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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{15}=c^{24}=[b,c]=1, b^{a}=b^{11}, c^{a}=c^{17} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_8\times C_3^2:C_{20}$ 1A $1$ $1$ $C_8\times C_3^2:C_{20}$ 1A 1A 1A $1$
$C_8\times C_3^2:C_{20}$ 2A $2$ $1$ $C_8\times C_3^2:C_{20}$ 1A 2A 2A $a^{2}$
$C_8\times C_3^2:C_{20}$ 2B $2$ $1$ $C_8\times C_3^2:C_{20}$ 1A 2B 2B $a^{2}c^{12}$
$C_8\times C_3^2:C_{20}$ 2C $2$ $1$ $C_8\times C_3^2:C_{20}$ 1A 2C 2C $c^{12}$
$C_8\times C_3^2:C_{20}$ 3A $3$ $2$ $C_6\times C_{120}$ 3A 1A 3A $b^{10}$
$C_8\times C_3^2:C_{20}$ 3B $3$ $2$ $C_6\times C_{120}$ 3B 1A 3B $c^{8}$
$C_8\times C_3^2:C_{20}$ 3C $3$ $2$ $C_6\times C_{120}$ 3C 1A 3C $b^{10}c^{8}$
$C_8\times C_3^2:C_{20}$ 3D $3$ $2$ $C_6\times C_{120}$ 3D 1A 3D $b^{10}c^{16}$
$C_8\times C_3^2:C_{20}$ 4A1 $4$ $1$ $C_8\times C_3^2:C_{20}$ 2C 4A-1 4A1 $a^{2}c^{18}$
$C_8\times C_3^2:C_{20}$ 4A-1 $4$ $1$ $C_8\times C_3^2:C_{20}$ 2C 4A1 4A-1 $a^{2}c^{6}$
$C_8\times C_3^2:C_{20}$ 4B1 $4$ $1$ $C_8\times C_3^2:C_{20}$ 2C 4B-1 4B1 $c^{6}$
$C_8\times C_3^2:C_{20}$ 4B-1 $4$ $1$ $C_8\times C_3^2:C_{20}$ 2C 4B1 4B-1 $c^{18}$
$C_8\times C_3^2:C_{20}$ 4C1 $4$ $9$ $C_4\times C_{40}$ 2A 4C-1 4C1 $a$
$C_8\times C_3^2:C_{20}$ 4C-1 $4$ $9$ $C_4\times C_{40}$ 2A 4C1 4C-1 $a^{3}$
$C_8\times C_3^2:C_{20}$ 4D1 $4$ $9$ $C_4\times C_{40}$ 2A 4D-1 4D1 $ac^{4}$
$C_8\times C_3^2:C_{20}$ 4D-1 $4$ $9$ $C_4\times C_{40}$ 2A 4D1 4D-1 $a^{3}c^{4}$
$C_8\times C_3^2:C_{20}$ 4E1 $4$ $9$ $C_4\times C_{40}$ 2B 4E-1 4E1 $ac^{2}$
$C_8\times C_3^2:C_{20}$ 4E-1 $4$ $9$ $C_4\times C_{40}$ 2B 4E1 4E-1 $a^{3}c^{14}$
$C_8\times C_3^2:C_{20}$ 4F1 $4$ $9$ $C_4\times C_{40}$ 2B 4F-1 4F1 $ac^{6}$
$C_8\times C_3^2:C_{20}$ 4F-1 $4$ $9$ $C_4\times C_{40}$ 2B 4F1 4F-1 $a^{3}c^{18}$
$C_8\times C_3^2:C_{20}$ 5A1 $5$ $1$ $C_8\times C_3^2:C_{20}$ 5A2 5A-2 1A $b^{12}$
$C_8\times C_3^2:C_{20}$ 5A-1 $5$ $1$ $C_8\times C_3^2:C_{20}$ 5A-2 5A2 1A $b^{3}$
$C_8\times C_3^2:C_{20}$ 5A2 $5$ $1$ $C_8\times C_3^2:C_{20}$ 5A-1 5A1 1A $b^{9}$
$C_8\times C_3^2:C_{20}$ 5A-2 $5$ $1$ $C_8\times C_3^2:C_{20}$ 5A1 5A-1 1A $b^{6}$
