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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{16}=c^{15}=[a,c]=1, a^{4}=b^{8}, b^{a}=b^{15}, c^{b}=c^{11} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_{60}.D_8$ 1A $1$ $1$ $C_{60}.D_8$ 1A 1A 1A $1$
$C_{60}.D_8$ 2A $2$ $1$ $C_{60}.D_8$ 1A 2A 2A $b^{8}$
$C_{60}.D_8$ 2B $2$ $2$ $C_6:C_{80}$ 1A 2B 2B $a^{2}b^{4}$
$C_{60}.D_8$ 3A $3$ $2$ $C_8.C_{60}$ 3A 1A 3A $c^{10}$
$C_{60}.D_8$ 4A1 $4$ $1$ $C_{60}.D_8$ 2A 4A-1 4A1 $a^{2}$
$C_{60}.D_8$ 4A-1 $4$ $1$ $C_{60}.D_8$ 2A 4A1 4A-1 $a^{2}b^{8}$
$C_{60}.D_8$ 4B $4$ $2$ $C_6:C_{80}$ 2A 4B 4B $b^{4}$
$C_{60}.D_8$ 5A1 $5$ $1$ $C_{60}.D_8$ 5A2 5A-2 1A $c^{6}$
$C_{60}.D_8$ 5A-1 $5$ $1$ $C_{60}.D_8$ 5A-2 5A2 1A $c^{9}$
$C_{60}.D_8$ 5A2 $5$ $1$ $C_{60}.D_8$ 5A-1 5A1 1A $c^{12}$
$C_{60}.D_8$ 5A-2 $5$ $1$ $C_{60}.D_8$ 5A1 5A-1 1A $c^{3}$
$C_{60}.D_8$ 6A $6$ $2$ $C_8.C_{60}$ 3A 2A 6A $b^{8}c^{5}$
$C_{60}.D_8$ 6B $6$ $4$ $C_2\times C_{120}$ 3A 2B 6B $a^{2}b^{4}c^{5}$
$C_{60}.D_8$ 8A1 $8$ $2$ $C_6:C_{80}$ 4B 8A3 8A3 $b^{10}$
$C_{60}.D_8$ 8A3 $8$ $2$ $C_6:C_{80}$ 4B 8A1 8A1 $b^{14}$
$C_{60}.D_8$ 8B1 $8$ $2$ $C_6:C_{80}$ 4B 8B1 8B-1 $a^{2}b^{6}$
$C_{60}.D_8$ 8B-1 $8$ $2$ $C_6:C_{80}$ 4B 8B-1 8B1 $a^{2}b^{2}$
$C_{60}.D_8$ 8C1 $8$ $8$ $C_{120}$ 4A-1 8C-1 8C1 $a^{3}b^{8}$
$C_{60}.D_8$ 8C-1 $8$ $8$ $C_{120}$ 4A1 8C1 8C-1 $a$
$C_{60}.D_8$ 8D1 $8$ $24$ $C_{40}$ 4A1 8D-1 8D1 $ab^{9}$
$C_{60}.D_8$ 8D-1 $8$ $24$ $C_{40}$ 4A-1 8D1 8D-1 $a^{3}b$
$C_{60}.D_8$ 10A1 $10$ $1$ $C_{60}.D_8$ 5A-1 10A3 2A $b^{8}c^{12}$
$C_{60}.D_8$ 10A-1 $10$ $1$ $C_{60}.D_8$ 5A1 10A-3 2A $b^{8}c^{3}$
$C_{60}.D_8$ 10A3 $10$ $1$ $C_{60}.D_8$ 5A2 10A-1 2A $b^{8}c^{6}$
$C_{60}.D_8$ 10A-3 $10$ $1$ $C_{60}.D_8$ 5A-2 10A1 2A $b^{8}c^{9}$
$C_{60}.D_8$ 10B1 $10$ $2$ $C_6:C_{80}$ 5A1 10B3 2B $a^{2}b^{4}c^{3}$
