↑

Learn more

Refine search

Group Order Size
Sort order Select

Results (1-50 of 72 matches)

Next   displayed columns for results

Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{12}=b^{6}=c^{6}=[b,c]=1, b^{a}=b^{5}c^{3}, c^{a}=b^{5}c^{4} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_6^2:C_{12}$ 1A $1$ $1$ $C_6^2:C_{12}$ 1A 1A $1$
$C_6^2:C_{12}$ 2A $2$ $1$ $C_6^2:C_{12}$ 1A 2A $a^{6}$
$C_6^2:C_{12}$ 2B $2$ $3$ $C_6^2:C_4$ 1A 2B $b^{3}c^{3}$
$C_6^2:C_{12}$ 2C $2$ $3$ $C_6^2:C_4$ 1A 2C $a^{6}b^{3}c^{3}$
$C_6^2:C_{12}$ 3A1 $3$ $1$ $C_6^2:C_{12}$ 3A-1 1A $b^{2}c^{2}$
$C_6^2:C_{12}$ 3A-1 $3$ $1$ $C_6^2:C_{12}$ 3A1 1A $b^{4}c^{4}$
$C_6^2:C_{12}$ 3B $3$ $2$ $C_6^2:C_6$ 3B 1A $b^{4}$
$C_6^2:C_{12}$ 3C1 $3$ $2$ $C_6^2:C_6$ 3C-1 1A $c^{4}$
$C_6^2:C_{12}$ 3C-1 $3$ $2$ $C_6^2:C_6$ 3C1 1A $c^{2}$
$C_6^2:C_{12}$ 3D1 $3$ $4$ $C_3^2:C_{12}$ 3D-1 1A $a^{4}$
$C_6^2:C_{12}$ 3D-1 $3$ $4$ $C_3^2:C_{12}$ 3D1 1A $a^{8}$
$C_6^2:C_{12}$ 3E1 $3$ $4$ $C_3^2:C_{12}$ 3E-1 1A $a^{4}b^{2}c^{2}$
$C_6^2:C_{12}$ 3E-1 $3$ $4$ $C_3^2:C_{12}$ 3E1 1A $a^{8}b^{4}c^{4}$
$C_6^2:C_{12}$ 3F1 $3$ $4$ $C_3^2:C_{12}$ 3F-1 1A $a^{4}b^{4}c$
$C_6^2:C_{12}$ 3F-1 $3$ $4$ $C_3^2:C_{12}$ 3F1 1A $a^{8}b^{5}c^{5}$
$C_6^2:C_{12}$ 3G1 $3$ $8$ $C_3^2\times C_6$ 3G-1 1A $a^{4}c^{4}$
$C_6^2:C_{12}$ 3G-1 $3$ $8$ $C_3^2\times C_6$ 3G1 1A $a^{8}c^{2}$
$C_6^2:C_{12}$ 3H1 $3$ $8$ $C_3^2\times C_6$ 3H-1 1A $a^{4}b^{3}c^{2}$
$C_6^2:C_{12}$ 3H-1 $3$ $8$ $C_3^2\times C_6$ 3H1 1A $a^{8}c$
$C_6^2:C_{12}$ 3I1 $3$ $8$ $C_3^2\times C_6$ 3I-1 1A $a^{4}b^{4}$
$C_6^2:C_{12}$ 3I-1 $3$ $8$ $C_3^2\times C_6$ 3I1 1A $a^{8}b^{2}$
$C_6^2:C_{12}$ 4A1 $4$ $3$ $C_{12}\times A_4$ 2A 4A-1 $a^{9}b^{4}$
$C_6^2:C_{12}$ 4A-1 $4$ $3$ $C_{12}\times A_4$ 2A 4A1 $a^{3}b^{4}$