$C_8\times C_3^2:C_{20}$ 6A $6$ $2$ $C_6\times C_{120}$ 3A 2A 6A $a^{2}b^{5}$
$C_8\times C_3^2:C_{20}$ 6B $6$ $2$ $C_6\times C_{120}$ 3B 2A 6B $a^{2}c^{16}$
$C_8\times C_3^2:C_{20}$ 6C $6$ $2$ $C_6\times C_{120}$ 3B 2B 6C $a^{2}c^{20}$
$C_8\times C_3^2:C_{20}$ 6D $6$ $2$ $C_6\times C_{120}$ 3C 2A 6D $a^{2}b^{5}c^{16}$
$C_8\times C_3^2:C_{20}$ 6E $6$ $2$ $C_6\times C_{120}$ 3D 2B 6E $a^{2}b^{5}c^{20}$
$C_8\times C_3^2:C_{20}$ 6F $6$ $2$ $C_6\times C_{120}$ 3D 2A 6F $a^{2}b^{5}c^{8}$
$C_8\times C_3^2:C_{20}$ 6G $6$ $2$ $C_6\times C_{120}$ 3C 2B 6G $a^{2}b^{10}c^{20}$
$C_8\times C_3^2:C_{20}$ 6H $6$ $2$ $C_6\times C_{120}$ 3A 2B 6H $a^{2}b^{5}c^{12}$
$C_8\times C_3^2:C_{20}$ 6I $6$ $2$ $C_6\times C_{120}$ 3B 2C 6I $c^{20}$
$C_8\times C_3^2:C_{20}$ 6J $6$ $2$ $C_6\times C_{120}$ 3C 2C 6J $b^{10}c^{20}$
$C_8\times C_3^2:C_{20}$ 6K $6$ $2$ $C_6\times C_{120}$ 3D 2C 6K $b^{5}c^{20}$
$C_8\times C_3^2:C_{20}$ 6L $6$ $2$ $C_6\times C_{120}$ 3A 2C 6L $b^{10}c^{12}$
$C_8\times C_3^2:C_{20}$ 8A1 $8$ $1$ $C_8\times C_3^2:C_{20}$ 4B1 8A3 8A-3 $c^{15}$
$C_8\times C_3^2:C_{20}$ 8A-1 $8$ $1$ $C_8\times C_3^2:C_{20}$ 4B-1 8A-3 8A3 $c^{9}$
$C_8\times C_3^2:C_{20}$ 8A3 $8$ $1$ $C_8\times C_3^2:C_{20}$ 4B-1 8A1 8A-1 $c^{21}$
$C_8\times C_3^2:C_{20}$ 8A-3 $8$ $1$ $C_8\times C_3^2:C_{20}$ 4B1 8A-1 8A1 $c^{3}$
$C_8\times C_3^2:C_{20}$ 8B1 $8$ $1$ $C_8\times C_3^2:C_{20}$ 4B1 8B3 8B-3 $a^{2}c^{15}$
$C_8\times C_3^2:C_{20}$ 8B-1 $8$ $1$ $C_8\times C_3^2:C_{20}$ 4B-1 8B-3 8B3 $a^{2}c^{9}$
$C_8\times C_3^2:C_{20}$ 8B3 $8$ $1$ $C_8\times C_3^2:C_{20}$ 4B-1 8B1 8B-1 $a^{2}c^{21}$
$C_8\times C_3^2:C_{20}$ 8B-3 $8$ $1$ $C_8\times C_3^2:C_{20}$ 4B1 8B-1 8B1 $a^{2}c^{3}$
$C_8\times C_3^2:C_{20}$ 8C1 $8$ $9$ $C_4\times C_{40}$ 4A1 8C3 8C-3 $ac^{13}$
$C_8\times C_3^2:C_{20}$ 8C-1 $8$ $9$ $C_4\times C_{40}$ 4A-1 8C-3 8C3 $a^{3}c^{19}$
$C_8\times C_3^2:C_{20}$ 8C3 $8$ $9$ $C_4\times C_{40}$ 4A-1 8C1 8C-1 $a^{3}c^{7}$
$C_8\times C_3^2:C_{20}$ 8C-3 $8$ $9$ $C_4\times C_{40}$ 4A1 8C-1 8C1 $ac$
$C_8\times C_3^2:C_{20}$ 8D1 $8$ $9$ $C_4\times C_{40}$ 4A-1 8D3 8D-3 $ac^{15}$
$C_8\times C_3^2:C_{20}$ 8D-1 $8$ $9$ $C_4\times C_{40}$ 4A1 8D-3 8D3 $a^{3}c^{9}$
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