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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{2}=c^{10}=d^{10}=[a,b]=[a,c]=[a,d]=[b,c]=[c,d]=1, d^{b}=d^{9} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P
$C_{10}^2:C_2^2$ 1A $1$ $1$ $C_{10}^2:C_2^2$ 1A 1A $1$
$C_{10}^2:C_2^2$ 2A $2$ $1$ $C_{10}^2:C_2^2$ 1A 2A $c^{5}$
$C_{10}^2:C_2^2$ 2B $2$ $1$ $C_{10}^2:C_2^2$ 1A 2B $a$
$C_{10}^2:C_2^2$ 2C $2$ $1$ $C_{10}^2:C_2^2$ 1A 2C $ac^{5}$
$C_{10}^2:C_2^2$ 2D $2$ $1$ $C_{10}^2:C_2^2$ 1A 2D $d^{5}$
$C_{10}^2:C_2^2$ 2E $2$ $1$ $C_{10}^2:C_2^2$ 1A 2E $c^{5}d^{5}$
$C_{10}^2:C_2^2$ 2F $2$ $1$ $C_{10}^2:C_2^2$ 1A 2F $ad^{5}$
$C_{10}^2:C_2^2$ 2G $2$ $1$ $C_{10}^2:C_2^2$ 1A 2G $ac^{5}d^{5}$
$C_{10}^2:C_2^2$ 2H $2$ $5$ $C_2^3\times C_{10}$ 1A 2H $b$
$C_{10}^2:C_2^2$ 2I $2$ $5$ $C_2^3\times C_{10}$ 1A 2I $bc^{5}$
$C_{10}^2:C_2^2$ 2J $2$ $5$ $C_2^3\times C_{10}$ 1A 2J $bd$
$C_{10}^2:C_2^2$ 2K $2$ $5$ $C_2^3\times C_{10}$ 1A 2K $bc^{5}d$
$C_{10}^2:C_2^2$ 2L $2$ $5$ $C_2^3\times C_{10}$ 1A 2L $ab$
$C_{10}^2:C_2^2$ 2M $2$ $5$ $C_2^3\times C_{10}$ 1A 2M $abc^{5}$
$C_{10}^2:C_2^2$ 2N $2$ $5$ $C_2^3\times C_{10}$ 1A 2N $abd$
$C_{10}^2:C_2^2$ 2O $2$ $5$ $C_2^3\times C_{10}$ 1A 2O $abc^{5}d$
$C_{10}^2:C_2^2$ 5A1 $5$ $1$ $C_{10}^2:C_2^2$ 5A2 1A $c^{2}$
$C_{10}^2:C_2^2$ 5A-1 $5$ $1$ $C_{10}^2:C_2^2$ 5A-2 1A $c^{8}$
$C_{10}^2:C_2^2$ 5A2 $5$ $1$ $C_{10}^2:C_2^2$ 5A-1 1A $c^{4}$
$C_{10}^2:C_2^2$ 5A-2 $5$ $1$ $C_{10}^2:C_2^2$ 5A1 1A $c^{6}$
$C_{10}^2:C_2^2$ 5B1 $5$ $2$ $C_2\times C_{10}^2$ 5B2 1A $d^{2}$
$C_{10}^2:C_2^2$ 5B2 $5$ $2$ $C_2\times C_{10}^2$ 5B1 1A $d^{4}$
$C_{10}^2:C_2^2$ 5C1 $5$ $2$ $C_2\times C_{10}^2$ 5C2 1A $c^{4}d^{2}$
$C_{10}^2:C_2^2$ 5C-1 $5$ $2$ $C_2\times C_{10}^2$ 5C-2 1A $c^{6}d^{8}$
$C_{10}^2:C_2^2$ 5C2 $5$ $2$ $C_2\times C_{10}^2$ 5C-1 1A $c^{8}d^{4}$
