Refine search

Group Order Size
Sort order Select

Results (24 matches)

  displayed columns for results

Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{12}=b^{9}=c^{9}=[b,c]=1, b^{a}=b^{7}c^{4}, c^{a}=b^{7}c^{2} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_9^2:C_{12}$ 1A $1$ $1$ $C_9^2:C_{12}$ 1A 1A $1$
$C_9^2:C_{12}$ 2A $2$ $81$ $C_{12}$ 1A 2A $a^{6}bc^{5}$
$C_9^2:C_{12}$ 3A $3$ $4$ $C_9^2:C_3$ 3A 1A $c^{3}$
$C_9^2:C_{12}$ 3B $3$ $4$ $C_9^2:C_3$ 3B 1A $b^{3}$
$C_9^2:C_{12}$ 3C1 $3$ $9$ $C_3^2:C_{12}$ 3C-1 1A $a^{8}b^{3}c^{6}$
$C_9^2:C_{12}$ 3C-1 $3$ $9$ $C_3^2:C_{12}$ 3C1 1A $a^{4}b^{6}c^{3}$
$C_9^2:C_{12}$ 4A1 $4$ $81$ $C_{12}$ 2A 4A-1 $a^{3}b^{8}c^{8}$
$C_9^2:C_{12}$ 4A-1 $4$ $81$ $C_{12}$ 2A 4A1 $a^{9}b^{2}c^{6}$
$C_9^2:C_{12}$ 6A1 $6$ $81$ $C_{12}$ 3C1 2A $a^{10}b^{4}c^{2}$
$C_9^2:C_{12}$ 6A-1 $6$ $81$ $C_{12}$ 3C-1 2A $a^{2}b^{7}c^{8}$
$C_9^2:C_{12}$ 9A $9$ $12$ $C_9^2$ 9A 3A $c$
$C_9^2:C_{12}$ 9B $9$ $12$ $C_9^2$ 9B 3B $b$
$C_9^2:C_{12}$ 9C $9$ $12$ $C_9^2$ 9C 3A $b^{3}c$
$C_9^2:C_{12}$ 9D $9$ $12$ $C_9^2$ 9D 3B $bc^{3}$
$C_9^2:C_{12}$ 9E $9$ $12$ $C_9^2$ 9E 3A $b^{3}c^{2}$
$C_9^2:C_{12}$ 9F $9$ $12$ $C_9^2$ 9F 3B $bc^{6}$
$C_9^2:C_{12}$ 9G1 $9$ $36$ $C_3\times C_9$ 9G-1 3A $a^{8}b^{2}c^{7}$
$C_9^2:C_{12}$ 9G-1 $9$ $36$ $C_3\times C_9$ 9G1 3A $a^{4}b^{4}c^{5}$
$C_9^2:C_{12}$ 9H1 $9$ $36$ $C_3\times C_9$ 9H-1 3B $a^{8}b^{7}c^{6}$
$C_9^2:C_{12}$ 9H-1 $9$ $36$ $C_3\times C_9$ 9H1 3B $a^{4}b^{5}c^{3}$
$C_9^2:C_{12}$ 12A1 $12$ $81$ $C_{12}$ 6A1 4A1 $a^{5}b^{2}c^{3}$
$C_9^2:C_{12}$ 12A-1 $12$ $81$ $C_{12}$ 6A-1 4A-1 $a^{7}b^{8}c^{5}$
$C_9^2:C_{12}$ 12A5 $12$ $81$ $C_{12}$ 6A-1 4A1 $ab^{2}$
$C_9^2:C_{12}$ 12A-5 $12$ $81$ $C_{12}$ 6A1 4A-1 $a^{11}b^{8}c^{2}$
  displayed columns for results