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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{10}=c^{220}=1, b^{22}=c^{22}, b^{a}=b^{13}c^{188}, c^{a}=c^{101}, c^{b}=c^{131} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 11P
$C_{55}:(Q_8\times F_{11})$ 1A $1$ $1$ $C_{55}:(Q_8\times F_{11})$ 1A 1A 1A $1$
$C_{55}:(Q_8\times F_{11})$ 2A $2$ $1$ $C_{55}:(Q_8\times F_{11})$ 1A 2A 2A $c^{110}$
$C_{55}:(Q_8\times F_{11})$ 2B $2$ $121$ $C_4.C_{10}^2$ 1A 2B 2B $a^{5}$
$C_{55}:(Q_8\times F_{11})$ 2C $2$ $121$ $C_4.C_{10}^2$ 1A 2C 2C $a^{5}c^{150}$
$C_{55}:(Q_8\times F_{11})$ 4A $4$ $2$ $C_{220}:F_{11}$ 2A 4A 4A $c^{55}$
$C_{55}:(Q_8\times F_{11})$ 4B $4$ $22$ $C_{20}\times F_{11}$ 2A 4B 4B $b^{11}c^{44}$
$C_{55}:(Q_8\times F_{11})$ 4C $4$ $22$ $C_{20}\times F_{11}$ 2A 4C 4C $b^{11}c^{89}$
$C_{55}:(Q_8\times F_{11})$ 4D $4$ $22$ $C_{20}\times F_{11}$ 2A 4D 4D $a^{5}bc^{54}$
$C_{55}:(Q_8\times F_{11})$ 4E $4$ $22$ $C_{20}\times F_{11}$ 2A 4E 4E $a^{5}bc^{219}$
$C_{55}:(Q_8\times F_{11})$ 4F $4$ $242$ $C_{10}\times C_{20}$ 2A 4F 4F $a^{5}c^{205}$
$C_{55}:(Q_8\times F_{11})$ 5A1 $5$ $1$ $C_{55}:(Q_8\times F_{11})$ 5A2 1A 5A1 $c^{88}$
$C_{55}:(Q_8\times F_{11})$ 5A-1 $5$ $1$ $C_{55}:(Q_8\times F_{11})$ 5A-2 1A 5A-1 $c^{132}$
$C_{55}:(Q_8\times F_{11})$ 5A2 $5$ $1$ $C_{55}:(Q_8\times F_{11})$ 5A-1 1A 5A2 $c^{176}$
$C_{55}:(Q_8\times F_{11})$ 5A-2 $5$ $1$ $C_{55}:(Q_8\times F_{11})$ 5A1 1A 5A-2 $c^{44}$
$C_{55}:(Q_8\times F_{11})$ 5B1 $5$ $121$ $C_4.C_{10}^2$ 5B2 1A 5B1 $a^{2}$
$C_{55}:(Q_8\times F_{11})$ 5B-1 $5$ $121$ $C_4.C_{10}^2$ 5B-2 1A 5B-1 $a^{8}$
$C_{55}:(Q_8\times F_{11})$ 5B2 $5$ $121$ $C_4.C_{10}^2$ 5B-1 1A 5B2 $a^{4}$
$C_{55}:(Q_8\times F_{11})$ 5B-2 $5$ $121$ $C_4.C_{10}^2$ 5B1 1A 5B-2 $a^{6}$
$C_{55}:(Q_8\times F_{11})$ 5C1 $5$ $121$ $C_4.C_{10}^2$ 5C2 1A 5C1 $a^{2}c^{188}$
$C_{55}:(Q_8\times F_{11})$ 5C-1 $5$ $121$ $C_4.C_{10}^2$ 5C-2 1A 5C-1 $a^{8}c^{52}$
$C_{55}:(Q_8\times F_{11})$ 5C2 $5$ $121$ $C_4.C_{10}^2$ 5C-1 1A 5C2 $a^{4}c^{16}$
$C_{55}:(Q_8\times F_{11})$ 5C-2 $5$ $121$ $C_4.C_{10}^2$ 5C1 1A 5C-2 $a^{6}c^{164}$
$C_{55}:(Q_8\times F_{11})$ 5D1 $5$ $121$ $C_4.C_{10}^2$ 5D2 1A 5D1 $a^{2}c^{204}$
$C_{55}:(Q_8\times F_{11})$ 5D-1 $5$ $121$ $C_4.C_{10}^2$ 5D-2 1A 5D-1 $a^{8}c^{136}$
