↑

Learn more

Refine search

Group Order Size
Sort order Select

Results (1-50 of 87 matches)

Next   displayed columns for results

Elements of the group are displayed as words in the presentation $\langle a, b, c, d, e \mid a^{12}=b^{10}=c^{3}=d^{5}=e^{5}=[b,d]=[d,e]=1, b^{a}=b^{3}cd^{3}, c^{a}=c^{2}e^{2}, d^{a}=e^{2}, e^{a}=d^{2}, c^{b}=c^{2}d^{2}e^{3}, e^{b}=de^{4}, d^{c}=d^{4}e, e^{c}=d^{4} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_5^3:(S_3\times C_{12})$ 1A $1$ $1$ $C_5^3:(S_3\times C_{12})$ 1A 1A 1A $1$
$C_5^3:(S_3\times C_{12})$ 2A $2$ $15$ $C_{30}:F_5$ 1A 2A 2A $b^{5}$
$C_5^3:(S_3\times C_{12})$ 2B $2$ $75$ $C_6\times F_5$ 1A 2B 2B $a^{6}b^{5}d$
$C_5^3:(S_3\times C_{12})$ 2C $2$ $125$ $S_3\times C_{12}$ 1A 2C 2C $a^{6}b^{4}$
$C_5^3:(S_3\times C_{12})$ 3A1 $3$ $1$ $C_5^3:(S_3\times C_{12})$ 3A-1 1A 3A-1 $a^{8}$
$C_5^3:(S_3\times C_{12})$ 3A-1 $3$ $1$ $C_5^3:(S_3\times C_{12})$ 3A1 1A 3A1 $a^{4}$
$C_5^3:(S_3\times C_{12})$ 3B $3$ $50$ $C_3^2\times F_5$ 3B 1A 3B $c^{2}d^{2}e^{3}$
$C_5^3:(S_3\times C_{12})$ 3C1 $3$ $50$ $C_3^2\times F_5$ 3C-1 1A 3C-1 $a^{4}c^{2}d^{2}$
$C_5^3:(S_3\times C_{12})$ 3C-1 $3$ $50$ $C_3^2\times F_5$ 3C1 1A 3C1 $a^{8}cd^{2}e^{3}$
$C_5^3:(S_3\times C_{12})$ 4A1 $4$ $125$ $S_3\times C_{12}$ 2C 4A-1 4A1 $a^{3}bc^{2}d^{3}e^{3}$
$C_5^3:(S_3\times C_{12})$ 4A-1 $4$ $125$ $S_3\times C_{12}$ 2C 4A1 4A-1 $a^{9}b^{7}c^{2}de^{3}$
$C_5^3:(S_3\times C_{12})$ 4B1 $4$ $375$ $C_2\times C_{12}$ 2C 4B-1 4B1 $a^{3}b^{8}$
$C_5^3:(S_3\times C_{12})$ 4B-1 $4$ $375$ $C_2\times C_{12}$ 2C 4B1 4B-1 $a^{9}b^{6}$
$C_5^3:(S_3\times C_{12})$ 5A $5$ $4$ $C_3\times C_5\wr S_3$ 5A 5A 1A $b^{6}$
$C_5^3:(S_3\times C_{12})$ 5B $5$ $12$ $C_5^2:C_{30}$ 5B 5B 1A $b^{6}d^{3}$
$C_5^3:(S_3\times C_{12})$ 5C $5$ $12$ $C_5^2:C_{30}$ 5C 5C 1A $b^{6}d$
$C_5^3:(S_3\times C_{12})$ 5D $5$ $12$ $C_5^2:C_{30}$ 5D 5D 1A $b^{6}e$
$C_5^3:(S_3\times C_{12})$ 5E $5$ $12$ $C_5^2:C_{30}$ 5E 5E 1A $b^{6}d^{2}$
$C_5^3:(S_3\times C_{12})$ 5F $5$ $12$ $C_5^2:C_{30}$ 5F 5F 1A $d^{3}$
$C_5^3:(S_3\times C_{12})$ 5G $5$ $12$ $C_5^2:C_{30}$ 5G 5G 1A $de^{3}$
$C_5^3:(S_3\times C_{12})$ 5H $5$ $24$ $C_5^2\times C_{15}$ 5H 5H 1A $b^{6}d^{3}e^{3}$
$C_5^3:(S_3\times C_{12})$ 5I $5$ $24$ $C_5^2\times C_{15}$ 5I 5I 1A $b^{6}d^{3}e$
$C_5^3:(S_3\times C_{12})$ 6A1 $6$ $15$ $C_{30}:F_5$ 3A-1 2A 6A-1 $a^{8}b^{5}$
$C_5^3:(S_3\times C_{12})$ 6A-1 $6$ $15$ $C_{30}:F_5$ 3A1 2A 6A1 $a^{4}b^{5}$
