↑

Learn more

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 of the abelian group $\langle a, b, c \mid a^{2}=b^{2}=c^{6}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_2^2\times C_6$ 1A $1$ $1$ $C_2^2\times C_6$ 1A 1A $1$
$C_2^2\times C_6$ 2A $2$ $1$ $C_2^2\times C_6$ 1A 2A $c^{3}$
$C_2^2\times C_6$ 2B $2$ $1$ $C_2^2\times C_6$ 1A 2B $b$
$C_2^2\times C_6$ 2C $2$ $1$ $C_2^2\times C_6$ 1A 2C $bc^{3}$
$C_2^2\times C_6$ 2D $2$ $1$ $C_2^2\times C_6$ 1A 2D $a$
$C_2^2\times C_6$ 2E $2$ $1$ $C_2^2\times C_6$ 1A 2E $ac^{3}$
$C_2^2\times C_6$ 2F $2$ $1$ $C_2^2\times C_6$ 1A 2F $ab$
$C_2^2\times C_6$ 2G $2$ $1$ $C_2^2\times C_6$ 1A 2G $abc^{3}$
$C_2^2\times C_6$ 3A1 $3$ $1$ $C_2^2\times C_6$ 3A-1 1A $c^{2}$
$C_2^2\times C_6$ 3A-1 $3$ $1$ $C_2^2\times C_6$ 3A1 1A $c^{4}$
$C_2^2\times C_6$ 6A1 $6$ $1$ $C_2^2\times C_6$ 3A1 2A $c$
$C_2^2\times C_6$ 6A-1 $6$ $1$ $C_2^2\times C_6$ 3A-1 2A $c^{5}$
$C_2^2\times C_6$ 6B1 $6$ $1$ $C_2^2\times C_6$ 3A-1 2B $bc^{2}$
$C_2^2\times C_6$ 6B-1 $6$ $1$ $C_2^2\times C_6$ 3A1 2B $bc^{4}$
$C_2^2\times C_6$ 6C1 $6$ $1$ $C_2^2\times C_6$ 3A1 2C $bc$
$C_2^2\times C_6$ 6C-1 $6$ $1$ $C_2^2\times C_6$ 3A-1 2C $bc^{5}$
$C_2^2\times C_6$ 6D1 $6$ $1$ $C_2^2\times C_6$ 3A-1 2D $ac^{2}$
$C_2^2\times C_6$ 6D-1 $6$ $1$ $C_2^2\times C_6$ 3A1 2D $ac^{4}$
$C_2^2\times C_6$ 6E1 $6$ $1$ $C_2^2\times C_6$ 3A1 2E $ac$
$C_2^2\times C_6$ 6E-1 $6$ $1$ $C_2^2\times C_6$ 3A-1 2E $ac^{5}$
$C_2^2\times C_6$ 6F1 $6$ $1$ $C_2^2\times C_6$ 3A-1 2F $abc^{2}$
$C_2^2\times C_6$ 6F-1 $6$ $1$ $C_2^2\times C_6$ 3A1 2F $abc^{4}$
$C_2^2\times C_6$ 6G1 $6$ $1$ $C_2^2\times C_6$ 3A1 2G $abc$
$C_2^2\times C_6$ 6G-1 $6$ $1$ $C_2^2\times C_6$ 3A-1 2G $abc^{5}$
  displayed columns for results