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

Group Label Order Size Centralizer Powers Representative
2P 5P 11P
$C_{22}:F_{11}$ 1A $1$ $1$ $C_{22}:F_{11}$ 1A 1A 1A $1$
$C_{22}:F_{11}$ 2A $2$ $1$ $C_{22}:F_{11}$ 1A 2A 2A $c^{11}$
$C_{22}:F_{11}$ 2B $2$ $121$ $C_2\times C_{10}$ 1A 2B 2B $a^{5}b^{8}c^{18}$
$C_{22}:F_{11}$ 2C $2$ $121$ $C_2\times C_{10}$ 1A 2C 2C $a^{5}b^{4}c^{5}$
$C_{22}:F_{11}$ 5A1 $5$ $121$ $C_2\times C_{10}$ 5A2 1A 5A1 $a^{6}b^{10}c^{4}$
$C_{22}:F_{11}$ 5A-1 $5$ $121$ $C_2\times C_{10}$ 5A-2 1A 5A-1 $a^{4}b^{3}c^{6}$
$C_{22}:F_{11}$ 5A2 $5$ $121$ $C_2\times C_{10}$ 5A-1 1A 5A2 $a^{2}b^{6}c^{16}$
$C_{22}:F_{11}$ 5A-2 $5$ $121$ $C_2\times C_{10}$ 5A1 1A 5A-2 $a^{8}bc^{8}$
$C_{22}:F_{11}$ 10A1 $10$ $121$ $C_2\times C_{10}$ 5A1 2B 10A1 $a^{3}b^{7}c^{10}$
$C_{22}:F_{11}$ 10A-1 $10$ $121$ $C_2\times C_{10}$ 5A-1 2B 10A-1 $a^{7}b^{2}c^{2}$
$C_{22}:F_{11}$ 10A3 $10$ $121$ $C_2\times C_{10}$ 5A-2 2B 10A3 $a^{9}b^{5}c^{12}$
$C_{22}:F_{11}$ 10A-3 $10$ $121$ $C_2\times C_{10}$ 5A2 2B 10A-3 $ab^{9}c^{14}$
$C_{22}:F_{11}$ 10B1 $10$ $121$ $C_2\times C_{10}$ 5A1 2A 10B1 $a^{8}b^{3}c^{3}$
$C_{22}:F_{11}$ 10B-1 $10$ $121$ $C_2\times C_{10}$ 5A-1 2A 10B-1 $a^{2}b^{7}c^{17}$
$C_{22}:F_{11}$ 10B3 $10$ $121$ $C_2\times C_{10}$ 5A-2 2A 10B3 $a^{4}b^{9}c^{5}$
$C_{22}:F_{11}$ 10B-3 $10$ $121$ $C_2\times C_{10}$ 5A2 2A 10B-3 $a^{6}b^{8}c^{7}$
$C_{22}:F_{11}$ 10C1 $10$ $121$ $C_2\times C_{10}$ 5A-1 2C 10C1 $a^{7}bc^{3}$
$C_{22}:F_{11}$ 10C-1 $10$ $121$ $C_2\times C_{10}$ 5A1 2C 10C-1 $a^{3}b^{9}c^{15}$
$C_{22}:F_{11}$ 10C3 $10$ $121$ $C_2\times C_{10}$ 5A2 2C 10C3 $ab^{10}c^{21}$
$C_{22}:F_{11}$ 10C-3 $10$ $121$ $C_2\times C_{10}$ 5A-2 2C 10C-3 $a^{9}b^{8}c^{7}$
$C_{22}:F_{11}$ 11A $11$ $10$ $C_{11}\times C_{22}$ 11A 11A 1A $c^{2}$
$C_{22}:F_{11}$ 11B $11$ $10$ $C_{11}\times C_{22}$ 11B 11B 1A $b^{2}$
$C_{22}:F_{11}$ 11C1 $11$ $10$ $C_{11}\times C_{22}$ 11C2 11C5 1A $b^{2}c^{2}$
$C_{22}:F_{11}$ 11C2 $11$ $10$ $C_{11}\times C_{22}$ 11C4 11C1 1A $b^{4}c^{4}$
$C_{22}:F_{11}$ 11C3 $11$ $10$ $C_{11}\times C_{22}$ 11C5 11C4 1A $b^{6}c^{6}$
$C_{22}:F_{11}$ 11C4 $11$ $10$ $C_{11}\times C_{22}$ 11C3 11C2 1A $b^{8}c^{8}$
$C_{22}:F_{11}$ 11C5 $11$ $10$ $C_{11}\times C_{22}$ 11C1 11C3 1A $b^{10}c^{10}$
$C_{22}:F_{11}$ 11D1 $11$ $10$ $C_{11}\times C_{22}$ 11D2 11D5 1A $b^{4}c^{2}$
$C_{22}:F_{11}$ 11D2 $11$ $10$ $C_{11}\times C_{22}$ 11D4 11D1 1A $b^{8}c^{4}$
$C_{22}:F_{11}$ 11D3 $11$ $10$ $C_{11}\times C_{22}$ 11D5 11D4 1A $bc^{6}$
$C_{22}:F_{11}$ 11D4 $11$ $10$ $C_{11}\times C_{22}$ 11D3 11D2 1A $b^{5}c^{8}$
$C_{22}:F_{11}$ 11D5 $11$ $10$ $C_{11}\times C_{22}$ 11D1 11D3 1A $b^{9}c^{10}$
$C_{22}:F_{11}$ 22A $22$ $10$ $C_{11}\times C_{22}$ 11A 22A 2A $c$
$C_{22}:F_{11}$ 22B $22$ $10$ $C_{11}\times C_{22}$ 11B 22B 2A $bc^{11}$
$C_{22}:F_{11}$ 22C1 $22$ $10$ $C_{11}\times C_{22}$ 11C1 22C5 2A $bc$
$C_{22}:F_{11}$ 22C3 $22$ $10$ $C_{11}\times C_{22}$ 11C3 22C7 2A $b^{9}c$
$C_{22}:F_{11}$ 22C5 $22$ $10$ $C_{11}\times C_{22}$ 11C5 22C3 2A $b^{3}c$
$C_{22}:F_{11}$ 22C7 $22$ $10$ $C_{11}\times C_{22}$ 11C4 22C9 2A $b^{5}c$
$C_{22}:F_{11}$ 22C9 $22$ $10$ $C_{11}\times C_{22}$ 11C2 22C1 2A $b^{4}c$
$C_{22}:F_{11}$ 22D1 $22$ $10$ $C_{11}\times C_{22}$ 11D1 22D5 2A $b^{2}c$
$C_{22}:F_{11}$ 22D3 $22$ $10$ $C_{11}\times C_{22}$ 11D3 22D7 2A $b^{7}c$
$C_{22}:F_{11}$ 22D5 $22$ $10$ $C_{11}\times C_{22}$ 11D5 22D3 2A $b^{6}c$
$C_{22}:F_{11}$ 22D7 $22$ $10$ $C_{11}\times C_{22}$ 11D4 22D9 2A $b^{10}c$
$C_{22}:F_{11}$ 22D9 $22$ $10$ $C_{11}\times C_{22}$ 11D2 22D1 2A $b^{8}c$
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