7}d$
$C_2\times C_{11}^2:F_{11}$ 22D-7 $22$ $110$ $C_{11}\times C_{22}$ 11D4 22D9 2A $b^{4}d$
$C_2\times C_{11}^2:F_{11}$ 22D9 $22$ $110$ $C_{11}\times C_{22}$ 11D-2 22D1 2A $b^{9}d$
$C_2\times C_{11}^2:F_{11}$ 22D-9 $22$ $110$ $C_{11}\times C_{22}$ 11D2 22D-1 2A $b^{2}d$
$C_2\times C_{11}^2:F_{11}$ 22E1 $22$ $605$ $C_2\times C_{22}$ 11B-1 22E1 2B $a^{5}b^{8}c^{9}d$
$C_2\times C_{11}^2:F_{11}$ 22E-1 $22$ $605$ $C_2\times C_{22}$ 11B1 22E-1 2B $a^{5}b^{3}c^{10}d$
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