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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{2}=c^{4}=d^{20}=[a,b]=[b,c]=[c,d]=1, c^{a}=cd^{10}, d^{a}=c^{2}d^{11}, d^{b}=d^{11} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P
$C_4^2:C_2^2\times C_5$ 1A $1$ $1$ $C_4^2:C_2^2\times C_5$ 1A 1A $1$
$C_4^2:C_2^2\times C_5$ 2A $2$ $1$ $C_4^2:C_2^2\times C_5$ 1A 2A $c^{2}$
$C_4^2:C_2^2\times C_5$ 2B $2$ $1$ $C_4^2:C_2^2\times C_5$ 1A 2B $d^{10}$
$C_4^2:C_2^2\times C_5$ 2C $2$ $1$ $C_4^2:C_2^2\times C_5$ 1A 2C $c^{2}d^{10}$
$C_4^2:C_2^2\times C_5$ 2D $2$ $2$ $C_2^3:C_{20}$ 1A 2D $b$
$C_4^2:C_2^2\times C_5$ 2E $2$ $2$ $C_2^3:C_{20}$ 1A 2E $bc^{2}$
$C_4^2:C_2^2\times C_5$ 2F $2$ $4$ $C_2^2\times C_{20}$ 1A 2F $bd^{5}$
$C_4^2:C_2^2\times C_5$ 2G $2$ $4$ $C_2^3\times C_{10}$ 1A 2G $a$
$C_4^2:C_2^2\times C_5$ 2H $2$ $4$ $C_2^3\times C_{10}$ 1A 2H $ab$
$C_4^2:C_2^2\times C_5$ 2I $2$ $4$ $C_2^2\times C_{20}$ 1A 2I $abcd^{5}$
$C_4^2:C_2^2\times C_5$ 4A1 $4$ $2$ $D_4\times C_{20}$ 2A 4A1 $c$
$C_4^2:C_2^2\times C_5$ 4A-1 $4$ $2$ $D_4\times C_{20}$ 2A 4A-1 $c^{3}$
$C_4^2:C_2^2\times C_5$ 4B1 $4$ $2$ $D_4\times C_{20}$ 2A 4B1 $bc$
$C_4^2:C_2^2\times C_5$ 4B-1 $4$ $2$ $D_4\times C_{20}$ 2A 4B-1 $bc^{3}$
$C_4^2:C_2^2\times C_5$ 4C $4$ $4$ $C_4\times C_{20}$ 2B 4C $d^{5}$
$C_4^2:C_2^2\times C_5$ 4D $4$ $4$ $C_4\times C_{20}$ 2C 4D $cd^{5}$
$C_4^2:C_2^2\times C_5$ 4E $4$ $4$ $C_2^2\times C_{20}$ 2A 4E $ad^{5}$
$C_4^2:C_2^2\times C_5$ 4F $4$ $4$ $C_2^2\times C_{20}$ 2A 4F $bcd^{5}$
$C_4^2:C_2^2\times C_5$ 4G $4$ $4$ $C_2^2\times C_{20}$ 2C 4G $ac$
$C_4^2:C_2^2\times C_5$ 4H $4$ $4$ $C_4\times C_{20}$ 2B 4H $acd^{5}$
$C_4^2:C_2^2\times C_5$ 4I $4$ $4$ $C_4\times C_{20}$ 2C 4I $abd^{5}$
$C_4^2:C_2^2\times C_5$ 4J $4$ $4$ $C_2^2\times C_{20}$ 2C 4J $abc$
$C_4^2:C_2^2\times C_5$ 5A1 $5$ $1$ $C_4^2:C_2^2\times C_5$ 5A2 1A $d^{8}$
$C_4^2:C_2^2\times C_5$ 5A-1 $5$ $1$ $C_4^2:C_2^2\times C_5$ 5A-2 1A $d^{12}$
$C_4^2:C_2^2\times C_5$ 5A2 $5$ $1$ $C_4^2:C_2^2\times C_5$ 5A-1 1A $d^{16}$
$C_4^2:C_2^2\times C_5$ 5A-2 $5$ $1$ $C_4^2:C_2^2\times C_5$ 5A1 1A $d^{4}$
$C_4^2:C_2^2\times C_5$ 10A1 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A2 2A $c^{2}d^{8}$
$C_4^2:C_2^2\times C_5$ 10A-1 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A-2 2A $c^{2}d^{12}$
$C_4^2:C_2^2\times C_5$ 10A3 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A1 2A $c^{2}d^{4}$
$C_4^2:C_2^2\times C_5$ 10A-3 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A-1 2A $c^{2}d^{16}$
$C_4^2:C_2^2\times C_5$ 10B1 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A-2 2B $d^{2}$
$C_4^2:C_2^2\times C_5$ 10B-1 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A2 2B $d^{18}$
$C_4^2:C_2^2\times C_5$ 10B3 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A-1 2B $d^{6}$
$C_4^2:C_2^2\times C_5$ 10B-3 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A1 2B $d^{14}$
$C_4^2:C_2^2\times C_5$ 10C1 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A-2 2C $c^{2}d^{2}$
$C_4^2:C_2^2\times C_5$ 10C-1 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A2 2C $c^{2}d^{18}$
$C_4^2:C_2^2\times C_5$ 10C3 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A-1 2C $c^{2}d^{6}$
$C_4^2:C_2^2\times C_5$ 10C-3 $10$ $1$ $C_4^2:C_2^2\times C_5$ 5A1 2C $c^{2}d^{14}$
$C_4^2:C_2^2\times C_5$ 10D1 $10$ $2$ $C_2^3:C_{20}$ 5A1 2D $bd^{4}$
$C_4^2:C_2^2\times C_5$ 10D-1 $10$ $2$ $C_2^3:C_{20}$ 5A-1 2D $bd^{16}$
$C_4^2:C_2^2\times C_5$ 10D3 $10$ $2$ $C_2^3:C_{20}$ 5A-2 2D $bd^{2}$
$C_4^2:C_2^2\times C_5$ 10D-3 $10$ $2$ $C_2^3:C_{20}$ 5A2 2D $bd^{8}$
$C_4^2:C_2^2\times C_5$ 10E1 $10$ $2$ $C_2^3:C_{20}$ 5A1 2E $bc^{2}d^{4}$
$C_4^2:C_2^2\times C_5$ 10E-1 $10$ $2$ $C_2^3:C_{20}$ 5A-1 2E $bc^{2}d^{16}$
$C_4^2:C_2^2\times C_5$ 10E3 $10$ $2$ $C_2^3:C_{20}$ 5A-2 2E $bc^{2}d^{2}$
$C_4^2:C_2^2\times C_5$ 10E-3 $10$ $2$ $C_2^3:C_{20}$ 5A2 2E $bc^{2}d^{8}$
$C_4^2:C_2^2\times C_5$ 10F1 $10$ $4$ $C_2^2\times C_{20}$ 5A-1 2F $bd$
$C_4^2:C_2^2\times C_5$ 10F-1 $10$ $4$ $C_2^2\times C_{20}$ 5A1 2F $bd^{9}$
$C_4^2:C_2^2\times C_5$ 10F3 $10$ $4$ $C_2^2\times C_{20}$ 5A2 2F $bd^{3}$
$C_4^2:C_2^2\times C_5$ 10F-3 $10$ $4$ $C_2^2\times C_{20}$ 5A-2 2F $bd^{17}$
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