Finite Group DatabasebetaFinite Group Databasebeta| order | 15774 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C239 · Schur multiplier (H2) = C1 |
| direct product | D33×C239 |
| unambiguous semidirect product | C3⋊(D11×C239) |
| unambiguous semidirect product | C11⋊(D3×C239) |
| Fitting, socle, Hall | C3×C11×C239 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C2×C239 |
| Hall | C11×C239 ⋊ D3 |
| Hall | C3×C239 ⋊ D11 |
| Sylow | C11 ⋊ D3×C239 |
| Sylow | C3 ⋊ D11×C239 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C239 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C2×C239 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C239 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C239 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7887 |
4302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15774, 7);