Finite Group DatabasebetaFinite Group Databasebeta| order | 18657 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C691⋊C3) |
| unambiguous semidirect product | C691⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C691⋊C3)⋊C3 |
| Fitting | C32×C691 ⋊ C3 |
| Sylow | C691 ⋊ H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C691⋊C3 |
| commutator, socle, cosocle | C3×C691 | C32 |
| Fitting | C32×C691 | C3 |
| hypercenter | C32 | C691⋊C3 |
| hypocenter | C691 | H(3,𝔽3) |
| LCS | G ▷ C3×C691 ▷ C691 | |
| UCS | C1 ◁ C3 ◁ C32 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6219 |
Polycyclic presentation:
3^3,691|b^a=bc,d^b=d^4372081 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18657, 9);