Finite Group DatabasebetaFinite Group Databasebeta| order | 10782 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1797 |
| unambiguous semidirect product | C3⋊(C3×D599) |
| unambiguous semidirect product | C599⋊(C3×D3) |
| Fitting, socle, Hall | C32×C599 ⋊ C2 |
| derived | C3×C599 ⋊ C2×C3 |
| Sylow | C599 ⋊ C3×D3 |
| Sylow | C32 ⋊ D599 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1797 |
| commutator, cosocle, hypocenter | C3×C599 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C599 | C2 |
| LCS | G ▷ C3×C599 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
2700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D599, D3×D1797, (C3⋊D3)⋊D599, … |
| maximal normal subgroup of | C3×D3×D599, D3×D1797, (C3⋊D3)⋊D599, … |
| maximal quotient of | C3×Dic1797, C2×C3×D1797 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10782, 8);