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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{2}=c^{30}=[a,b]=[b,c]=1, c^{a}=bc^{17} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$D_{10}.D_6$ 1A $1$ $1$ $D_{10}.D_6$ 1A 1A 1A $1$
$D_{10}.D_6$ 2A $2$ $1$ $D_{10}.D_6$ 1A 2A 2A $b$
$D_{10}.D_6$ 2B $2$ $2$ $C_6\times D_{10}$ 1A 2B 2B $c^{15}$
$D_{10}.D_6$ 2C $2$ $5$ $C_6.D_4$ 1A 2C 2C $a^{2}c^{12}$
$D_{10}.D_6$ 2D $2$ $5$ $C_6.D_4$ 1A 2D 2D $a^{2}bc^{12}$
$D_{10}.D_6$ 2E $2$ $10$ $C_2^2\times C_6$ 1A 2E 2E $a^{2}c^{21}$
$D_{10}.D_6$ 3A $3$ $2$ $C_6\times D_{10}$ 3A 1A 3A $c^{10}$
$D_{10}.D_6$ 4A1 $4$ $30$ $C_2\times C_4$ 2C 4A-1 4A1 $a^{3}c^{22}$
$D_{10}.D_6$ 4A-1 $4$ $30$ $C_2\times C_4$ 2C 4A1 4A-1 $ac^{16}$
$D_{10}.D_6$ 4B1 $4$ $30$ $C_2\times C_4$ 2D 4B-1 4B1 $ac^{17}$
$D_{10}.D_6$ 4B-1 $4$ $30$ $C_2\times C_4$ 2D 4B1 4B-1 $a^{3}bc^{29}$
$D_{10}.D_6$ 5A $5$ $4$ $C_2\times C_{30}$ 5A 5A 1A $c^{12}$
$D_{10}.D_6$ 6A $6$ $2$ $C_6\times D_{10}$ 3A 2A 6A $bc^{10}$
$D_{10}.D_6$ 6B1 $6$ $2$ $C_6\times D_{10}$ 3A 2B 6B-1 $c^{5}$
$D_{10}.D_6$ 6B-1 $6$ $2$ $C_6\times D_{10}$ 3A 2B 6B1 $c^{25}$
$D_{10}.D_6$ 6C $6$ $10$ $C_2^2\times C_6$ 3A 2C 6C $a^{2}c^{2}$
$D_{10}.D_6$ 6D $6$ $10$ $C_2^2\times C_6$ 3A 2D 6D $a^{2}bc^{2}$
$D_{10}.D_6$ 6E1 $6$ $10$ $C_2^2\times C_6$ 3A 2E 6E-1 $a^{2}c$
$D_{10}.D_6$ 6E-1 $6$ $10$ $C_2^2\times C_6$ 3A 2E 6E1 $a^{2}bc$
$D_{10}.D_6$ 10A $10$ $4$ $C_2\times C_{30}$ 5A 10A 2A $bc^{6}$
$D_{10}.D_6$ 10B1 $10$ $4$ $C_2\times C_{30}$ 5A 10B3 2B $c^{3}$
$D_{10}.D_6$ 10B3 $10$ $4$ $C_2\times C_{30}$ 5A 10B1 2B $c^{9}$
$D_{10}.D_6$ 15A1 $15$ $4$ $C_2\times C_{30}$ 15A1 5A 3A $c^{4}$
$D_{10}.D_6$ 15A-1 $15$ $4$ $C_2\times C_{30}$ 15A-1 5A 3A $c^{26}$
$D_{10}.D_6$ 30A1 $30$ $4$ $C_2\times C_{30}$ 15A1 10A 6A $bc^{2}$
$D_{10}.D_6$ 30A-1 $30$ $4$ $C_2\times C_{30}$ 15A-1 10A 6A $bc^{14}$
$D_{10}.D_6$ 30B1 $30$ $4$ $C_2\times C_{30}$ 15A1 10B1 6B1 $c$
$D_{10}.D_6$ 30B-1 $30$ $4$ $C_2\times C_{30}$ 15A-1 10B1 6B-1 $bc^{7}$
$D_{10}.D_6$ 30B7 $30$ $4$ $C_2\times C_{30}$ 15A-1 10B3 6B1 $c^{7}$
$D_{10}.D_6$ 30B-7 $30$ $4$ $C_2\times C_{30}$ 15A1 10B3 6B-1 $bc$
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