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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{10}=c^{110}=[a,b]=[a,c]=1, c^{b}=c^{101} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 11P
$C_{22}:C_{10}^2$ 1A $1$ $1$ $C_{22}:C_{10}^2$ 1A 1A 1A $1$
$C_{22}:C_{10}^2$ 2A $2$ $1$ $C_{22}:C_{10}^2$ 1A 2A 2A $c^{55}$
$C_{22}:C_{10}^2$ 2B $2$ $1$ $C_{22}:C_{10}^2$ 1A 2B 2B $a$
$C_{22}:C_{10}^2$ 2C $2$ $1$ $C_{22}:C_{10}^2$ 1A 2C 2C $ac^{55}$
$C_{22}:C_{10}^2$ 2D $2$ $11$ $C_2\times C_{10}^2$ 1A 2D 2D $b^{5}$
$C_{22}:C_{10}^2$ 2E $2$ $11$ $C_2\times C_{10}^2$ 1A 2E 2E $b^{5}c^{75}$
$C_{22}:C_{10}^2$ 2F $2$ $11$ $C_2\times C_{10}^2$ 1A 2F 2F $ab^{5}$
$C_{22}:C_{10}^2$ 2G $2$ $11$ $C_2\times C_{10}^2$ 1A 2G 2G $ab^{5}c^{75}$
$C_{22}:C_{10}^2$ 5A1 $5$ $1$ $C_{22}:C_{10}^2$ 5A2 1A 5A1 $c^{44}$
$C_{22}:C_{10}^2$ 5A-1 $5$ $1$ $C_{22}:C_{10}^2$ 5A-2 1A 5A-1 $c^{66}$
$C_{22}:C_{10}^2$ 5A2 $5$ $1$ $C_{22}:C_{10}^2$ 5A-1 1A 5A2 $c^{88}$
$C_{22}:C_{10}^2$ 5A-2 $5$ $1$ $C_{22}:C_{10}^2$ 5A1 1A 5A-2 $c^{22}$
$C_{22}:C_{10}^2$ 5B1 $5$ $11$ $C_2\times C_{10}^2$ 5B2 1A 5B1 $b^{2}$
$C_{22}:C_{10}^2$ 5B-1 $5$ $11$ $C_2\times C_{10}^2$ 5B-2 1A 5B-1 $b^{8}$
$C_{22}:C_{10}^2$ 5B2 $5$ $11$ $C_2\times C_{10}^2$ 5B-1 1A 5B2 $b^{4}$
$C_{22}:C_{10}^2$ 5B-2 $5$ $11$ $C_2\times C_{10}^2$ 5B1 1A 5B-2 $b^{6}$
$C_{22}:C_{10}^2$ 5C1 $5$ $11$ $C_2\times C_{10}^2$ 5C2 1A 5C1 $b^{4}c^{82}$
$C_{22}:C_{10}^2$ 5C-1 $5$ $11$ $C_2\times C_{10}^2$ 5C-2 1A 5C-1 $b^{6}c^{98}$
$C_{22}:C_{10}^2$ 5C2 $5$ $11$ $C_2\times C_{10}^2$ 5C-1 1A 5C2 $b^{8}c^{74}$
$C_{22}:C_{10}^2$ 5C-2 $5$ $11$ $C_2\times C_{10}^2$ 5C1 1A 5C-2 $b^{2}c^{56}$
$C_{22}:C_{10}^2$ 5D1 $5$ $11$ $C_2\times C_{10}^2$ 5D2 1A 5D1 $b^{2}c^{94}$
$C_{22}:C_{10}^2$ 5D-1 $5$ $11$ $C_2\times C_{10}^2$ 5D-2 1A 5D-1 $b^{8}c^{26}$
$C_{22}:C_{10}^2$ 5D2 $5$ $11$ $C_2\times C_{10}^2$ 5D-1 1A 5D2 $b^{4}c^{8}$
$C_{22}:C_{10}^2$ 5D-2 $5$ $11$ $C_2\times C_{10}^2$ 5D1 1A 5D-2 $b^{6}c^{82}$
