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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{10}=b^{110}=1, b^{a}=b^{51} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 11P
$C_{10}\times F_{11}$ 1A $1$ $1$ $C_{10}\times F_{11}$ 1A 1A 1A $1$
$C_{10}\times F_{11}$ 2A $2$ $1$ $C_{10}\times F_{11}$ 1A 2A 2A $b^{55}$
$C_{10}\times F_{11}$ 2B $2$ $11$ $C_{10}^2$ 1A 2B 2B $a^{5}$
$C_{10}\times F_{11}$ 2C $2$ $11$ $C_{10}^2$ 1A 2C 2C $a^{5}b^{95}$
$C_{10}\times F_{11}$ 5A1 $5$ $1$ $C_{10}\times F_{11}$ 5A2 1A 5A1 $b^{44}$
$C_{10}\times F_{11}$ 5A-1 $5$ $1$ $C_{10}\times F_{11}$ 5A-2 1A 5A-1 $b^{66}$
$C_{10}\times F_{11}$ 5A2 $5$ $1$ $C_{10}\times F_{11}$ 5A-1 1A 5A2 $b^{88}$
$C_{10}\times F_{11}$ 5A-2 $5$ $1$ $C_{10}\times F_{11}$ 5A1 1A 5A-2 $b^{22}$
$C_{10}\times F_{11}$ 5B1 $5$ $11$ $C_{10}^2$ 5B2 1A 5B1 $a^{2}$
$C_{10}\times F_{11}$ 5B-1 $5$ $11$ $C_{10}^2$ 5B-2 1A 5B-1 $a^{8}$
$C_{10}\times F_{11}$ 5B2 $5$ $11$ $C_{10}^2$ 5B-1 1A 5B2 $a^{4}$
$C_{10}\times F_{11}$ 5B-2 $5$ $11$ $C_{10}^2$ 5B1 1A 5B-2 $a^{6}$
$C_{10}\times F_{11}$ 5C1 $5$ $11$ $C_{10}^2$ 5C2 1A 5C1 $a^{4}b^{72}$
$C_{10}\times F_{11}$ 5C-1 $5$ $11$ $C_{10}^2$ 5C-2 1A 5C-1 $a^{6}b^{108}$
$C_{10}\times F_{11}$ 5C2 $5$ $11$ $C_{10}^2$ 5C-1 1A 5C2 $a^{8}b^{24}$
$C_{10}\times F_{11}$ 5C-2 $5$ $11$ $C_{10}^2$ 5C1 1A 5C-2 $a^{2}b^{56}$
$C_{10}\times F_{11}$ 5D1 $5$ $11$ $C_{10}^2$ 5D2 1A 5D1 $a^{2}b^{104}$
$C_{10}\times F_{11}$ 5D-1 $5$ $11$ $C_{10}^2$ 5D-2 1A 5D-1 $a^{8}b^{76}$
$C_{10}\times F_{11}$ 5D2 $5$ $11$ $C_{10}^2$ 5D-1 1A 5D2 $a^{4}b^{8}$
$C_{10}\times F_{11}$ 5D-2 $5$ $11$ $C_{10}^2$ 5D1 1A 5D-2 $a^{6}b^{12}$
$C_{10}\times F_{11}$ 5E1 $5$ $11$ $C_{10}^2$ 5E2 1A 5E1 $a^{2}b^{52}$
$C_{10}\times F_{11}$ 5E-1 $5$ $11$ $C_{10}^2$ 5E-2 1A 5E-1 $a^{8}b^{38}$
$C_{10}\times F_{11}$ 5E2 $5$ $11$ $C_{10}^2$ 5E-1 1A 5E2 $a^{4}b^{4}$
$C_{10}\times F_{11}$ 5E-2 $5$ $11$ $C_{10}^2$ 5E1 1A 5E-2 $a^{6}b^{6}$
