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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{10}=c^{44}=[a,b]=1, a^{2}=c^{22}, c^{a}=c^{23}, c^{b}=c^{13} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 11P
$Q_8\times F_{11}$ 1A $1$ $1$ $Q_8\times F_{11}$ 1A 1A 1A $1$
$Q_8\times F_{11}$ 2A $2$ $1$ $Q_8\times F_{11}$ 1A 2A 2A $c^{22}$
$Q_8\times F_{11}$ 2B $2$ $11$ $Q_8\times C_{10}$ 1A 2B 2B $b^{5}$
$Q_8\times F_{11}$ 2C $2$ $11$ $Q_8\times C_{10}$ 1A 2C 2C $b^{5}c^{18}$
$Q_8\times F_{11}$ 4A $4$ $2$ $C_4\times F_{11}$ 2A 4A 4A $c^{33}$
$Q_8\times F_{11}$ 4B $4$ $2$ $C_4\times F_{11}$ 2A 4B 4B $a$
$Q_8\times F_{11}$ 4C $4$ $2$ $C_4\times F_{11}$ 2A 4C 4C $ac^{33}$
$Q_8\times F_{11}$ 4D $4$ $22$ $C_2\times C_{20}$ 2A 4D 4D $b^{5}c^{9}$
$Q_8\times F_{11}$ 4E $4$ $22$ $C_2\times C_{20}$ 2A 4E 4E $ab^{5}$
$Q_8\times F_{11}$ 4F $4$ $22$ $C_2\times C_{20}$ 2A 4F 4F $ab^{5}c^{9}$
$Q_8\times F_{11}$ 5A1 $5$ $11$ $Q_8\times C_{10}$ 5A2 1A 5A1 $b^{2}$
$Q_8\times F_{11}$ 5A-1 $5$ $11$ $Q_8\times C_{10}$ 5A-2 1A 5A-1 $b^{8}$
$Q_8\times F_{11}$ 5A2 $5$ $11$ $Q_8\times C_{10}$ 5A-1 1A 5A2 $b^{4}$
$Q_8\times F_{11}$ 5A-2 $5$ $11$ $Q_8\times C_{10}$ 5A1 1A 5A-2 $b^{6}$
$Q_8\times F_{11}$ 10A1 $10$ $11$ $Q_8\times C_{10}$ 5A1 2B 10A1 $b$
$Q_8\times F_{11}$ 10A-1 $10$ $11$ $Q_8\times C_{10}$ 5A-1 2B 10A-1 $b^{9}$
$Q_8\times F_{11}$ 10A3 $10$ $11$ $Q_8\times C_{10}$ 5A-2 2B 10A3 $b^{3}$
$Q_8\times F_{11}$ 10A-3 $10$ $11$ $Q_8\times C_{10}$ 5A2 2B 10A-3 $b^{7}$
$Q_8\times F_{11}$ 10B1 $10$ $11$ $Q_8\times C_{10}$ 5A1 2C 10B1 $bc^{2}$
$Q_8\times F_{11}$ 10B-1 $10$ $11$ $Q_8\times C_{10}$ 5A-1 2C 10B-1 $b^{9}c^{2}$
$Q_8\times F_{11}$ 10B3 $10$ $11$ $Q_8\times C_{10}$ 5A-2 2C 10B3 $b^{3}c^{2}$
$Q_8\times F_{11}$ 10B-3 $10$ $11$ $Q_8\times C_{10}$ 5A2 2C 10B-3 $b^{7}c^{2}$
$Q_8\times F_{11}$ 10C1 $10$ $11$ $Q_8\times C_{10}$ 5A-1 2A 10C1 $b^{4}c^{38}$
$Q_8\times F_{11}$ 10C-1 $10$ $11$ $Q_8\times C_{10}$ 5A1 2A 10C-1 $b^{6}c^{10}$
$Q_8\times F_{11}$ 10C3 $10$ $11$ $Q_8\times C_{10}$ 5A2 2A 10C3 $b^{2}c^{34}$
