↑

Learn more

Refine search

Group Order Size
Sort order Select

Results (1-50 of 234 matches)

Next   displayed columns for results

Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{15}=c^{15}=[b,c]=1, b^{a}=b^{14}, c^{a}=c^{4} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_{15}^2:C_4$ 1A $1$ $1$ $C_{15}^2:C_4$ 1A 1A 1A $1$
$C_{15}^2:C_4$ 2A $2$ $1$ $C_{15}^2:C_4$ 1A 2A 2A $a^{2}$
$C_{15}^2:C_4$ 3A1 $3$ $1$ $C_{15}^2:C_4$ 3A-1 1A 3A-1 $c^{10}$
$C_{15}^2:C_4$ 3A-1 $3$ $1$ $C_{15}^2:C_4$ 3A1 1A 3A1 $c^{5}$
$C_{15}^2:C_4$ 3B $3$ $2$ $C_{15}\times C_{30}$ 3B 1A 3B $b^{10}$
$C_{15}^2:C_4$ 3C1 $3$ $2$ $C_{15}\times C_{30}$ 3C-1 1A 3C-1 $b^{10}c^{10}$
$C_{15}^2:C_4$ 3C-1 $3$ $2$ $C_{15}\times C_{30}$ 3C1 1A 3C1 $b^{5}c^{5}$
$C_{15}^2:C_4$ 4A1 $4$ $75$ $C_{12}$ 2A 4A-1 4A1 $ab^{6}c^{9}$
$C_{15}^2:C_4$ 4A-1 $4$ $75$ $C_{12}$ 2A 4A1 4A-1 $a^{3}b^{6}c^{9}$
$C_{15}^2:C_4$ 5A1 $5$ $2$ $C_{15}\times C_{30}$ 5A2 5A2 1A $c^{6}$
$C_{15}^2:C_4$ 5A2 $5$ $2$ $C_{15}\times C_{30}$ 5A1 5A1 1A $c^{12}$
$C_{15}^2:C_4$ 5B1 $5$ $2$ $C_{15}\times C_{30}$ 5B2 5B2 1A $b^{6}$
$C_{15}^2:C_4$ 5B2 $5$ $2$ $C_{15}\times C_{30}$ 5B1 5B1 1A $b^{12}$
$C_{15}^2:C_4$ 5C1 $5$ $2$ $C_{15}\times C_{30}$ 5C2 5C2 1A $b^{3}c^{6}$
$C_{15}^2:C_4$ 5C2 $5$ $2$ $C_{15}\times C_{30}$ 5C1 5C1 1A $b^{6}c^{12}$
$C_{15}^2:C_4$ 5D1 $5$ $2$ $C_{15}\times C_{30}$ 5D2 5D2 1A $b^{6}c^{3}$
$C_{15}^2:C_4$ 5D2 $5$ $2$ $C_{15}\times C_{30}$ 5D1 5D1 1A $b^{12}c^{6}$
$C_{15}^2:C_4$ 5E1 $5$ $2$ $C_{15}\times C_{30}$ 5E2 5E2 1A $b^{3}c^{12}$
$C_{15}^2:C_4$ 5E2 $5$ $2$ $C_{15}\times C_{30}$ 5E1 5E1 1A $b^{6}c^{9}$
$C_{15}^2:C_4$ 5F1 $5$ $2$ $C_{15}\times C_{30}$ 5F2 5F2 1A $b^{6}c^{6}$
$C_{15}^2:C_4$ 5F2 $5$ $2$ $C_{15}\times C_{30}$ 5F1 5F1 1A $b^{12}c^{12}$
$C_{15}^2:C_4$ 6A1 $6$ $1$ $C_{15}^2:C_4$ 3A1 2A 6A-1 $a^{2}c^{5}$
$C_{15}^2:C_4$ 6A-1 $6$ $1$ $C_{15}^2:C_4$ 3A-1 2A 6A1 $a^{2}c^{10}$
$C_{15}^2:C_4$ 6B $6$ $2$ $C_{15}\times C_{30}$ 3B 2A 6B $a^{2}b^{5}$
