↑

Learn more

Refine search

Group Order Size
Sort order Select

Results (1-50 of 120 matches)

Next   displayed columns for results

Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{12}=c^{20}=[a,c]=1, a^{2}=b^{6}, b^{a}=b^{11}, c^{b}=c^{11} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_{60}:Q_8$ 1A $1$ $1$ $C_{60}:Q_8$ 1A 1A 1A $1$
$C_{60}:Q_8$ 2A $2$ $1$ $C_{60}:Q_8$ 1A 2A 2A $b^{6}$
$C_{60}:Q_8$ 2B $2$ $1$ $C_{60}:Q_8$ 1A 2B 2B $b^{6}c^{10}$
$C_{60}:Q_8$ 2C $2$ $1$ $C_{60}:Q_8$ 1A 2C 2C $c^{10}$
$C_{60}:Q_8$ 3A $3$ $2$ $C_4:C_{60}$ 3A 1A 3A $b^{8}$
$C_{60}:Q_8$ 4A $4$ $2$ $C_{12}:C_{20}$ 2C 4A 4A $c^{15}$
$C_{60}:Q_8$ 4B $4$ $2$ $C_{12}:C_{20}$ 2C 4B 4B $b^{6}c^{15}$
$C_{60}:Q_8$ 4C $4$ $4$ $C_2\times C_{60}$ 2A 4C 4C $b^{3}$
$C_{60}:Q_8$ 4D $4$ $4$ $C_2\times C_{60}$ 2A 4D 4D $b^{3}c^{5}$
$C_{60}:Q_8$ 4E $4$ $6$ $C_4\times C_{20}$ 2A 4E 4E $a$
$C_{60}:Q_8$ 4F $4$ $6$ $C_4\times C_{20}$ 2A 4F 4F $ac^{10}$
$C_{60}:Q_8$ 4G $4$ $6$ $C_4\times C_{20}$ 2B 4G 4G $ac^{5}$
$C_{60}:Q_8$ 4H $4$ $6$ $C_4\times C_{20}$ 2B 4H 4H $ac^{15}$
$C_{60}:Q_8$ 4I $4$ $12$ $C_2\times C_{20}$ 2A 4I 4I $ab$
$C_{60}:Q_8$ 4J $4$ $12$ $C_2\times C_{20}$ 2A 4J 4J $abc^{5}$
$C_{60}:Q_8$ 5A1 $5$ $1$ $C_{60}:Q_8$ 5A2 5A-2 1A $c^{16}$
$C_{60}:Q_8$ 5A-1 $5$ $1$ $C_{60}:Q_8$ 5A-2 5A2 1A $c^{4}$
$C_{60}:Q_8$ 5A2 $5$ $1$ $C_{60}:Q_8$ 5A-1 5A1 1A $c^{12}$
$C_{60}:Q_8$ 5A-2 $5$ $1$ $C_{60}:Q_8$ 5A1 5A-1 1A $c^{8}$
$C_{60}:Q_8$ 6A $6$ $2$ $C_4:C_{60}$ 3A 2B 6A $b^{10}c^{10}$
$C_{60}:Q_8$ 6B $6$ $2$ $C_4:C_{60}$ 3A 2C 6B $b^{4}c^{10}$
$C_{60}:Q_8$ 6C $6$ $2$ $C_4:C_{60}$ 3A 2A 6C $b^{10}$
$C_{60}:Q_8$ 10A1 $10$ $1$ $C_{60}:Q_8$ 5A1 10A3 2A $b^{6}c^{8}$
$C_{60}:Q_8$ 10A-1 $10$ $1$ $C_{60}:Q_8$ 5A-1 10A-3 2A $b^{6}c^{12}$