$Q_8\times F_{11}$ 10C-3 $10$ $11$ $Q_8\times C_{10}$ 5A-2 2A 10C-3 $b^{8}c^{30}$
$Q_8\times F_{11}$ 11A $11$ $10$ $Q_8\times C_{11}$ 11A 11A 1A $c^{4}$
$Q_8\times F_{11}$ 20A1 $20$ $22$ $C_2\times C_{20}$ 10C1 4A 20A1 $b^{2}c$
$Q_8\times F_{11}$ 20A-1 $20$ $22$ $C_2\times C_{20}$ 10C-1 4A 20A-1 $b^{8}c$
$Q_8\times F_{11}$ 20A3 $20$ $22$ $C_2\times C_{20}$ 10C3 4A 20A3 $b^{6}c$
$Q_8\times F_{11}$ 20A-3 $20$ $22$ $C_2\times C_{20}$ 10C-3 4A 20A-3 $b^{4}c$
$Q_8\times F_{11}$ 20B1 $20$ $22$ $C_2\times C_{20}$ 10C3 4D 20B1 $bc$
$Q_8\times F_{11}$ 20B-1 $20$ $22$ $C_2\times C_{20}$ 10C-3 4D 20B-1 $b^{9}c$
$Q_8\times F_{11}$ 20B3 $20$ $22$ $C_2\times C_{20}$ 10C-1 4D 20B3 $b^{3}c$
$Q_8\times F_{11}$ 20B-3 $20$ $22$ $C_2\times C_{20}$ 10C1 4D 20B-3 $b^{7}c$
$Q_8\times F_{11}$ 20C1 $20$ $22$ $C_2\times C_{20}$ 10C1 4B 20C1 $ab^{2}$
$Q_8\times F_{11}$ 20C-1 $20$ $22$ $C_2\times C_{20}$ 10C-1 4B 20C-1 $ab^{8}$
$Q_8\times F_{11}$ 20C3 $20$ $22$ $C_2\times C_{20}$ 10C3 4B 20C3 $ab^{6}$
$Q_8\times F_{11}$ 20C-3 $20$ $22$ $C_2\times C_{20}$ 10C-3 4B 20C-3 $ab^{4}$
$Q_8\times F_{11}$ 20D1 $20$ $22$ $C_2\times C_{20}$ 10C3 4E 20D1 $ab$
$Q_8\times F_{11}$ 20D-1 $20$ $22$ $C_2\times C_{20}$ 10C-3 4E 20D-1 $ab^{9}$
$Q_8\times F_{11}$ 20D3 $20$ $22$ $C_2\times C_{20}$ 10C-1 4E 20D3 $ab^{3}$
$Q_8\times F_{11}$ 20D-3 $20$ $22$ $C_2\times C_{20}$ 10C1 4E 20D-3 $ab^{7}$
$Q_8\times F_{11}$ 20E1 $20$ $22$ $C_2\times C_{20}$ 10C1 4C 20E1 $ab^{2}c$
$Q_8\times F_{11}$ 20E-1 $20$ $22$ $C_2\times C_{20}$ 10C-1 4C 20E-1 $ab^{8}c$
$Q_8\times F_{11}$ 20E3 $20$ $22$ $C_2\times C_{20}$ 10C3 4C 20E3 $ab^{6}c$
$Q_8\times F_{11}$ 20E-3 $20$ $22$ $C_2\times C_{20}$ 10C-3 4C 20E-3 $ab^{4}c$
$Q_8\times F_{11}$ 20F1 $20$ $22$ $C_2\times C_{20}$ 10C3 4F 20F1 $abc$
$Q_8\times F_{11}$ 20F-1 $20$ $22$ $C_2\times C_{20}$ 10C-3 4F 20F-1 $ab^{9}c$
$Q_8\times F_{11}$ 20F3 $20$ $22$ $C_2\times C_{20}$ 10C-1 4F 20F3 $ab^{3}c$
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