Finite Group DatabasebetaFinite Group Databasebeta| order | 5412 |
| isoclinism | isoclinic class of D123 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic123 |
| unambiguous semidirect product | C3⋊(C11×Dic41) |
| derived, Hall | C3×C41 ⋊ C4×C11 |
| Hall | C3×C11×C41 ⋊ C4 |
| Hall | C11×C41 ⋊ Dic3 |
| Sylow | C41 ⋊ C11×Dic3 |
| Hall | C3×C11 ⋊ Dic41 |
| Sylow | C3 ⋊ C11×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D123 |
| commutator, hypocenter | C3×C41 | C4×C11 |
| Frattini | C2 | C11×D123 |
| Fitting, socle | C2×C3×C11×C41 | C2 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
1386 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5412, 6);