$C_6^2:C_{12}$ 4B1 $4$ $9$ $C_2^2\times C_{12}$ 2A 4B-1 $a^{9}b^{2}c^{3}$
$C_6^2:C_{12}$ 4B-1 $4$ $9$ $C_2^2\times C_{12}$ 2A 4B1 $a^{3}b^{2}c^{3}$
$C_6^2:C_{12}$ 6A1 $6$ $1$ $C_6^2:C_{12}$ 3A1 2A $a^{6}b^{4}c^{4}$
$C_6^2:C_{12}$ 6A-1 $6$ $1$ $C_6^2:C_{12}$ 3A-1 2A $a^{6}b^{2}c^{2}$
$C_6^2:C_{12}$ 6B $6$ $2$ $C_6^2:C_6$ 3B 2A $a^{6}b^{2}$
$C_6^2:C_{12}$ 6C1 $6$ $2$ $C_6^2:C_6$ 3C1 2A $a^{6}c^{2}$
$C_6^2:C_{12}$ 6C-1 $6$ $2$ $C_6^2:C_6$ 3C-1 2A $a^{6}c^{4}$
$C_6^2:C_{12}$ 6D1 $6$ $3$ $C_6^2:C_4$ 3A1 2B $bc$
$C_6^2:C_{12}$ 6D-1 $6$ $3$ $C_6^2:C_4$ 3A-1 2B $b^{2}c^{5}$
$C_6^2:C_{12}$ 6E1 $6$ $3$ $C_6^2:C_4$ 3A1 2C $a^{6}bc$
$C_6^2:C_{12}$ 6E-1 $6$ $3$ $C_6^2:C_4$ 3A-1 2C $a^{6}b^{2}c^{5}$
$C_6^2:C_{12}$ 6F1 $6$ $4$ $C_3^2:C_{12}$ 3D1 2A $a^{2}$
$C_6^2:C_{12}$ 6F-1 $6$ $4$ $C_3^2:C_{12}$ 3D-1 2A $a^{10}$
$C_6^2:C_{12}$ 6G1 $6$ $4$ $C_3^2:C_{12}$ 3E1 2A $a^{2}b^{4}c^{4}$
$C_6^2:C_{12}$ 6G-1 $6$ $4$ $C_3^2:C_{12}$ 3E-1 2A $a^{10}b^{2}c^{2}$
$C_6^2:C_{12}$ 6H1 $6$ $4$ $C_3^2:C_{12}$ 3F1 2A $a^{2}b^{5}c^{5}$
$C_6^2:C_{12}$ 6H-1 $6$ $4$ $C_3^2:C_{12}$ 3F-1 2A $a^{10}b^{4}c$
$C_6^2:C_{12}$ 6I $6$ $6$ $C_2\times C_6^2$ 3B 2B $b$
$C_6^2:C_{12}$ 6J $6$ $6$ $C_2\times C_6^2$ 3B 2C $a^{6}b$
$C_6^2:C_{12}$ 6K1 $6$ $6$ $C_2\times C_6^2$ 3C-1 2B $c$
$C_6^2:C_{12}$ 6K-1 $6$ $6$ $C_2\times C_6^2$ 3C1 2B $bc^{2}$
$C_6^2:C_{12}$ 6L1 $6$ $6$ $C_2\times C_6^2$ 3C-1 2C $a^{6}c$
$C_6^2:C_{12}$ 6L-1 $6$ $6$ $C_2\times C_6^2$ 3C1 2C $a^{6}bc^{2}$
$C_6^2:C_{12}$ 6M1 $6$ $8$ $C_3^2\times C_6$ 3G1 2A $a^{2}c^{2}$
$C_6^2:C_{12}$ 6M-1 $6$ $8$ $C_3^2\times C_6$ 3G-1 2A $a^{10}c$
$C_6^2:C_{12}$ 6N1 $6$ $8$ $C_3^2\times C_6$ 3H1 2A $a^{2}c$
$C_6^2:C_{12}$ 6N-1 $6$ $8$ $C_3^2\times C_6$ 3H-1 2A $a^{10}c^{2}$
Next   displayed columns for results