Finite Group DatabasebetaFinite Group Databasebeta| order | 5412 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×#4223 |
| Fitting, socle, Hall | C3×C11×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C3×C4×C11 |
| Hall | C11×C41 ⋊ C3×C4 |
| Hall | C3×C41 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | #4223 |
| commutator, hypocenter | C41 | C3×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C41 | C4 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C3×C11 | |
24 conjugacy classes of subgroups.
462 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5412, 10);