$C_{60}.D_8$ 10B-1 $10$ $2$ $C_6:C_{80}$ 5A-1 10B-3 2B $a^{2}b^{4}c^{12}$
$C_{60}.D_8$ 10B3 $10$ $2$ $C_6:C_{80}$ 5A-2 10B-1 2B $a^{2}b^{4}c^{9}$
$C_{60}.D_8$ 10B-3 $10$ $2$ $C_6:C_{80}$ 5A2 10B1 2B $a^{2}b^{4}c^{6}$
$C_{60}.D_8$ 12A1 $12$ $2$ $C_8.C_{60}$ 6A 4A-1 12A1 $a^{2}c^{10}$
$C_{60}.D_8$ 12A-1 $12$ $2$ $C_8.C_{60}$ 6A 4A1 12A-1 $a^{2}b^{8}c^{5}$
$C_{60}.D_8$ 12B $12$ $4$ $C_2\times C_{120}$ 6A 4B 12B $b^{4}c^{10}$
$C_{60}.D_8$ 15A1 $15$ $2$ $C_8.C_{60}$ 15A2 5A1 3A $c^{2}$
$C_{60}.D_8$ 15A-1 $15$ $2$ $C_8.C_{60}$ 15A-2 5A-1 3A $c^{13}$
$C_{60}.D_8$ 15A2 $15$ $2$ $C_8.C_{60}$ 15A-1 5A2 3A $c^{4}$
$C_{60}.D_8$ 15A-2 $15$ $2$ $C_8.C_{60}$ 15A1 5A-2 3A $c^{11}$
$C_{60}.D_8$ 16A1 $16$ $6$ $C_2\times C_{80}$ 8A1 16A3 16A5 $b^{5}$
$C_{60}.D_8$ 16A3 $16$ $6$ $C_2\times C_{80}$ 8A3 16A7 16A1 $b^{15}$
$C_{60}.D_8$ 16A5 $16$ $6$ $C_2\times C_{80}$ 8A3 16A1 16A7 $b^{9}$
$C_{60}.D_8$ 16A7 $16$ $6$ $C_2\times C_{80}$ 8A1 16A5 16A3 $b^{3}$
$C_{60}.D_8$ 16B1 $16$ $6$ $C_2\times C_{80}$ 8A3 16B3 16B3 $a^{2}b^{5}$
$C_{60}.D_8$ 16B-1 $16$ $6$ $C_2\times C_{80}$ 8A3 16B-3 16B-3 $a^{2}b^{3}$
$C_{60}.D_8$ 16B3 $16$ $6$ $C_2\times C_{80}$ 8A1 16B-1 16B-1 $a^{2}b^{7}$
$C_{60}.D_8$ 16B-3 $16$ $6$ $C_2\times C_{80}$ 8A1 16B1 16B1 $a^{2}b$
$C_{60}.D_8$ 20A1 $20$ $1$ $C_{60}.D_8$ 10A1 20A3 4A1 $a^{2}c^{6}$
$C_{60}.D_8$ 20A-1 $20$ $1$ $C_{60}.D_8$ 10A-1 20A-3 4A-1 $a^{2}b^{8}c^{9}$
$C_{60}.D_8$ 20A3 $20$ $1$ $C_{60}.D_8$ 10A3 20A9 4A-1 $a^{2}b^{8}c^{3}$
$C_{60}.D_8$ 20A-3 $20$ $1$ $C_{60}.D_8$ 10A-3 20A-9 4A1 $a^{2}c^{12}$
$C_{60}.D_8$ 20A7 $20$ $1$ $C_{60}.D_8$ 10A-3 20A1 4A-1 $a^{2}b^{8}c^{12}$
$C_{60}.D_8$ 20A-7 $20$ $1$ $C_{60}.D_8$ 10A3 20A-1 4A1 $a^{2}c^{3}$
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