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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid b^{2}=c^{4}=d^{60}=[a,b]=[a,c]=[b,d]=[c,d]=1, a^{2}=d^{30}, d^{a}=d^{11}, c^{b}=cd^{30} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_5\times C_4^2.D_6$ 1A $1$ $1$ $C_5\times C_4^2.D_6$ 1A 1A 1A $1$
$C_5\times C_4^2.D_6$ 2A $2$ $1$ $C_5\times C_4^2.D_6$ 1A 2A 2A $d^{30}$
$C_5\times C_4^2.D_6$ 2B $2$ $1$ $C_5\times C_4^2.D_6$ 1A 2B 2B $c^{2}d^{30}$
$C_5\times C_4^2.D_6$ 2C $2$ $1$ $C_5\times C_4^2.D_6$ 1A 2C 2C $c^{2}$
$C_5\times C_4^2.D_6$ 2D $2$ $2$ $C_{60}.C_2^3$ 1A 2D 2D $b$
$C_5\times C_4^2.D_6$ 2E $2$ $2$ $C_{60}.C_2^3$ 1A 2E 2E $bc^{2}$
$C_5\times C_4^2.D_6$ 3A $3$ $2$ $C_4^2:C_{30}$ 3A 1A 3A $d^{40}$
$C_5\times C_4^2.D_6$ 4A $4$ $2$ $C_4^2:C_{30}$ 2A 4A 4A $d^{15}$
$C_5\times C_4^2.D_6$ 4B $4$ $2$ $C_4^2:C_{30}$ 2A 4B 4B $c^{2}d^{15}$
$C_5\times C_4^2.D_6$ 4C $4$ $2$ $(C_2\times C_{12}):C_{20}$ 2A 4C 4C $bd^{15}$
$C_5\times C_4^2.D_6$ 4D $4$ $2$ $(C_2\times C_{12}):C_{20}$ 2A 4D 4D $bc^{2}d^{15}$
$C_5\times C_4^2.D_6$ 4E1 $4$ $2$ $C_{60}:Q_8$ 2C 4E-1 4E1 $c^{3}$
$C_5\times C_4^2.D_6$ 4E-1 $4$ $2$ $C_{60}:Q_8$ 2C 4E1 4E-1 $c$
$C_5\times C_4^2.D_6$ 4F1 $4$ $2$ $C_{60}:Q_8$ 2B 4F-1 4F1 $c^{3}d^{15}$
$C_5\times C_4^2.D_6$ 4F-1 $4$ $2$ $C_{60}:Q_8$ 2B 4F1 4F-1 $cd^{45}$
$C_5\times C_4^2.D_6$ 4G1 $4$ $2$ $C_{60}:Q_8$ 2B 4G-1 4G1 $bc^{3}d^{30}$
$C_5\times C_4^2.D_6$ 4G-1 $4$ $2$ $C_{60}:Q_8$ 2B 4G1 4G-1 $bc$
$C_5\times C_4^2.D_6$ 4H1 $4$ $2$ $C_{60}:Q_8$ 2C 4H-1 4H1 $bc^{3}d^{45}$
$C_5\times C_4^2.D_6$ 4H-1 $4$ $2$ $C_{60}:Q_8$ 2C 4H1 4H-1 $bcd^{45}$
$C_5\times C_4^2.D_6$ 4I $4$ $6$ $C_4^2:C_{10}$ 2A 4I 4I $a$
$C_5\times C_4^2.D_6$ 4J $4$ $6$ $C_4^2:C_{10}$ 2A 4J 4J $ad^{25}$
$C_5\times C_4^2.D_6$ 4K $4$ $6$ $C_4^2:C_{10}$ 2A 4K 4K $ac^{2}$
$C_5\times C_4^2.D_6$ 4L $4$ $6$ $C_4^2:C_{10}$ 2A 4L 4L $ac^{2}d^{25}$
$C_5\times C_4^2.D_6$ 4M $4$ $6$ $C_4^2:C_{10}$ 2A 4M 4M $ab$
$C_5\times C_4^2.D_6$ 4N $4$ $6$ $C_4^2:C_{10}$ 2A 4N 4N $abd^{25}$
