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Results (24 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b, c, d, e, f \mid a^{8}=b^{3}=c^{3}=d^{3}=e^{3}=f^{3}=[b,d]=[b,e]=[b,f]=[c,d]=[c,e]=[c,f]=[d,e]=[d,f]=[e,f]=1, b^{a}=bcf^{2}, c^{a}=b^{2}cf, d^{a}=d^{2}e, e^{a}=d, f^{a}=f^{2}, c^{b}=cf^{2} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$\He_3:F_9$ 1A $1$ $1$ $\He_3:F_9$ 1A 1A $1$
$\He_3:F_9$ 2A $2$ $81$ $C_3:C_8$ 1A 2A $a^{4}bcf^{2}$
$\He_3:F_9$ 3A $3$ $2$ $(C_3^2\times \He_3):C_4$ 3A 1A $f$
$\He_3:F_9$ 3B $3$ $8$ $C_3^2\times \He_3$ 3B 1A $e$
$\He_3:F_9$ 3C1 $3$ $8$ $C_3^2\times \He_3$ 3C-1 1A $ef$
$\He_3:F_9$ 3C-1 $3$ $8$ $C_3^2\times \He_3$ 3C1 1A $df$
$\He_3:F_9$ 3D $3$ $24$ $C_3^4$ 3D 1A $c$
$\He_3:F_9$ 3E $3$ $24$ $C_3^4$ 3E 1A $ce$
$\He_3:F_9$ 3F $3$ $24$ $C_3^4$ 3F 1A $cd$
$\He_3:F_9$ 3G $3$ $24$ $C_3^4$ 3G 1A $be$
$\He_3:F_9$ 3H $3$ $24$ $C_3^4$ 3H 1A $bd$
$\He_3:F_9$ 3I $3$ $24$ $C_3^4$ 3I 1A $ce^{2}$
$\He_3:F_9$ 3J $3$ $24$ $C_3^4$ 3J 1A $cd^{2}$
$\He_3:F_9$ 3K $3$ $24$ $C_3^4$ 3K 1A $be^{2}$
$\He_3:F_9$ 3L $3$ $24$ $C_3^4$ 3L 1A $bd^{2}$
$\He_3:F_9$ 4A1 $4$ $81$ $C_3:C_8$ 2A 4A-1 $a^{2}c$
$\He_3:F_9$ 4A-1 $4$ $81$ $C_3:C_8$ 2A 4A1 $a^{6}bf$
$\He_3:F_9$ 6A $6$ $162$ $C_{12}$ 3A 2A $a^{4}bc^{2}de$
$\He_3:F_9$ 8A1 $8$ $243$ $C_8$ 4A1 8A3 $ab^{2}cf$
$\He_3:F_9$ 8A-1 $8$ $243$ $C_8$ 4A-1 8A-3 $a^{7}c^{2}$
$\He_3:F_9$ 8A3 $8$ $243$ $C_8$ 4A-1 8A1 $a^{3}bc^{2}$
$\He_3:F_9$ 8A-3 $8$ $243$ $C_8$ 4A1 8A-1 $a^{5}b^{2}f^{2}$
$\He_3:F_9$ 12A1 $12$ $162$ $C_{12}$ 6A 4A1 $a^{6}c^{2}de^{2}f$
$\He_3:F_9$ 12A-1 $12$ $162$ $C_{12}$ 6A 4A-1 $a^{2}be^{2}f$
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