$C_5^3:(S_3\times C_{12})$ 6B1 $6$ $75$ $C_6\times F_5$ 3A1 2B 6B-1 $a^{10}b^{5}d$
$C_5^3:(S_3\times C_{12})$ 6B-1 $6$ $75$ $C_6\times F_5$ 3A-1 2B 6B1 $a^{2}b^{5}d$
$C_5^3:(S_3\times C_{12})$ 6C1 $6$ $125$ $S_3\times C_{12}$ 3A-1 2C 6C-1 $a^{2}b^{4}$
$C_5^3:(S_3\times C_{12})$ 6C-1 $6$ $125$ $S_3\times C_{12}$ 3A1 2C 6C1 $a^{10}b^{4}$
$C_5^3:(S_3\times C_{12})$ 6D $6$ $250$ $C_3\times C_{12}$ 3B 2C 6D $a^{6}cd^{2}e^{4}$
$C_5^3:(S_3\times C_{12})$ 6E1 $6$ $250$ $C_3\times C_{12}$ 3C1 2C 6E-1 $a^{2}b^{8}cd^{3}e^{2}$
$C_5^3:(S_3\times C_{12})$ 6E-1 $6$ $250$ $C_3\times C_{12}$ 3C-1 2C 6E1 $a^{10}b^{8}c^{2}d^{2}e$
$C_5^3:(S_3\times C_{12})$ 10A $10$ $60$ $C_5\times C_{30}$ 5A 10A 2A $b^{3}$
$C_5^3:(S_3\times C_{12})$ 10B $10$ $60$ $C_5\times C_{30}$ 5B 10B 2A $b^{3}de$
$C_5^3:(S_3\times C_{12})$ 10C $10$ $60$ $C_5\times C_{30}$ 5C 10C 2A $b^{3}d^{3}$
$C_5^3:(S_3\times C_{12})$ 10D $10$ $60$ $C_5\times C_{30}$ 5D 10D 2A $b^{3}ce^{2}$
$C_5^3:(S_3\times C_{12})$ 10E $10$ $60$ $C_5\times C_{30}$ 5E 10E 2A $b^{3}d$
$C_5^3:(S_3\times C_{12})$ 10F $10$ $60$ $C_5\times C_{30}$ 5F 10F 2A $b^{5}de$
$C_5^3:(S_3\times C_{12})$ 10G $10$ $300$ $C_{30}$ 5G 10G 2B $a^{6}b^{5}d^{4}e^{4}$
$C_5^3:(S_3\times C_{12})$ 12A1 $12$ $125$ $S_3\times C_{12}$ 6C-1 4A1 12A5 $a^{5}b^{9}c^{2}$
$C_5^3:(S_3\times C_{12})$ 12A-1 $12$ $125$ $S_3\times C_{12}$ 6C1 4A-1 12A-5 $a^{7}b^{7}c^{2}e^{4}$
$C_5^3:(S_3\times C_{12})$ 12A5 $12$ $125$ $S_3\times C_{12}$ 6C1 4A1 12A1 $ab^{9}c^{2}$
$C_5^3:(S_3\times C_{12})$ 12A-5 $12$ $125$ $S_3\times C_{12}$ 6C-1 4A-1 12A-1 $a^{11}b^{7}c^{2}e^{4}$
$C_5^3:(S_3\times C_{12})$ 12B1 $12$ $250$ $C_3\times C_{12}$ 6D 4A-1 12B1 $a^{3}b^{5}cd^{4}e^{4}$
$C_5^3:(S_3\times C_{12})$ 12B-1 $12$ $250$ $C_3\times C_{12}$ 6D 4A1 12B-1 $a^{9}b^{5}e^{2}$
$C_5^3:(S_3\times C_{12})$ 12C1 $12$ $250$ $C_3\times C_{12}$ 6E1 4A1 12C5 $ab^{7}ce$
$C_5^3:(S_3\times C_{12})$ 12C-1 $12$ $250$ $C_3\times C_{12}$ 6E-1 4A-1 12C-5 $a^{11}bde$
$C_5^3:(S_3\times C_{12})$ 12C5 $12$ $250$ $C_3\times C_{12}$ 6E-1 4A1 12C1 $a^{5}b^{7}d^{3}e^{4}$
$C_5^3:(S_3\times C_{12})$ 12C-5 $12$ $250$ $C_3\times C_{12}$ 6E1 4A-1 12C-1 $a^{7}bce^{4}$
$C_5^3:(S_3\times C_{12})$ 12D1 $12$ $375$ $C_2\times C_{12}$ 6C1 4B1 12D5 $ab^{6}$
$C_5^3:(S_3\times C_{12})$ 12D-1 $12$ $375$ $C_2\times C_{12}$ 6C-1 4B-1 12D-5 $a^{11}b^{8}$
Next   displayed columns for results