Finite Group DatabasebetaFinite Group Databasebeta| order | 10719 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×#16813210 |
| unambiguous semidirect product | (C397⋊C3)⋊C9 |
| Fitting, socle | C3×C397 ⋊ C9 |
| derived, Sylow | C397 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16813210 |
| commutator, hypocenter | C397 | C3×C9 |
| Frattini | C1 | G |
| Fitting, socle | C3×C397 | C9 |
| prime radical | C3×C397⋊C3 | C3 |
| cosocle | C397⋊C3 | C32 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C3 | |
20 conjugacy classes of subgroups.
159 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#16813210, C32⋊#16813210, #44565456, … |
| maximal normal subgroup of | C9×#16813210, C32⋊#16813210, #44565456, … |
| maximal quotient of | C9×#16813210, C32⋊#16813210, #44565456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10719, 15);