$C_{15}^2:C_4$ 6C1 $6$ $2$ $C_{15}\times C_{30}$ 3C1 2A 6C-1 $a^{2}b^{5}c^{5}$
$C_{15}^2:C_4$ 6C-1 $6$ $2$ $C_{15}\times C_{30}$ 3C-1 2A 6C1 $a^{2}b^{10}c^{10}$
$C_{15}^2:C_4$ 10A1 $10$ $2$ $C_{15}\times C_{30}$ 5A1 10A3 2A $a^{2}c^{3}$
$C_{15}^2:C_4$ 10A3 $10$ $2$ $C_{15}\times C_{30}$ 5A2 10A1 2A $a^{2}c^{9}$
$C_{15}^2:C_4$ 10B1 $10$ $2$ $C_{15}\times C_{30}$ 5B1 10B3 2A $a^{2}b^{3}$
$C_{15}^2:C_4$ 10B3 $10$ $2$ $C_{15}\times C_{30}$ 5B2 10B1 2A $a^{2}b^{9}$
$C_{15}^2:C_4$ 10C1 $10$ $2$ $C_{15}\times C_{30}$ 5C1 10C3 2A $a^{2}b^{9}c^{3}$
$C_{15}^2:C_4$ 10C3 $10$ $2$ $C_{15}\times C_{30}$ 5C2 10C1 2A $a^{2}b^{12}c^{9}$
$C_{15}^2:C_4$ 10D1 $10$ $2$ $C_{15}\times C_{30}$ 5D1 10D3 2A $a^{2}b^{3}c^{9}$
$C_{15}^2:C_4$ 10D3 $10$ $2$ $C_{15}\times C_{30}$ 5D2 10D1 2A $a^{2}b^{9}c^{12}$
$C_{15}^2:C_4$ 10E1 $10$ $2$ $C_{15}\times C_{30}$ 5E1 10E3 2A $a^{2}b^{9}c^{6}$
$C_{15}^2:C_4$ 10E3 $10$ $2$ $C_{15}\times C_{30}$ 5E2 10E1 2A $a^{2}b^{12}c^{3}$
$C_{15}^2:C_4$ 10F1 $10$ $2$ $C_{15}\times C_{30}$ 5F1 10F3 2A $a^{2}b^{3}c^{3}$
$C_{15}^2:C_4$ 10F3 $10$ $2$ $C_{15}\times C_{30}$ 5F2 10F1 2A $a^{2}b^{9}c^{9}$
$C_{15}^2:C_4$ 12A1 $12$ $75$ $C_{12}$ 6A1 4A1 12A5 $a^{3}b^{6}c^{4}$
$C_{15}^2:C_4$ 12A-1 $12$ $75$ $C_{12}$ 6A-1 4A-1 12A-5 $ab^{6}c^{14}$
$C_{15}^2:C_4$ 12A5 $12$ $75$ $C_{12}$ 6A-1 4A1 12A1 $a^{3}b^{6}c^{14}$
$C_{15}^2:C_4$ 12A-5 $12$ $75$ $C_{12}$ 6A1 4A-1 12A-1 $ab^{6}c^{4}$
$C_{15}^2:C_4$ 15A1 $15$ $2$ $C_{15}\times C_{30}$ 15A2 5A1 3A1 $c^{2}$
$C_{15}^2:C_4$ 15A-1 $15$ $2$ $C_{15}\times C_{30}$ 15A-2 5A1 3A-1 $c^{13}$
$C_{15}^2:C_4$ 15A2 $15$ $2$ $C_{15}\times C_{30}$ 15A1 5A2 3A-1 $c^{4}$
$C_{15}^2:C_4$ 15A-2 $15$ $2$ $C_{15}\times C_{30}$ 15A-1 5A2 3A1 $c^{11}$
$C_{15}^2:C_4$ 15B1 $15$ $2$ $C_{15}\times C_{30}$ 15B2 5B1 3B $b^{2}$
$C_{15}^2:C_4$ 15B2 $15$ $2$ $C_{15}\times C_{30}$ 15B4 5B2 3B $b^{4}$
$C_{15}^2:C_4$ 15B4 $15$ $2$ $C_{15}\times C_{30}$ 15B7 5B1 3B $b^{8}$
$C_{15}^2:C_4$ 15B7 $15$ $2$ $C_{15}\times C_{30}$ 15B1 5B2 3B $b^{14}$
Next   displayed columns for results