Finite Group DatabasebetaFinite Group Databasebeta| order | 5148 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C11⋊(Dic13⋊C3) |
| unambiguous semidirect product | C11⋊(C3×Dic13⋊C3) |
| unambiguous semidirect product | Dic143⋊C32 |
| unambiguous semidirect product | (C3×Dic143)⋊C3 |
| derived, Hall | C11×C13 ⋊ C32×C4 |
| Hall | C3×C11×C13⋊C3 ⋊ C4 |
| Hall | Dic143 ⋊ C32 |
| Hall | C3×C13⋊C3 ⋊ Dic11 |
| Sylow | C13 ⋊ C32×Dic11 |
| Sylow | C11 ⋊ C3×Dic13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C11⋊(D13⋊C3) |
| commutator, hypocenter | C11×C13 | C32×C4 |
| Frattini | C2 | C3×C11⋊(D13⋊C3) |
| Fitting, socle | C2×C3×C11×C13 | C2×C3 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
258 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5148, 43);