Elements of the group are displayed as words in the presentation $\langle a, b, c, d, e \mid a^{2}=b^{6}=d^{2}=e^{20}=[c,d]=1, c^{2}=e^{10}, b^{a}=b^{5}e^{10}, c^{a}=e^{15}, d^{a}=cde^{5}, e^{a}=ce^{6}, c^{b}=ce^{5}, d^{b}=de^{5}, e^{b}=ce^{4}, e^{c}=e^{11}, e^{d}=e^{11} \rangle$ .
Group Label Order Size Centralizer Powers Representative
2P
3P
5P
$\GL(2,3):D_{10}$ 1A $1$
$1$
$\GL(2,3):D_{10}$ 1A 1A 1A $1$
$\GL(2,3):D_{10}$ 2A $2$
$1$
$\GL(2,3):D_{10}$ 1A 2A 2A $e^{10}$
$\GL(2,3):D_{10}$ 2B $2$
$6$
$C_8:D_{10}$ 1A 2B 2B $d$
$\GL(2,3):D_{10}$ 2C $2$
$10$
$\SL(2,3):C_2^2$ 1A 2C 2C $b^{3}e^{14}$
$\GL(2,3):D_{10}$ 2D $2$
$12$
$C_4\times D_{10}$ 1A 2D 2D $a$
$\GL(2,3):D_{10}$ 2E $2$
$30$
$D_4:C_2^2$ 1A 2E 2E $b^{3}d$
$\GL(2,3):D_{10}$ 2F $2$
$60$
$C_2^2\times C_4$ 1A 2F 2F $ab^{3}cde^{8}$
$\GL(2,3):D_{10}$ 3A $3$
$8$
$D_5\times C_{12}$ 3A 1A 3A $b^{4}ce^{15}$
$\GL(2,3):D_{10}$ 4A1 $4$
$1$
$\GL(2,3):D_{10}$ 2A 4A-1 4A1 $cd$
$\GL(2,3):D_{10}$ 4A-1 $4$
$1$
$\GL(2,3):D_{10}$ 2A 4A1 4A-1 $cde^{10}$
$\GL(2,3):D_{10}$ 4B $4$
$6$
$C_8:D_{10}$ 2A 4B 4B $ce^{15}$
$\GL(2,3):D_{10}$ 4C $4$
$10$
$\SL(2,3):C_2^2$ 2A 4C 4C $b^{3}cde^{6}$
$\GL(2,3):D_{10}$ 4D $4$
$12$
$C_4\times D_{10}$ 2A 4D 4D $ade^{5}$
$\GL(2,3):D_{10}$ 4E $4$
$30$
$D_4:C_2^2$ 2A 4E 4E $b^{3}e$
$\GL(2,3):D_{10}$ 4F $4$
$60$
$C_2^2\times C_4$ 2A 4F 4F $ab^{3}ce^{7}$
$\GL(2,3):D_{10}$ 5A1 $5$
$2$
$\GL(2,3):C_{10}$ 5A2 5A2 1A $e^{8}$
$\GL(2,3):D_{10}$ 5A2 $5$
$2$
$\GL(2,3):C_{10}$ 5A1 5A1 1A $e^{16}$
$\GL(2,3):D_{10}$ 6A $6$
$8$
$D_5\times C_{12}$ 3A 2A 6A $b^{2}ce^{10}$
$\GL(2,3):D_{10}$ 6B1 $6$
$40$
$C_2\times C_{12}$ 3A 2C 6B-1 $be^{14}$
$\GL(2,3):D_{10}$ 6B-1 $6$
$40$
$C_2\times C_{12}$ 3A 2C 6B1 $b^{5}e^{14}$
$\GL(2,3):D_{10}$ 8A $8$
$12$
$C_2\times C_{40}$ 4B 8A 8A $ae^{15}$
$\GL(2,3):D_{10}$ 8B $8$
$12$
$C_2\times C_{40}$ 4B 8B 8B $ade^{10}$
$\GL(2,3):D_{10}$ 8C $8$
$60$
$C_2\times C_8$ 4B 8C 8C $ab^{3}de^{12}$
$\GL(2,3):D_{10}$ 8D $8$
$60$
$C_2\times C_8$ 4B 8D 8D $ab^{3}ce^{10}$