$C_{10}\times F_{11}$ 5F1 $5$ $11$ $C_{10}^2$ 5F2 1A 5F1 $a^{8}b^{92}$
$C_{10}\times F_{11}$ 5F-1 $5$ $11$ $C_{10}^2$ 5F-2 1A 5F-1 $a^{2}b^{68}$
$C_{10}\times F_{11}$ 5F2 $5$ $11$ $C_{10}^2$ 5F-1 1A 5F2 $a^{6}b^{84}$
$C_{10}\times F_{11}$ 5F-2 $5$ $11$ $C_{10}^2$ 5F1 1A 5F-2 $a^{4}b^{56}$
$C_{10}\times F_{11}$ 10A1 $10$ $1$ $C_{10}\times F_{11}$ 5A-2 2A 10A1 $b^{11}$
$C_{10}\times F_{11}$ 10A-1 $10$ $1$ $C_{10}\times F_{11}$ 5A2 2A 10A-1 $b^{99}$
$C_{10}\times F_{11}$ 10A3 $10$ $1$ $C_{10}\times F_{11}$ 5A-1 2A 10A3 $b^{33}$
$C_{10}\times F_{11}$ 10A-3 $10$ $1$ $C_{10}\times F_{11}$ 5A1 2A 10A-3 $b^{77}$
$C_{10}\times F_{11}$ 10B1 $10$ $11$ $C_{10}^2$ 5B1 2B 10B1 $a$
$C_{10}\times F_{11}$ 10B-1 $10$ $11$ $C_{10}^2$ 5B-1 2B 10B-1 $a^{9}$
$C_{10}\times F_{11}$ 10B3 $10$ $11$ $C_{10}^2$ 5B-2 2B 10B3 $a^{3}$
$C_{10}\times F_{11}$ 10B-3 $10$ $11$ $C_{10}^2$ 5B2 2B 10B-3 $a^{7}$
$C_{10}\times F_{11}$ 10C1 $10$ $11$ $C_{10}^2$ 5C1 2A 10C1 $a^{2}b$
$C_{10}\times F_{11}$ 10C-1 $10$ $11$ $C_{10}^2$ 5C-1 2A 10C-1 $a^{8}b^{9}$
$C_{10}\times F_{11}$ 10C3 $10$ $11$ $C_{10}^2$ 5C-2 2A 10C3 $a^{6}b^{3}$
$C_{10}\times F_{11}$ 10C-3 $10$ $11$ $C_{10}^2$ 5C2 2A 10C-3 $a^{4}b^{7}$
$C_{10}\times F_{11}$ 10D1 $10$ $11$ $C_{10}^2$ 5D1 2B 10D1 $ab^{2}$
$C_{10}\times F_{11}$ 10D-1 $10$ $11$ $C_{10}^2$ 5D-1 2B 10D-1 $a^{9}b^{8}$
$C_{10}\times F_{11}$ 10D3 $10$ $11$ $C_{10}^2$ 5D-2 2B 10D3 $a^{3}b^{6}$
$C_{10}\times F_{11}$ 10D-3 $10$ $11$ $C_{10}^2$ 5D2 2B 10D-3 $a^{7}b^{4}$
$C_{10}\times F_{11}$ 10E1 $10$ $11$ $C_{10}^2$ 5E1 2C 10E1 $ab$
$C_{10}\times F_{11}$ 10E-1 $10$ $11$ $C_{10}^2$ 5E-1 2C 10E-1 $a^{9}b^{9}$
$C_{10}\times F_{11}$ 10E3 $10$ $11$ $C_{10}^2$ 5E-2 2C 10E3 $a^{3}b^{3}$
$C_{10}\times F_{11}$ 10E-3 $10$ $11$ $C_{10}^2$ 5E2 2C 10E-3 $a^{7}b^{7}$
$C_{10}\times F_{11}$ 10F1 $10$ $11$ $C_{10}^2$ 5F1 2A 10F1 $a^{4}b$
$C_{10}\times F_{11}$ 10F-1 $10$ $11$ $C_{10}^2$ 5F-1 2A 10F-1 $a^{6}b^{9}$
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