Finite Group DatabasebetaFinite Group Databasebeta| order | 1782 |
| isoclinism | isoclinic class of D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D99 |
| unambiguous semidirect product | C11⋊(C9×D9) |
| Fitting, Hall | C92×C11 ⋊ C2 |
| derived | C9×C11 ⋊ C2×C9 |
| Sylow | C92 ⋊ D11 |
| Sylow | C11 ⋊ C9×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D99 |
| commutator, hypocenter | C9×C11 | C2×C9 |
| Frattini | C32 | C3×D33 |
| Fitting | C92×C11 | C2 |
| socle | C32×C11 | C3×D3 |
| prime radical | C3×D99 | C3 |
| cosocle | C3×C9×C11 | C2×C3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C9 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1782, 27);