Finite Group DatabasebetaFinite Group Databasebeta| order | 5148 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊(Dic13⋊C3)) |
| unambiguous semidirect product | C11⋊(C3⋊(Dic13⋊C3)) |
| unambiguous semidirect product | Dic429⋊C3 |
| derived | C3×C11×C13 ⋊ C3×C4 |
| Hall | C3×C11×C13⋊C3 ⋊ C4 |
| Hall | C11×C13 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ Dic11 |
| Sylow | C13 ⋊ C3×Dic33 |
| Sylow | C11 ⋊ C3⋊(Dic13⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C11⋊(D13⋊C3)) |
| commutator, hypocenter | C3×C11×C13 | C3×C4 |
| Fitting, socle | C2×C3×C11×C13 | C2×C3 |
| LCS | G ▷ C3×C11×C13 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,11,13,2|a^2=f,c^a=c^2,d^a=d^10,e^a=e^12,e^b=e^3240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5148, 47);