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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{12}=c^{15}=1, a^{2}=b^{6}, b^{a}=b^{5}, c^{a}=c^{11}, c^{b}=c^{4} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_{30}.D_6$ 1A $1$ $1$ $C_{30}.D_6$ 1A 1A 1A $1$
$C_{30}.D_6$ 2A $2$ $1$ $C_{30}.D_6$ 1A 2A 2A $b^{6}$
$C_{30}.D_6$ 2B $2$ $45$ $C_2\times C_4$ 1A 2B 2B $ab^{9}c^{7}$
$C_{30}.D_6$ 2C $2$ $45$ $C_2\times C_4$ 1A 2C 2C $ab^{3}c^{14}$
$C_{30}.D_6$ 3A $3$ $2$ $C_{15}:C_{12}$ 3A 1A 3A $b^{4}$
$C_{30}.D_6$ 3B $3$ $2$ $C_{15}:C_{12}$ 3B 1A 3B $b^{4}c^{10}$
$C_{30}.D_6$ 3C $3$ $2$ $C_{15}:C_{12}$ 3C 1A 3C $b^{4}c^{5}$
$C_{30}.D_6$ 3D $3$ $2$ $C_{15}:C_{12}$ 3D 1A 3D $c^{10}$
$C_{30}.D_6$ 4A1 $4$ $5$ $C_{12}:S_3$ 2A 4A-1 4A1 $b^{3}$
$C_{30}.D_6$ 4A-1 $4$ $5$ $C_{12}:S_3$ 2A 4A1 4A-1 $b^{9}$
$C_{30}.D_6$ 4B1 $4$ $9$ $C_4\times D_5$ 2A 4B-1 4B1 $a$
$C_{30}.D_6$ 4B-1 $4$ $9$ $C_4\times D_5$ 2A 4B1 4B-1 $ab^{6}$
$C_{30}.D_6$ 5A1 $5$ $2$ $C_3^2:C_{20}$ 5A2 5A2 1A $c^{12}$
$C_{30}.D_6$ 5A2 $5$ $2$ $C_3^2:C_{20}$ 5A1 5A1 1A $c^{9}$
$C_{30}.D_6$ 6A $6$ $2$ $C_{15}:C_{12}$ 3A 2A 6A $b^{2}$
$C_{30}.D_6$ 6B $6$ $2$ $C_{15}:C_{12}$ 3B 2A 6B $b^{2}c^{5}$
$C_{30}.D_6$ 6C $6$ $2$ $C_{15}:C_{12}$ 3C 2A 6C $b^{2}c^{10}$
$C_{30}.D_6$ 6D $6$ $2$ $C_{15}:C_{12}$ 3D 2A 6D $b^{6}c^{5}$
$C_{30}.D_6$ 10A1 $10$ $2$ $C_3^2:C_{20}$ 5A1 10A3 2A $b^{6}c^{6}$
$C_{30}.D_6$ 10A3 $10$ $2$ $C_3^2:C_{20}$ 5A2 10A1 2A $b^{6}c^{3}$
$C_{30}.D_6$ 12A1 $12$ $10$ $C_3\times C_{12}$ 6A 4A1 12A1 $b$
$C_{30}.D_6$ 12A-1 $12$ $10$ $C_3\times C_{12}$ 6A 4A-1 12A-1 $b^{7}$
$C_{30}.D_6$ 12B1 $12$ $10$ $C_3\times C_{12}$ 6B 4A1 12B1 $bc$
$C_{30}.D_6$ 12B-1 $12$ $10$ $C_3\times C_{12}$ 6B 4A-1 12B-1 $b^{7}c$
$C_{30}.D_6$ 12C1 $12$ $10$ $C_3\times C_{12}$ 6C 4A1 12C1 $bc^{2}$
$C_{30}.D_6$ 12C-1 $12$ $10$ $C_3\times C_{12}$ 6C 4A-1 12C-1 $b^{7}c^{2}$
$C_{30}.D_6$ 12D1 $12$ $10$ $C_3\times C_{12}$ 6D 4A-1 12D1 $b^{3}c$
$C_{30}.D_6$ 12D-1 $12$ $10$ $C_3\times C_{12}$ 6D 4A1 12D-1 $b^{9}c$
$C_{30}.D_6$ 15A1 $15$ $4$ $C_3\times C_{30}$ 15A2 5A1 3A $b^{4}c^{6}$
$C_{30}.D_6$ 15A2 $15$ $4$ $C_3\times C_{30}$ 15A1 5A2 3A $b^{8}c^{12}$
$C_{30}.D_6$ 15B1 $15$ $4$ $C_3\times C_{30}$ 15B2 5A2 3C $b^{4}c^{2}$
$C_{30}.D_6$ 15B2 $15$ $4$ $C_3\times C_{30}$ 15B1 5A1 3C $b^{8}c^{4}$
$C_{30}.D_6$ 15C1 $15$ $4$ $C_3\times C_{30}$ 15C2 5A1 3B $b^{4}c^{4}$
$C_{30}.D_6$ 15C2 $15$ $4$ $C_3\times C_{30}$ 15C1 5A2 3B $b^{8}c^{8}$
$C_{30}.D_6$ 15D1 $15$ $4$ $C_3\times C_{30}$ 15D2 5A2 3D $c^{2}$
$C_{30}.D_6$ 15D2 $15$ $4$ $C_3\times C_{30}$ 15D1 5A1 3D $c^{4}$
$C_{30}.D_6$ 20A1 $20$ $18$ $C_{20}$ 10A1 20A3 4B1 $ac^{3}$
$C_{30}.D_6$ 20A-1 $20$ $18$ $C_{20}$ 10A1 20A-3 4B-1 $ab^{2}c^{3}$
$C_{30}.D_6$ 20A3 $20$ $18$ $C_{20}$ 10A3 20A1 4B-1 $ab^{2}c$
$C_{30}.D_6$ 20A-3 $20$ $18$ $C_{20}$ 10A3 20A-1 4B1 $ac$
$C_{30}.D_6$ 30A1 $30$ $4$ $C_3\times C_{30}$ 15A1 10A1 6A $b^{2}c^{3}$
$C_{30}.D_6$ 30A7 $30$ $4$ $C_3\times C_{30}$ 15A2 10A3 6A $b^{2}c^{6}$
$C_{30}.D_6$ 30B1 $30$ $4$ $C_3\times C_{30}$ 15B1 10A3 6C $b^{2}c$
$C_{30}.D_6$ 30B7 $30$ $4$ $C_3\times C_{30}$ 15B2 10A1 6C $b^{2}c^{7}$
$C_{30}.D_6$ 30C1 $30$ $4$ $C_3\times C_{30}$ 15C1 10A1 6B $b^{2}c^{2}$
$C_{30}.D_6$ 30C7 $30$ $4$ $C_3\times C_{30}$ 15C2 10A3 6B $b^{10}c$
$C_{30}.D_6$ 30D1 $30$ $4$ $C_3\times C_{30}$ 15D1 10A3 6D $b^{6}c$
$C_{30}.D_6$ 30D7 $30$ $4$ $C_3\times C_{30}$ 15D2 10A1 6D $b^{6}c^{2}$
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