$C_{10}^2:C_2^2$ 5C-2 $5$ $2$ $C_2\times C_{10}^2$ 5C1 1A $c^{2}d^{6}$
$C_{10}^2:C_2^2$ 5D1 $5$ $2$ $C_2\times C_{10}^2$ 5D2 1A $c^{2}d^{2}$
$C_{10}^2:C_2^2$ 5D-1 $5$ $2$ $C_2\times C_{10}^2$ 5D-2 1A $c^{8}d^{8}$
$C_{10}^2:C_2^2$ 5D2 $5$ $2$ $C_2\times C_{10}^2$ 5D-1 1A $c^{4}d^{4}$
$C_{10}^2:C_2^2$ 5D-2 $5$ $2$ $C_2\times C_{10}^2$ 5D1 1A $c^{6}d^{6}$
$C_{10}^2:C_2^2$ 10A1 $10$ $1$ $C_{10}^2:C_2^2$ 5A1 2A $c$
$C_{10}^2:C_2^2$ 10A-1 $10$ $1$ $C_{10}^2:C_2^2$ 5A-1 2A $c^{9}$
$C_{10}^2:C_2^2$ 10A3 $10$ $1$ $C_{10}^2:C_2^2$ 5A-2 2A $c^{3}$
$C_{10}^2:C_2^2$ 10A-3 $10$ $1$ $C_{10}^2:C_2^2$ 5A2 2A $c^{7}$
$C_{10}^2:C_2^2$ 10B1 $10$ $1$ $C_{10}^2:C_2^2$ 5A2 2B $ac^{2}$
$C_{10}^2:C_2^2$ 10B-1 $10$ $1$ $C_{10}^2:C_2^2$ 5A-2 2B $ac^{8}$
$C_{10}^2:C_2^2$ 10B3 $10$ $1$ $C_{10}^2:C_2^2$ 5A1 2B $ac^{6}$
$C_{10}^2:C_2^2$ 10B-3 $10$ $1$ $C_{10}^2:C_2^2$ 5A-1 2B $ac^{4}$
$C_{10}^2:C_2^2$ 10C1 $10$ $1$ $C_{10}^2:C_2^2$ 5A1 2C $ac$
$C_{10}^2:C_2^2$ 10C-1 $10$ $1$ $C_{10}^2:C_2^2$ 5A-1 2C $ac^{9}$
$C_{10}^2:C_2^2$ 10C3 $10$ $1$ $C_{10}^2:C_2^2$ 5A-2 2C $ac^{3}$
$C_{10}^2:C_2^2$ 10C-3 $10$ $1$ $C_{10}^2:C_2^2$ 5A2 2C $ac^{7}$
$C_{10}^2:C_2^2$ 10D1 $10$ $1$ $C_{10}^2:C_2^2$ 5A2 2D $c^{2}d^{5}$
$C_{10}^2:C_2^2$ 10D-1 $10$ $1$ $C_{10}^2:C_2^2$ 5A-2 2D $c^{8}d^{5}$
$C_{10}^2:C_2^2$ 10D3 $10$ $1$ $C_{10}^2:C_2^2$ 5A1 2D $c^{6}d^{5}$
$C_{10}^2:C_2^2$ 10D-3 $10$ $1$ $C_{10}^2:C_2^2$ 5A-1 2D $c^{4}d^{5}$
$C_{10}^2:C_2^2$ 10E1 $10$ $1$ $C_{10}^2:C_2^2$ 5A1 2E $cd^{5}$
$C_{10}^2:C_2^2$ 10E-1 $10$ $1$ $C_{10}^2:C_2^2$ 5A-1 2E $c^{9}d^{5}$
$C_{10}^2:C_2^2$ 10E3 $10$ $1$ $C_{10}^2:C_2^2$ 5A-2 2E $c^{3}d^{5}$
$C_{10}^2:C_2^2$ 10E-3 $10$ $1$ $C_{10}^2:C_2^2$ 5A2 2E $c^{7}d^{5}$
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