Finite Group DatabasebetaFinite Group Databasebeta| order | 19188 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C13⋊C3×#4223 |
| unambiguous semidirect product | (C13×#4223)⋊C32 |
| unambiguous semidirect product | (C3×C13×#4223)⋊C3 |
| Fitting, socle | C3×C13×C41 ⋊ C3×C4 |
| derived, Hall | C13×C41 ⋊ C32×C4 |
| Hall | C3×C13⋊C3×C41 ⋊ C4 |
| Hall | C13×#4223 ⋊ C32 |
| Sylow | C41 ⋊ C3×C4×C13⋊C3 |
| Sylow | C13 ⋊ C32×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C13⋊C3×#4223 |
| commutator, hypocenter | C13×C41 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C41 | C3×C4 |
| prime radical | C3×C13⋊C3×D41 | C2 |
| cosocle | C13×D41 | C2×C32 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1599 |
294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19188, 80);