Finite Group DatabasebetaFinite Group Databasebeta| order | 19044 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#15691772⋊C2 |
| unambiguous semidirect product | #15691772⋊(C2×C3) |
| unambiguous semidirect product | ((C23⋊D23)⋊C3)⋊(C2×C3) |
| Fitting, socle | C3×C232 ⋊ C2×D3 |
| derived | C232⋊C3 ⋊ C22×C3 |
| Hall | C3×C232⋊C3 ⋊ C22 |
| Sylow | C232 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15691772⋊C2 |
| commutator, cosocle, hypocenter | C232⋊C3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C232 | C2×D3 |
| LCS | G ▷ C232⋊C3 | |
| UCS | C1 ◁ C3 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 207 |
249 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19044, 77);