Finite Group DatabasebetaFinite Group Databasebeta| order | 1782 |
| isoclinism | isoclinic class of C3⋊D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊D99 |
| unambiguous semidirect product | C3⋊(C3×D99) |
| unambiguous semidirect product | C11⋊(C3×C3⋊D9) |
| Fitting, Hall | C32×C9×C11 ⋊ C2 |
| derived | C3×C9×C11 ⋊ C2×C3 |
| Sylow | C32×C9 ⋊ D11 |
| Sylow | C11 ⋊ C3×C3⋊D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊D99 |
| commutator, cosocle, hypocenter | C3×C9×C11 | C2×C3 |
| Frattini | C3 | C3×C3⋊D33 |
| Fitting | C32×C9×C11 | C2 |
| socle | C33×C11 | D3 |
| LCS | G ▷ C3×C9×C11 | |
| UCS | C1 ◁ C3 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 594 |
450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1782, 86);