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Results (42 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{10}=c^{15}=1, b^{a}=b^{7}, c^{a}=c^{7}, c^{b}=c^{4} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$D_5^2.C_6$ 1A $1$ $1$ $D_5^2.C_6$ 1A 1A 1A $1$
$D_5^2.C_6$ 2A $2$ $5$ $C_6\times F_5$ 1A 2A 2A $b^{5}c^{6}$
$D_5^2.C_6$ 2B $2$ $5$ $C_6\times F_5$ 1A 2B 2B $a^{2}b$
$D_5^2.C_6$ 2C $2$ $25$ $C_2\times C_{12}$ 1A 2C 2C $a^{2}b^{4}c^{3}$
$D_5^2.C_6$ 3A1 $3$ $1$ $D_5^2.C_6$ 3A-1 1A 3A-1 $c^{5}$
$D_5^2.C_6$ 3A-1 $3$ $1$ $D_5^2.C_6$ 3A1 1A 3A1 $c^{10}$
$D_5^2.C_6$ 4A1 $4$ $25$ $C_2\times C_{12}$ 2C 4A-1 4A1 $ab^{8}c^{6}$
$D_5^2.C_6$ 4A-1 $4$ $25$ $C_2\times C_{12}$ 2C 4A1 4A-1 $a^{3}b^{6}c^{12}$
$D_5^2.C_6$ 4B1 $4$ $25$ $C_2\times C_{12}$ 2C 4B-1 4B1 $a^{3}b^{7}c^{3}$
$D_5^2.C_6$ 4B-1 $4$ $25$ $C_2\times C_{12}$ 2C 4B1 4B-1 $abc^{6}$
$D_5^2.C_6$ 5A $5$ $4$ $D_5\times C_{15}$ 5A 5A 1A $b^{6}$
$D_5^2.C_6$ 5B $5$ $4$ $D_5\times C_{15}$ 5B 5B 1A $c^{6}$
$D_5^2.C_6$ 5C $5$ $8$ $C_5\times C_{15}$ 5C 5C 1A $b^{6}c^{3}$
$D_5^2.C_6$ 5D $5$ $8$ $C_5\times C_{15}$ 5D 5D 1A $b^{6}c^{6}$
$D_5^2.C_6$ 6A1 $6$ $5$ $C_6\times F_5$ 3A-1 2A 6A-1 $b^{5}c^{11}$
$D_5^2.C_6$ 6A-1 $6$ $5$ $C_6\times F_5$ 3A1 2A 6A1 $b^{5}c$
$D_5^2.C_6$ 6B1 $6$ $5$ $C_6\times F_5$ 3A-1 2B 6B-1 $a^{2}bc^{5}$
$D_5^2.C_6$ 6B-1 $6$ $5$ $C_6\times F_5$ 3A1 2B 6B1 $a^{2}bc^{10}$
$D_5^2.C_6$ 6C1 $6$ $25$ $C_2\times C_{12}$ 3A-1 2C 6C-1 $a^{2}b^{4}c^{8}$
$D_5^2.C_6$ 6C-1 $6$ $25$ $C_2\times C_{12}$ 3A1 2C 6C1 $a^{2}b^{4}c^{13}$
$D_5^2.C_6$ 10A $10$ $20$ $C_{30}$ 5A 10A 2A $b^{3}c^{6}$
$D_5^2.C_6$ 10B $10$ $20$ $C_{30}$ 5B 10B 2B $a^{2}bc^{3}$
$D_5^2.C_6$ 12A1 $12$ $25$ $C_2\times C_{12}$ 6C1 4A1 12A5 $a^{3}b^{6}c^{7}$
$D_5^2.C_6$ 12A-1 $12$ $25$ $C_2\times C_{12}$ 6C-1 4A-1 12A-5 $ab^{8}c^{11}$
$D_5^2.C_6$ 12A5 $12$ $25$ $C_2\times C_{12}$ 6C-1 4A1 12A1 $a^{3}b^{6}c^{2}$
$D_5^2.C_6$ 12A-5 $12$ $25$ $C_2\times C_{12}$ 6C1 4A-1 12A-1 $ab^{8}c$
$D_5^2.C_6$ 12B1 $12$ $25$ $C_2\times C_{12}$ 6C1 4B1 12B5 $abc$
$D_5^2.C_6$ 12B-1 $12$ $25$ $C_2\times C_{12}$ 6C-1 4B-1 12B-5 $a^{3}b^{7}c^{8}$
$D_5^2.C_6$ 12B5 $12$ $25$ $C_2\times C_{12}$ 6C-1 4B1 12B1 $abc^{11}$
$D_5^2.C_6$ 12B-5 $12$ $25$ $C_2\times C_{12}$ 6C1 4B-1 12B-1 $a^{3}b^{7}c^{13}$
$D_5^2.C_6$ 15A1 $15$ $4$ $D_5\times C_{15}$ 15A-1 5A 3A-1 $b^{2}c^{5}$
$D_5^2.C_6$ 15A-1 $15$ $4$ $D_5\times C_{15}$ 15A1 5A 3A1 $b^{8}c^{10}$
$D_5^2.C_6$ 15B1 $15$ $4$ $D_5\times C_{15}$ 15B-1 5B 3A-1 $c^{2}$
$D_5^2.C_6$ 15B-1 $15$ $4$ $D_5\times C_{15}$ 15B1 5B 3A1 $c^{13}$
$D_5^2.C_6$ 15C1 $15$ $8$ $C_5\times C_{15}$ 15C-1 5C 3A1 $b^{2}c$
$D_5^2.C_6$ 15C-1 $15$ $8$ $C_5\times C_{15}$ 15C1 5C 3A-1 $b^{4}c^{2}$
$D_5^2.C_6$ 15D1 $15$ $8$ $C_5\times C_{15}$ 15D-1 5D 3A-1 $b^{2}c^{2}$
$D_5^2.C_6$ 15D-1 $15$ $8$ $C_5\times C_{15}$ 15D1 5D 3A1 $b^{4}c$
$D_5^2.C_6$ 30A1 $30$ $20$ $C_{30}$ 15A1 10A 6A1 $bc$
$D_5^2.C_6$ 30A-1 $30$ $20$ $C_{30}$ 15A-1 10A 6A-1 $bc^{2}$
$D_5^2.C_6$ 30B1 $30$ $20$ $C_{30}$ 15B1 10B 6B1 $a^{2}bc$
$D_5^2.C_6$ 30B-1 $30$ $20$ $C_{30}$ 15B-1 10B 6B-1 $a^{2}bc^{2}$
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