$\GL(2,3):D_{10}$ 10A1 $10$
$2$
$\GL(2,3):C_{10}$ 5A2 10A3 2A $e^{2}$
$\GL(2,3):D_{10}$ 10A3 $10$
$2$
$\GL(2,3):C_{10}$ 5A1 10A1 2A $e^{6}$
$\GL(2,3):D_{10}$ 10B1 $10$
$12$
$C_2\times C_{40}$ 5A1 10B3 2B $de^{4}$
$\GL(2,3):D_{10}$ 10B3 $10$
$12$
$C_2\times C_{40}$ 5A2 10B1 2B $de^{2}$
$\GL(2,3):D_{10}$ 10C1 $10$
$24$
$C_2\times C_{20}$ 5A1 10C3 2D $ae^{4}$
$\GL(2,3):D_{10}$ 10C3 $10$
$24$
$C_2\times C_{20}$ 5A2 10C1 2D $ae^{2}$
$\GL(2,3):D_{10}$ 12A1 $12$
$8$
$D_5\times C_{12}$ 6A 4A1 12A1 $b^{4}de^{15}$
$\GL(2,3):D_{10}$ 12A-1 $12$
$8$
$D_5\times C_{12}$ 6A 4A-1 12A-1 $b^{2}de^{10}$
$\GL(2,3):D_{10}$ 12B1 $12$
$40$
$C_2\times C_{12}$ 6A 4C 12B5 $b^{5}cde$
$\GL(2,3):D_{10}$ 12B5 $12$
$40$
$C_2\times C_{12}$ 6A 4C 12B1 $bde^{16}$
$\GL(2,3):D_{10}$ 15A1 $15$
$16$
$C_{60}$ 15A2 5A1 3A $b^{2}ce^{16}$
$\GL(2,3):D_{10}$ 15A2 $15$
$16$
$C_{60}$ 15A1 5A2 3A $b^{4}ce^{7}$
$\GL(2,3):D_{10}$ 20A1 $20$
$2$
$\GL(2,3):C_{10}$ 10A3 20A3 4A1 $cde^{12}$
$\GL(2,3):D_{10}$ 20A-1 $20$
$2$
$\GL(2,3):C_{10}$ 10A3 20A-3 4A-1 $cde^{18}$
$\GL(2,3):D_{10}$ 20A3 $20$
$2$
$\GL(2,3):C_{10}$ 10A1 20A1 4A-1 $cde^{6}$
$\GL(2,3):D_{10}$ 20A-3 $20$
$2$
$\GL(2,3):C_{10}$ 10A1 20A-1 4A1 $cde^{4}$
$\GL(2,3):D_{10}$ 20B1 $20$
$12$
$C_2\times C_{40}$ 10A3 20B3 4B $ce^{7}$
$\GL(2,3):D_{10}$ 20B3 $20$
$12$
$C_2\times C_{40}$ 10A1 20B1 4B $ce$
$\GL(2,3):D_{10}$ 20C1 $20$
$24$
$C_2\times C_{20}$ 10A1 20C3 4D $ade$
$\GL(2,3):D_{10}$ 20C3 $20$
$24$
$C_2\times C_{20}$ 10A3 20C1 4D $ade^{3}$
$\GL(2,3):D_{10}$ 30A1 $30$
$16$
$C_{60}$ 15A1 10A3 6A $b^{4}ce^{13}$
$\GL(2,3):D_{10}$ 30A7 $30$
$16$
$C_{60}$ 15A2 10A1 6A $b^{4}ce$
$\GL(2,3):D_{10}$ 40A1 $40$
$12$
$C_2\times C_{40}$ 20B1 40A3 8A $ae$
$\GL(2,3):D_{10}$ 40A3 $40$
$12$
$C_2\times C_{40}$ 20B3 40A9 8A $ae^{13}$
$\GL(2,3):D_{10}$ 40A9 $40$
$12$
$C_2\times C_{40}$ 20B1 40A13 8A $ae^{9}$
$\GL(2,3):D_{10}$ 40A13 $40$
$12$
$C_2\times C_{40}$ 20B3 40A1 8A $ae^{3}$
Next
Download
displayed columns for
to
Text
