Finite Group DatabasebetaFinite Group Databasebeta| order | 5412 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C11⋊#4223 |
| unambiguous semidirect product | C11⋊(C3×#4223) |
| Fitting, socle, Hall | C3×C11×C41 ⋊ C4 |
| derived, Hall | C11×C41 ⋊ C3×C4 |
| Hall | C3×C41 ⋊ Dic11 |
| Sylow | C41 ⋊ C3×Dic11 |
| Hall | C3×C11 ⋊ #4223 |
| Sylow | C11 ⋊ C3×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊#4223 |
| commutator, hypocenter | C11×C41 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C41 | C4 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
372 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5412, 11);