$C_{55}:(Q_8\times F_{11})$ 5D2 $5$ $121$ $C_4.C_{10}^2$ 5D-1 1A 5D2 $a^{4}c^{8}$
$C_{55}:(Q_8\times F_{11})$ 5D-2 $5$ $121$ $C_4.C_{10}^2$ 5D1 1A 5D-2 $a^{6}c^{192}$
$C_{55}:(Q_8\times F_{11})$ 5E1 $5$ $121$ $C_4.C_{10}^2$ 5E2 1A 5E1 $a^{2}c^{156}$
$C_{55}:(Q_8\times F_{11})$ 5E-1 $5$ $121$ $C_4.C_{10}^2$ 5E-2 1A 5E-1 $a^{8}c^{104}$
$C_{55}:(Q_8\times F_{11})$ 5E2 $5$ $121$ $C_4.C_{10}^2$ 5E-1 1A 5E2 $a^{4}c^{32}$
$C_{55}:(Q_8\times F_{11})$ 5E-2 $5$ $121$ $C_4.C_{10}^2$ 5E1 1A 5E-2 $a^{6}c^{108}$
$C_{55}:(Q_8\times F_{11})$ 5F1 $5$ $121$ $C_4.C_{10}^2$ 5F2 1A 5F1 $a^{2}b^{18}c^{154}$
$C_{55}:(Q_8\times F_{11})$ 5F-1 $5$ $121$ $C_4.C_{10}^2$ 5F-2 1A 5F-1 $a^{8}b^{12}c^{176}$
$C_{55}:(Q_8\times F_{11})$ 5F2 $5$ $121$ $C_4.C_{10}^2$ 5F-1 1A 5F2 $a^{4}b^{2}c^{22}$
$C_{55}:(Q_8\times F_{11})$ 5F-2 $5$ $121$ $C_4.C_{10}^2$ 5F1 1A 5F-2 $a^{6}b^{4}c^{132}$
$C_{55}:(Q_8\times F_{11})$ 10A1 $10$ $1$ $C_{55}:(Q_8\times F_{11})$ 5A-2 2A 10A1 $c^{22}$
$C_{55}:(Q_8\times F_{11})$ 10A-1 $10$ $1$ $C_{55}:(Q_8\times F_{11})$ 5A2 2A 10A-1 $c^{198}$
$C_{55}:(Q_8\times F_{11})$ 10A3 $10$ $1$ $C_{55}:(Q_8\times F_{11})$ 5A-1 2A 10A3 $c^{66}$
$C_{55}:(Q_8\times F_{11})$ 10A-3 $10$ $1$ $C_{55}:(Q_8\times F_{11})$ 5A1 2A 10A-3 $c^{154}$
$C_{55}:(Q_8\times F_{11})$ 10B1 $10$ $121$ $C_4.C_{10}^2$ 5B1 2B 10B1 $a$
$C_{55}:(Q_8\times F_{11})$ 10B-1 $10$ $121$ $C_4.C_{10}^2$ 5B-1 2B 10B-1 $a^{9}$
$C_{55}:(Q_8\times F_{11})$ 10B3 $10$ $121$ $C_4.C_{10}^2$ 5B-2 2B 10B3 $a^{3}$
$C_{55}:(Q_8\times F_{11})$ 10B-3 $10$ $121$ $C_4.C_{10}^2$ 5B2 2B 10B-3 $a^{7}$
$C_{55}:(Q_8\times F_{11})$ 10C1 $10$ $121$ $C_4.C_{10}^2$ 5C1 2B 10C1 $ac^{4}$
$C_{55}:(Q_8\times F_{11})$ 10C-1 $10$ $121$ $C_4.C_{10}^2$ 5C-1 2B 10C-1 $a^{9}c^{16}$
$C_{55}:(Q_8\times F_{11})$ 10C3 $10$ $121$ $C_4.C_{10}^2$ 5C-2 2B 10C3 $a^{3}c^{12}$
$C_{55}:(Q_8\times F_{11})$ 10C-3 $10$ $121$ $C_4.C_{10}^2$ 5C2 2B 10C-3 $a^{7}c^{8}$
$C_{55}:(Q_8\times F_{11})$ 10D1 $10$ $121$ $C_4.C_{10}^2$ 5D1 2C 10D1 $ac^{2}$
$C_{55}:(Q_8\times F_{11})$ 10D-1 $10$ $121$ $C_4.C_{10}^2$ 5D-1 2C 10D-1 $a^{9}b^{18}$
$C_{55}:(Q_8\times F_{11})$ 10D3 $10$ $121$ $C_4.C_{10}^2$ 5D-2 2C 10D3 $a^{3}b^{6}$
$C_{55}:(Q_8\times F_{11})$ 10D-3 $10$ $121$ $C_4.C_{10}^2$ 5D2 2C 10D-3 $a^{7}b^{14}$
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