↑

Learn more

Refine search

Group Order Size
Sort order Select

Results (1-50 of 51 matches)

Next   displayed columns for results

Elements of the group are displayed as words in the presentation $\langle a, b, c, d, e \mid a^{2}=b^{6}=c^{6}=d^{9}=e^{3}=[a,c]=[a,d]=[a,e]=[b,d]=[d,e]=1, b^{a}=b^{5}, c^{b}=c^{5}, e^{b}=d^{6}e^{2}, d^{c}=d^{8}e, e^{c}=d^{3}e^{2} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_3^2.S_3^3$ 1A $1$ $1$ $C_3^2.S_3^3$ 1A 1A $1$
$C_3^2.S_3^3$ 2A $2$ $3$ $(C_3\times C_{18}):D_6$ 1A 2A $a$
$C_3^2.S_3^3$ 2B $2$ $9$ $S_3\times D_{18}$ 1A 2B $b^{3}$
$C_3^2.S_3^3$ 2C $2$ $27$ $S_3\times D_6$ 1A 2C $c^{3}d^{3}$
$C_3^2.S_3^3$ 2D $2$ $27$ $C_2\times D_{18}$ 1A 2D $abc^{4}$
$C_3^2.S_3^3$ 2E $2$ $27$ $S_3\times D_6$ 1A 2E $b^{3}c$
$C_3^2.S_3^3$ 2F $2$ $81$ $C_2\times D_6$ 1A 2F $ab^{3}c^{5}d^{3}$
$C_3^2.S_3^3$ 2G $2$ $81$ $C_2\times D_6$ 1A 2G $ab^{2}c^{3}d^{6}e$
$C_3^2.S_3^3$ 3A $3$ $2$ $C_3^3.S_3^2$ 3A 1A $b^{2}$
$C_3^2.S_3^3$ 3B $3$ $2$ $(C_3\times C_9):S_3^2$ 3B 1A $d^{6}$
$C_3^2.S_3^3$ 3C $3$ $4$ $(C_3^2\times C_9):S_3$ 3C 1A $b^{2}d^{6}$
$C_3^2.S_3^3$ 3D $3$ $6$ $C_3^2:D_{18}$ 3D 1A $e^{2}$
$C_3^2.S_3^3$ 3E $3$ $12$ $C_3^2\times D_9$ 3E 1A $b^{4}e^{2}$
$C_3^2.S_3^3$ 3F $3$ $18$ $C_3\times S_3^2$ 3F 1A $c^{4}$
$C_3^2.S_3^3$ 3G $3$ $36$ $S_3\times C_3^2$ 3G 1A $b^{2}c^{4}$
$C_3^2.S_3^3$ 6A $6$ $6$ $(C_3\times C_{18}):S_3$ 3B 2A $ad^{3}$
$C_3^2.S_3^3$ 6B $6$ $18$ $C_3\times D_{18}$ 3A 2B $b$
$C_3^2.S_3^3$ 6C $6$ $18$ $C_3\times D_{18}$ 3D 2A $ae$
$C_3^2.S_3^3$ 6D $6$ $18$ $S_3\times C_{18}$ 3B 2B $b^{3}d^{3}$
$C_3^2.S_3^3$ 6E $6$ $36$ $C_3\times C_{18}$ 3C 2B $be$
$C_3^2.S_3^3$ 6F $6$ $54$ $C_6\times S_3$ 3F 2A $ac^{2}$
$C_3^2.S_3^3$ 6G $6$ $54$ $C_2\times C_{18}$ 3B 2D $abc^{4}d^{3}$
$C_3^2.S_3^3$ 6H $6$ $54$ $C_6\times S_3$ 3A 2C $b^{2}c^{3}d^{2}$
$C_3^2.S_3^3$ 6I $6$ $54$ $C_6\times S_3$ 3F 2C $cd^{5}$
$C_3^2.S_3^3$ 6J $6$ $54$ $C_6\times S_3$ 3A 2E $bc^{5}d^{6}$
$C_3^2.S_3^3$ 6K $6$ $54$ $C_6\times S_3$ 3D 2E $b^{3}cd^{7}$
$C_3^2.S_3^3$ 6L $6$ $108$ $C_3\times C_6$ 3G 2C $b^{4}c^{5}d^{3}$
$C_3^2.S_3^3$ 6M $6$ $108$ $C_3\times C_6$ 3E 2E $b^{5}ce$
$C_3^2.S_3^3$ 6N $6$ $162$ $C_2\times C_6$ 3D 2F $ab^{3}c^{5}e^{2}$
$C_3^2.S_3^3$ 6O $6$ $162$ $C_2\times C_6$ 3F 2G $ab^{2}c^{5}d^{3}e$
$C_3^2.S_3^3$ 9A1 $9$ $6$ $C_9\times S_3^2$ 9A2 3B $d^{2}$
$C_3^2.S_3^3$ 9A2 $9$ $6$ $C_9\times S_3^2$ 9A4 3B $d^{4}$
$C_3^2.S_3^3$ 9A4 $9$ $6$ $C_9\times S_3^2$ 9A1 3B $d^{8}$
$C_3^2.S_3^3$ 9B1 $9$ $12$ $C_3^2:C_{18}$ 9B2 3B $b^{2}d^{2}$
$C_3^2.S_3^3$ 9B2 $9$ $12$ $C_3^2:C_{18}$ 9B4 3B $b^{4}d^{4}$
$C_3^2.S_3^3$ 9B4 $9$ $12$ $C_3^2:C_{18}$ 9B1 3B $b^{2}d^{8}$
$C_3^2.S_3^3$ 9C $9$ $36$ $S_3\times C_9$ 9C 3B $c^{2}d^{5}e$
$C_3^2.S_3^3$ 9D $9$ $72$ $C_3\times C_9$ 9D 3B $b^{2}c^{4}d^{4}e$
$C_3^2.S_3^3$ 18A1 $18$ $18$ $S_3\times C_{18}$ 9A1 6A $ad$
$C_3^2.S_3^3$ 18A5 $18$ $18$ $S_3\times C_{18}$ 9A4 6A $ad^{4}$
$C_3^2.S_3^3$ 18A7 $18$ $18$ $S_3\times C_{18}$ 9A2 6A $ad^{2}$
$C_3^2.S_3^3$ 18B1 $18$ $18$ $S_3\times C_{18}$ 9A1 6D $b^{3}d$
$C_3^2.S_3^3$ 18B5 $18$ $18$ $S_3\times C_{18}$ 9A4 6D $b^{3}de$
$C_3^2.S_3^3$ 18B7 $18$ $18$ $S_3\times C_{18}$ 9A2 6D $b^{3}d^{2}$
$C_3^2.S_3^3$ 18C1 $18$ $36$ $C_3\times C_{18}$ 9B1 6D $bd$
$C_3^2.S_3^3$ 18C5 $18$ $36$ $C_3\times C_{18}$ 9B4 6D $bde$
$C_3^2.S_3^3$ 18C7 $18$ $36$ $C_3\times C_{18}$ 9B2 6D $bd^{2}$
$C_3^2.S_3^3$ 18D1 $18$ $54$ $C_2\times C_{18}$ 9A4 6G $abc^{4}d^{7}e$
$C_3^2.S_3^3$ 18D5 $18$ $54$ $C_2\times C_{18}$ 9A2 6G $abc^{4}d^{8}e^{2}$
$C_3^2.S_3^3$ 18D7 $18$ $54$ $C_2\times C_{18}$ 9A1 6G $abc^{4}d^{4}e$
Next   displayed columns for results