Finite Group DatabasebetaFinite Group Databasebeta| order | 10719 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C397⋊C3) |
| unambiguous semidirect product | C397⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C397⋊C3)⋊C3 |
| Fitting | C32×C397 ⋊ C3 |
| Sylow | C397 ⋊ H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C397⋊C3 |
| commutator, socle, cosocle | C3×C397 | C32 |
| Fitting | C32×C397 | C3 |
| hypercenter | C32 | C397⋊C3 |
| hypocenter | C397 | H(3,𝔽3) |
| LCS | G ▷ C3×C397 ▷ C397 | |
| UCS | C1 ◁ C3 ◁ C32 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,397|b^a=bc,d^b=d^3621199 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44565432, #44565433, #44565435, … |
| maximal normal subgroup of | #44565432, #44565433, #44565435, … |
| maximal quotient of | #44565421, C32⋊#16813208, #44565431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10719, 9);