↑

Learn more

Refine search

Group Order Size
Sort order Select

Results (29 matches)

  displayed columns for results

Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid b^{6}=d^{20}=1, a^{2}=d^{10}, c^{2}=d^{10}, b^{a}=b^{5}d^{10}, c^{a}=d^{15}, d^{a}=cd^{6}, c^{b}=d^{5}, d^{b}=cd^{9}, d^{c}=d^{11} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$D_{10}.S_4$ 1A $1$ $1$ $D_{10}.S_4$ 1A 1A 1A $1$
$D_{10}.S_4$ 2A $2$ $1$ $D_{10}.S_4$ 1A 2A 2A $d^{10}$
$D_{10}.S_4$ 2B $2$ $10$ $C_2\times \SL(2,3)$ 1A 2B 2B $b^{3}d^{18}$
$D_{10}.S_4$ 2C $2$ $60$ $C_2\times C_4$ 1A 2C 2C $ab$
$D_{10}.S_4$ 3A $3$ $8$ $C_3\times D_{10}$ 3A 1A 3A $b^{2}$
$D_{10}.S_4$ 4A $4$ $6$ $C_{40}:C_2$ 2A 4A 4A $cd^{5}$
$D_{10}.S_4$ 4B $4$ $12$ $C_4\times D_5$ 2A 4B 4B $a$
$D_{10}.S_4$ 4C $4$ $30$ $D_4:C_2$ 2A 4C 4C $b^{3}cd^{13}$
$D_{10}.S_4$ 5A1 $5$ $2$ $C_{10}.S_4$ 5A2 5A2 1A $d^{12}$
$D_{10}.S_4$ 5A2 $5$ $2$ $C_{10}.S_4$ 5A1 5A1 1A $d^{4}$
$D_{10}.S_4$ 6A $6$ $8$ $C_3\times D_{10}$ 3A 2A 6A $b^{4}d^{10}$
$D_{10}.S_4$ 6B1 $6$ $40$ $C_2\times C_6$ 3A 2B 6B-1 $bd^{18}$
$D_{10}.S_4$ 6B-1 $6$ $40$ $C_2\times C_6$ 3A 2B 6B1 $b^{5}d^{18}$
$D_{10}.S_4$ 8A $8$ $12$ $C_{40}$ 4A 8A 8A $ad^{15}$
$D_{10}.S_4$ 8B $8$ $60$ $C_8$ 4A 8B 8B $ab^{3}d^{13}$
$D_{10}.S_4$ 10A1 $10$ $2$ $C_{10}.S_4$ 5A1 10A3 2A $d^{6}$
$D_{10}.S_4$ 10A3 $10$ $2$ $C_{10}.S_4$ 5A2 10A1 2A $d^{18}$
$D_{10}.S_4$ 15A1 $15$ $16$ $C_{30}$ 15A2 5A1 3A $b^{4}d^{4}$
$D_{10}.S_4$ 15A2 $15$ $16$ $C_{30}$ 15A1 5A2 3A $b^{2}d^{8}$
$D_{10}.S_4$ 20A1 $20$ $12$ $C_{40}$ 10A1 20A3 4A $cd^{17}$
$D_{10}.S_4$ 20A3 $20$ $12$ $C_{40}$ 10A3 20A1 4A $cd^{11}$
$D_{10}.S_4$ 20B1 $20$ $24$ $C_{20}$ 10A1 20B3 4B $ad^{12}$
$D_{10}.S_4$ 20B3 $20$ $24$ $C_{20}$ 10A3 20B1 4B $ad^{6}$
$D_{10}.S_4$ 30A1 $30$ $16$ $C_{30}$ 15A1 10A1 6A $b^{2}d^{2}$
$D_{10}.S_4$ 30A7 $30$ $16$ $C_{30}$ 15A2 10A3 6A $b^{2}d$
$D_{10}.S_4$ 40A1 $40$ $12$ $C_{40}$ 20A1 40A3 8A $ad$
$D_{10}.S_4$ 40A-1 $40$ $12$ $C_{40}$ 20A1 40A-3 8A $ab^{2}d$
$D_{10}.S_4$ 40A3 $40$ $12$ $C_{40}$ 20A3 40A-1 8A $ad^{3}$
$D_{10}.S_4$ 40A-3 $40$ $12$ $C_{40}$ 20A3 40A1 8A $ad^{13}$
  displayed columns for results