$C_5\times C_4^2.D_6$ 4O $4$ $6$ $C_4^2:C_{10}$ 2A 4O 4O $abc^{2}$
$C_5\times C_4^2.D_6$ 4P $4$ $6$ $C_4^2:C_{10}$ 2A 4P 4P $abc^{2}d^{25}$
$C_5\times C_4^2.D_6$ 4Q1 $4$ $6$ $Q_8\times C_{20}$ 2B 4Q-1 4Q1 $ac$
$C_5\times C_4^2.D_6$ 4Q-1 $4$ $6$ $Q_8\times C_{20}$ 2B 4Q1 4Q-1 $ac^{3}d^{30}$
$C_5\times C_4^2.D_6$ 4R1 $4$ $6$ $Q_8\times C_{20}$ 2B 4R-1 4R1 $acd^{25}$
$C_5\times C_4^2.D_6$ 4R-1 $4$ $6$ $Q_8\times C_{20}$ 2B 4R1 4R-1 $ac^{3}d^{55}$
$C_5\times C_4^2.D_6$ 4S1 $4$ $6$ $Q_8\times C_{20}$ 2C 4S-1 4S1 $abc$
$C_5\times C_4^2.D_6$ 4S-1 $4$ $6$ $Q_8\times C_{20}$ 2C 4S1 4S-1 $abc^{3}$
$C_5\times C_4^2.D_6$ 4T1 $4$ $6$ $Q_8\times C_{20}$ 2C 4T-1 4T1 $abcd^{25}$
$C_5\times C_4^2.D_6$ 4T-1 $4$ $6$ $Q_8\times C_{20}$ 2C 4T1 4T-1 $abc^{3}d^{25}$
$C_5\times C_4^2.D_6$ 5A1 $5$ $1$ $C_5\times C_4^2.D_6$ 5A2 5A-2 1A $d^{48}$
$C_5\times C_4^2.D_6$ 5A-1 $5$ $1$ $C_5\times C_4^2.D_6$ 5A-2 5A2 1A $d^{12}$
$C_5\times C_4^2.D_6$ 5A2 $5$ $1$ $C_5\times C_4^2.D_6$ 5A-1 5A1 1A $d^{36}$
$C_5\times C_4^2.D_6$ 5A-2 $5$ $1$ $C_5\times C_4^2.D_6$ 5A1 5A-1 1A $d^{24}$
$C_5\times C_4^2.D_6$ 6A $6$ $2$ $C_4^2:C_{30}$ 3A 2A 6A $d^{10}$
$C_5\times C_4^2.D_6$ 6B $6$ $2$ $C_4^2:C_{30}$ 3A 2C 6B $c^{2}d^{40}$
$C_5\times C_4^2.D_6$ 6C $6$ $2$ $C_4^2:C_{30}$ 3A 2B 6C $c^{2}d^{10}$
$C_5\times C_4^2.D_6$ 6D $6$ $4$ $C_2^2\times C_{60}$ 3A 2D 6D $bd^{20}$
$C_5\times C_4^2.D_6$ 6E $6$ $4$ $C_2^2\times C_{60}$ 3A 2E 6E $bc^{2}d^{20}$
$C_5\times C_4^2.D_6$ 10A1 $10$ $1$ $C_5\times C_4^2.D_6$ 5A1 10A3 2A $d^{54}$
$C_5\times C_4^2.D_6$ 10A-1 $10$ $1$ $C_5\times C_4^2.D_6$ 5A-1 10A-3 2A $d^{6}$
$C_5\times C_4^2.D_6$ 10A3 $10$ $1$ $C_5\times C_4^2.D_6$ 5A-2 10A-1 2A $d^{42}$
$C_5\times C_4^2.D_6$ 10A-3 $10$ $1$ $C_5\times C_4^2.D_6$ 5A2 10A1 2A $d^{18}$
$C_5\times C_4^2.D_6$ 10B1 $10$ $1$ $C_5\times C_4^2.D_6$ 5A1 10B3 2B $c^{2}d^{54}$
$C_5\times C_4^2.D_6$ 10B-1 $10$ $1$ $C_5\times C_4^2.D_6$ 5A-1 10B-3 2B $c^{2}d^{6}$
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