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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{2}=c^{2}=d^{50}=[a,b]=[a,c]=[a,d]=[b,c]=[b,d]=1, d^{c}=d^{49} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P
$C_2^2\times D_{50}$ 1A $1$ $1$ $C_2^2\times D_{50}$ 1A 1A $1$
$C_2^2\times D_{50}$ 2A $2$ $1$ $C_2^2\times D_{50}$ 1A 2A $d^{25}$
$C_2^2\times D_{50}$ 2B $2$ $1$ $C_2^2\times D_{50}$ 1A 2B $b$
$C_2^2\times D_{50}$ 2C $2$ $1$ $C_2^2\times D_{50}$ 1A 2C $bd^{25}$
$C_2^2\times D_{50}$ 2D $2$ $1$ $C_2^2\times D_{50}$ 1A 2D $a$
$C_2^2\times D_{50}$ 2E $2$ $1$ $C_2^2\times D_{50}$ 1A 2E $ad^{25}$
$C_2^2\times D_{50}$ 2F $2$ $1$ $C_2^2\times D_{50}$ 1A 2F $ab$
$C_2^2\times D_{50}$ 2G $2$ $1$ $C_2^2\times D_{50}$ 1A 2G $abd^{25}$
$C_2^2\times D_{50}$ 2H $2$ $25$ $C_2^4$ 1A 2H $cd^{41}$
$C_2^2\times D_{50}$ 2I $2$ $25$ $C_2^4$ 1A 2I $acd^{28}$
$C_2^2\times D_{50}$ 2J $2$ $25$ $C_2^4$ 1A 2J $bcd^{49}$
$C_2^2\times D_{50}$ 2K $2$ $25$ $C_2^4$ 1A 2K $bcd^{42}$
$C_2^2\times D_{50}$ 2L $2$ $25$ $C_2^4$ 1A 2L $cd^{46}$
$C_2^2\times D_{50}$ 2M $2$ $25$ $C_2^4$ 1A 2M $abcd^{4}$
$C_2^2\times D_{50}$ 2N $2$ $25$ $C_2^4$ 1A 2N $abcd^{17}$
$C_2^2\times D_{50}$ 2O $2$ $25$ $C_2^4$ 1A 2O $acd^{9}$
$C_2^2\times D_{50}$ 5A1 $5$ $2$ $C_2^2\times C_{50}$ 5A2 1A $d^{10}$
$C_2^2\times D_{50}$ 5A2 $5$ $2$ $C_2^2\times C_{50}$ 5A1 1A $d^{20}$
$C_2^2\times D_{50}$ 10A1 $10$ $2$ $C_2^2\times C_{50}$ 5A1 2A $d^{5}$
$C_2^2\times D_{50}$ 10A3 $10$ $2$ $C_2^2\times C_{50}$ 5A2 2A $d^{15}$
$C_2^2\times D_{50}$ 10B1 $10$ $2$ $C_2^2\times C_{50}$ 5A2 2B $bd^{10}$
$C_2^2\times D_{50}$ 10B3 $10$ $2$ $C_2^2\times C_{50}$ 5A1 2B $bd^{30}$
$C_2^2\times D_{50}$ 10C1 $10$ $2$ $C_2^2\times C_{50}$ 5A1 2C $bd^{5}$
$C_2^2\times D_{50}$ 10C3 $10$ $2$ $C_2^2\times C_{50}$ 5A2 2C $bd^{15}$
$C_2^2\times D_{50}$ 10D1 $10$ $2$ $C_2^2\times C_{50}$ 5A2 2D $ad^{10}$
$C_2^2\times D_{50}$ 10D3 $10$ $2$ $C_2^2\times C_{50}$ 5A1 2D $ad^{30}$
$C_2^2\times D_{50}$ 10E1 $10$ $2$ $C_2^2\times C_{50}$ 5A1 2E $ad^{5}$
$C_2^2\times D_{50}$ 10E3 $10$ $2$ $C_2^2\times C_{50}$ 5A2 2E $ad^{15}$
$C_2^2\times D_{50}$ 10F1 $10$ $2$ $C_2^2\times C_{50}$ 5A2 2F $abd^{10}$
$C_2^2\times D_{50}$ 10F3 $10$ $2$ $C_2^2\times C_{50}$ 5A1 2F $abd^{30}$
$C_2^2\times D_{50}$ 10G1 $10$ $2$ $C_2^2\times C_{50}$ 5A1 2G $abd^{5}$
$C_2^2\times D_{50}$ 10G3 $10$ $2$ $C_2^2\times C_{50}$ 5A2 2G $abd^{15}$
$C_2^2\times D_{50}$ 25A1 $25$ $2$ $C_2^2\times C_{50}$ 25A2 5A1 $d^{2}$
$C_2^2\times D_{50}$ 25A2 $25$ $2$ $C_2^2\times C_{50}$ 25A4 5A2 $d^{4}$
$C_2^2\times D_{50}$ 25A3 $25$ $2$ $C_2^2\times C_{50}$ 25A6 5A2 $d^{6}$
$C_2^2\times D_{50}$ 25A4 $25$ $2$ $C_2^2\times C_{50}$ 25A8 5A1 $d^{8}$
$C_2^2\times D_{50}$ 25A6 $25$ $2$ $C_2^2\times C_{50}$ 25A12 5A1 $d^{12}$
$C_2^2\times D_{50}$ 25A7 $25$ $2$ $C_2^2\times C_{50}$ 25A11 5A2 $d^{14}$
$C_2^2\times D_{50}$ 25A8 $25$ $2$ $C_2^2\times C_{50}$ 25A9 5A2 $d^{16}$
$C_2^2\times D_{50}$ 25A9 $25$ $2$ $C_2^2\times C_{50}$ 25A7 5A1 $d^{18}$
$C_2^2\times D_{50}$ 25A11 $25$ $2$ $C_2^2\times C_{50}$ 25A3 5A1 $d^{22}$
$C_2^2\times D_{50}$ 25A12 $25$ $2$ $C_2^2\times C_{50}$ 25A1 5A2 $d^{24}$
$C_2^2\times D_{50}$ 50A1 $50$ $2$ $C_2^2\times C_{50}$ 25A1 10A1 $d$
$C_2^2\times D_{50}$ 50A3 $50$ $2$ $C_2^2\times C_{50}$ 25A3 10A3 $d^{3}$
$C_2^2\times D_{50}$ 50A7 $50$ $2$ $C_2^2\times C_{50}$ 25A7 10A3 $d^{7}$
$C_2^2\times D_{50}$ 50A9 $50$ $2$ $C_2^2\times C_{50}$ 25A9 10A1 $d^{41}$
$C_2^2\times D_{50}$ 50A11 $50$ $2$ $C_2^2\times C_{50}$ 25A11 10A1 $d^{11}$
$C_2^2\times D_{50}$ 50A13 $50$ $2$ $C_2^2\times C_{50}$ 25A12 10A3 $d^{13}$
$C_2^2\times D_{50}$ 50A17 $50$ $2$ $C_2^2\times C_{50}$ 25A8 10A3 $d^{33}$
$C_2^2\times D_{50}$ 50A19 $50$ $2$ $C_2^2\times C_{50}$ 25A6 10A1 $d^{31}$
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