$C_{22}:C_{10}^2$ 5E1 $5$ $11$ $C_2\times C_{10}^2$ 5E2 1A 5E1 $b^{2}c^{102}$
$C_{22}:C_{10}^2$ 5E-1 $5$ $11$ $C_2\times C_{10}^2$ 5E-2 1A 5E-1 $b^{8}c^{68}$
$C_{22}:C_{10}^2$ 5E2 $5$ $11$ $C_2\times C_{10}^2$ 5E-1 1A 5E2 $b^{4}c^{4}$
$C_{22}:C_{10}^2$ 5E-2 $5$ $11$ $C_2\times C_{10}^2$ 5E1 1A 5E-2 $b^{6}c^{96}$
$C_{22}:C_{10}^2$ 5F1 $5$ $11$ $C_2\times C_{10}^2$ 5F2 1A 5F1 $b^{8}c^{72}$
$C_{22}:C_{10}^2$ 5F-1 $5$ $11$ $C_2\times C_{10}^2$ 5F-2 1A 5F-1 $b^{2}c^{108}$
$C_{22}:C_{10}^2$ 5F2 $5$ $11$ $C_2\times C_{10}^2$ 5F-1 1A 5F2 $b^{6}c^{24}$
$C_{22}:C_{10}^2$ 5F-2 $5$ $11$ $C_2\times C_{10}^2$ 5F1 1A 5F-2 $b^{4}c^{56}$
$C_{22}:C_{10}^2$ 10A1 $10$ $1$ $C_{22}:C_{10}^2$ 5A-2 2A 10A1 $c^{11}$
$C_{22}:C_{10}^2$ 10A-1 $10$ $1$ $C_{22}:C_{10}^2$ 5A2 2A 10A-1 $c^{99}$
$C_{22}:C_{10}^2$ 10A3 $10$ $1$ $C_{22}:C_{10}^2$ 5A-1 2A 10A3 $c^{33}$
$C_{22}:C_{10}^2$ 10A-3 $10$ $1$ $C_{22}:C_{10}^2$ 5A1 2A 10A-3 $c^{77}$
$C_{22}:C_{10}^2$ 10B1 $10$ $1$ $C_{22}:C_{10}^2$ 5A1 2B 10B1 $ac^{22}$
$C_{22}:C_{10}^2$ 10B-1 $10$ $1$ $C_{22}:C_{10}^2$ 5A-1 2B 10B-1 $ac^{88}$
$C_{22}:C_{10}^2$ 10B3 $10$ $1$ $C_{22}:C_{10}^2$ 5A-2 2B 10B3 $ac^{66}$
$C_{22}:C_{10}^2$ 10B-3 $10$ $1$ $C_{22}:C_{10}^2$ 5A2 2B 10B-3 $ac^{44}$
$C_{22}:C_{10}^2$ 10C1 $10$ $1$ $C_{22}:C_{10}^2$ 5A-2 2C 10C1 $ac^{11}$
$C_{22}:C_{10}^2$ 10C-1 $10$ $1$ $C_{22}:C_{10}^2$ 5A2 2C 10C-1 $ac^{99}$
$C_{22}:C_{10}^2$ 10C3 $10$ $1$ $C_{22}:C_{10}^2$ 5A-1 2C 10C3 $ac^{33}$
$C_{22}:C_{10}^2$ 10C-3 $10$ $1$ $C_{22}:C_{10}^2$ 5A1 2C 10C-3 $ac^{77}$
$C_{22}:C_{10}^2$ 10D1 $10$ $11$ $C_2\times C_{10}^2$ 5B1 2D 10D1 $b$
$C_{22}:C_{10}^2$ 10D-1 $10$ $11$ $C_2\times C_{10}^2$ 5B-1 2D 10D-1 $b^{9}$
$C_{22}:C_{10}^2$ 10D3 $10$ $11$ $C_2\times C_{10}^2$ 5B-2 2D 10D3 $b^{3}$
$C_{22}:C_{10}^2$ 10D-3 $10$ $11$ $C_2\times C_{10}^2$ 5B2 2D 10D-3 $b^{7}$
$C_{22}:C_{10}^2$ 10E1 $10$ $11$ $C_2\times C_{10}^2$ 5C1 2A 10E1 $b^{2}c$
$C_{22}:C_{10}^2$ 10E-1 $10$ $11$ $C_2\times C_{10}^2$ 5C-1 2A 10E-1 $b^{8}c^{9}$
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