$C_{60}:Q_8$ 10A3 $10$ $1$ $C_{60}:Q_8$ 5A-2 10A-1 2A $b^{6}c^{4}$
$C_{60}:Q_8$ 10A-3 $10$ $1$ $C_{60}:Q_8$ 5A2 10A1 2A $b^{6}c^{16}$
$C_{60}:Q_8$ 10B1 $10$ $1$ $C_{60}:Q_8$ 5A-1 10B3 2B $b^{6}c^{2}$
$C_{60}:Q_8$ 10B-1 $10$ $1$ $C_{60}:Q_8$ 5A1 10B-3 2B $b^{6}c^{18}$
$C_{60}:Q_8$ 10B3 $10$ $1$ $C_{60}:Q_8$ 5A2 10B-1 2B $b^{6}c^{6}$
$C_{60}:Q_8$ 10B-3 $10$ $1$ $C_{60}:Q_8$ 5A-2 10B1 2B $b^{6}c^{14}$
$C_{60}:Q_8$ 10C1 $10$ $1$ $C_{60}:Q_8$ 5A2 10C3 2C $c^{6}$
$C_{60}:Q_8$ 10C-1 $10$ $1$ $C_{60}:Q_8$ 5A-2 10C-3 2C $c^{14}$
$C_{60}:Q_8$ 10C3 $10$ $1$ $C_{60}:Q_8$ 5A1 10C-1 2C $c^{18}$
$C_{60}:Q_8$ 10C-3 $10$ $1$ $C_{60}:Q_8$ 5A-1 10C1 2C $c^{2}$
$C_{60}:Q_8$ 12A $12$ $4$ $C_2\times C_{60}$ 6B 4A 12A $b^{8}c^{5}$
$C_{60}:Q_8$ 12B $12$ $4$ $C_2\times C_{60}$ 6B 4B 12B $b^{10}c^{5}$
$C_{60}:Q_8$ 12C1 $12$ $4$ $C_2\times C_{60}$ 6C 4C 12C5 $b^{5}$
$C_{60}:Q_8$ 12C5 $12$ $4$ $C_2\times C_{60}$ 6C 4C 12C1 $b$
$C_{60}:Q_8$ 12D1 $12$ $4$ $C_2\times C_{60}$ 6C 4D 12D5 $b^{5}c^{5}$
$C_{60}:Q_8$ 12D5 $12$ $4$ $C_2\times C_{60}$ 6C 4D 12D1 $bc^{5}$
$C_{60}:Q_8$ 15A1 $15$ $2$ $C_4:C_{60}$ 15A2 5A2 3A $b^{4}c^{4}$
$C_{60}:Q_8$ 15A-1 $15$ $2$ $C_4:C_{60}$ 15A-2 5A-2 3A $b^{8}c^{16}$
$C_{60}:Q_8$ 15A2 $15$ $2$ $C_4:C_{60}$ 15A-1 5A-1 3A $b^{8}c^{8}$
$C_{60}:Q_8$ 15A-2 $15$ $2$ $C_4:C_{60}$ 15A1 5A1 3A $b^{4}c^{12}$
$C_{60}:Q_8$ 20A1 $20$ $2$ $C_{12}:C_{20}$ 10C1 20A3 4A $c^{3}$
$C_{60}:Q_8$ 20A-1 $20$ $2$ $C_{12}:C_{20}$ 10C-1 20A-3 4A $c^{17}$
$C_{60}:Q_8$ 20A3 $20$ $2$ $C_{12}:C_{20}$ 10C3 20A-1 4A $c^{9}$
$C_{60}:Q_8$ 20A-3 $20$ $2$ $C_{12}:C_{20}$ 10C-3 20A1 4A $c^{11}$
$C_{60}:Q_8$ 20B1 $20$ $2$ $C_{12}:C_{20}$ 10C1 20B3 4B $b^{6}c^{3}$
$C_{60}:Q_8$ 20B-1 $20$ $2$ $C_{12}:C_{20}$ 10C-1 20B-3 4B $b^{6}c^{17}$
Next   displayed columns for results