Finite Group DatabasebetaFinite Group Databasebeta| order | 10719 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C32×C397⋊C3 |
| unambiguous semidirect product | C397⋊C33 |
| unambiguous semidirect product | (C3×C397)⋊C32 |
| Fitting, socle | C32×C397 ⋊ C3 |
| derived, Sylow | C397 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C397⋊C3 |
| commutator, cosocle, hypocenter | C397 | C33 |
| Frattini | C1 | G |
| Fitting, socle | C32×C397 | C3 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C32 | |
56 conjugacy classes of subgroups.
1215 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44565421, #44565431, #44565433, … |
| maximal normal subgroup of | #44565421, #44565431, #44565433, … |
| maximal quotient of | C3×C9×C397⋊C3, C32×#16813208, H(3,𝔽3)×C397⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10719, 13);